Table of Contents

6. Discrete Elements - ConElas,ConMass,Bulk,Spring

Discrete elements are a general class of point or line elements which have applicability in both 2D and 3D space and are used in practice to idealize certain mass, stiffness or heat capacitance modelling situations. The ConElas and ConMass modules are useful for representing various types of concentrated or degree of freedom springs and masses. The Bulk module is used to represent a volumetric mass or heat capacitance. The Spring module is used to model various type of specialized elastic connections such as spot welds and flexible links.

Table of Contents

6.1 Concentrated and Degree of Freedom Springs - ConElas

The ConElas module is used to simulate abstract ground and line elastic springs and damper. Spring and damper stiffness coefficients may be entered explicitly at specified degrees of freedom at each of two points. This feature is sometimes referred to as a degree of freedom or "scalar" spring/damper. Intrinsic extensional and/or torsional spring/damper stiffnesses may be specified and the ConElas module will generate either a rank-one or a rank-two matrix with an extensional and/or torsional component introduced in the direction defined by the end point coordinates.

The methods associated with a ConElas object are the following.

Instance a ConElas object using vfe_ConElasBegin. Once a ConElas is instanced, define the spring/damper type and dimension using vfe_ConElasDef. If the spring/damper is defined to exist in 3D space, then all 3 translations and 3 rotations may exist in the element degree of freedom map. If the spring/damper is defined to exist in 2D space, then only the x and y translations and z rotation may appear in the element degree of freedom map.

There are two basic types of spring/dampers available in the ConElas module. The first type are termed degree-of-freedom or "dof" spring/dampers. These may contain either one or two nodes in which each node is connected to a single degree of freedom. A dof spring/damper may be either a scalar or a vector spring/damper. The scalar spring is similar to NASTRAN-like CELASx elements, while the scalar damper is similar to NASTRAN-like CDAMPx elements. The directions of the scalar spring degree of freedoms are assumed to be predetermined. Use vfe_ConElasSetDofScalar to define scalar springs A vector spring is similar to ABAQUS like SPRING1 and SPRING2 elements. The directions of the spring degrees of freedom are determined by the spring element local system which is evaluated at the spring nodes using the prescription specified by vfe_ConElasSetLocalSystem. Use vfe_ConElasSetDofVector to define vector spring/dampers.

ConElas supports damping properties. For reaction and damping matrix calculations the nodal velocities may be defined using vfe_ConElasSetPropPtr. If left undefined they are assumed zero.

The second basic spring/damper type is the intrinsic stiffness spring/damper with two nodes. An extension and/or torsional component may be specified for the intrinsic spring. An extensional component activates all translational freedoms at the spring nodes and a torsional component activates all rotational freedoms. The extensional and torsional components act along the line between the element endpoints. Therefore the element endpoints must not be coincident. If spring stiffness must be modelled between two coincident nodes a combination of vector dof springs may be used. Use vfe_ConElasSetIntrinsic to define the intrinsic extensional and/or torsional stiffness for an intrinsic spring. A purely extensional intrinsic spring is similar to ABAQUS SPRINGA elements.

The degree of freedom configuration for the element may be returned using vfe_ConElasNumDof and vfe_ConElasDofMap.

Unlike other, more general, finite elements, these elements do not require a material function interface using the MatlFun object. Element reactions, stiffness, and damping matrices are computed using vfe_ConElasStiff, vfe_ConElasReactStiff, vfe_ConElasReact, vfe_ConElasStiffDamp, and vfe_ConElasReactStiffDamp.

Table of Contents

6.2 Function Descriptions

The currently available ConElas functions are described in detail in this section.

Table of Contents , ConElas

NAME

*vfe_ConElasBegin - create an instance of a ConElas object

C SPECIFICATION

vfe_ConElas *vfe_ConElasBegin ()

ARGUMENTS

None

FUNCTION RETURN VALUE

The function returns a pointer to the newly created ConElas object. If the object creation fails, NULL is returned.

DESCRIPTION

Create an instance of a ConElas object. Memory is allocated for the object private data and the pointer to the object is returned.

Destroy an instance of a ConElas object using 

     void vfe_ConElasEnd (vfe_ConElas *conelas)

Return the current value of a ConElas object error flag using 

     Vint vfe_ConElasError (vfe_ConElas *conelas)

Table of Contents , ConElas

NAME

vfe_ConElasDef - define spring type and dimension

C SPECIFICATION

void vfe_ConElasDef (vfe_ConElas *conelas,
                     Vint type,
                     Vint dime)

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
type         Spring type
             =CONELAS_DOFSCALAR         Degree of freedom scalar spring
             =CONELAS_DOFVECTOR         Degree of freedom vector spring
             =CONELAS_INTRINSIC         Intrinsic spring stiffness
dime         Spring dimension
             =VFE_2D       2D analysis
             =VFE_3D       3D analysis

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type or dime is specified.

DESCRIPTION

Define the type and dimension of the spring to be specified. The type CONELAS_DOFSCALAR requires a call to vfe_ConElasSetDofScalar, CONELAS_DOFVECTOR requires a call to vfe_ConElasSetDofVector and CONELAS_INTRINSIC requires a call to vfe_ConElasSetIntrinsic.

Inquire of a defined type and dime as output arguments using 

     void vfe_ConElasInq (vfe_ConElas *conelas,
                          Vint *type,
                          Vint *dime)

Table of Contents , ConElas

NAME

vfe_ConElasSetDofScalar - set dof spring scalar properties

C SPECIFICATION

void vfe_ConElasSetDofScalar (vfe_ConElas *conelas,
                              Vint tag1,
                              Vint tag2,
                              Vdouble kl[3],
                              Vdouble dl[3])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
tag1         First degree of freedom type
tag2         Second degree of freedom type
kl           Lower triangle of symmetric stiffness matrix
dl           Lower triangle of damping matrix

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper tag1 or tag2 is specified.

DESCRIPTION

Define a scalar spring/damper symmetric matrix connecting a degree of freedom at each of two points. If the dimension of the element is 2D, then tag1 and tag2 must be one of SYS_DOF_TX, SYS_DOF_TY, or SYS_DOF_RZ, otherwise any translational or rotational degree of freedom type is allowed. The element stiffness and reaction calculation are independent of node coordinates.

Table of Contents , ConElas

NAME

vfe_ConElasSetDofVector - set dof spring vector properties

C SPECIFICATION

void vfe_ConElasSetDofVector (vfe_ConElas *conelas,
                              Vint tag1,
                              Vint tag2,
                              Vdouble kl[3],
                              Vdouble dl[3])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
tag1         First degree of freedom type
tag2         Second degree of freedom type
kl           Lower triangle of element local symmetric stiffness matrix
dl           Lower triangle of element local damping matrix

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper tag1 or tag2 is specified.

DESCRIPTION

Define a vector spring/damper symmetric matrix connecting a degree of freedom at each of two points in the element local system at each point. If the dimension of the element is 2D, then tag1 and tag2 must be one of SYS_DOF_TX, SYS_DOF_TY, or SYS_DOF_RZ, otherwise any translational or rotational degree of freedom type is allowed. The element local system at each point is specified by vfe_ConElasSetLocalSystem.

Table of Contents , ConElas

NAME

vfe_ConElasSetIntrinsic - set intrinsic spring stiffnesses

C SPECIFICATION

void vfe_ConElasSetIntrinsic (vfe_ConElas *conelas,
                              Vint type,
                              Vdouble kext,
                              Vdouble ktor,
                              Vdouble dext,
                              Vdouble dtor)

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
type         Spring stiffness type
             =CONELAS_EXT               Extensional only
             =CONELAS_TOR               Torsional only
             =CONELAS_EXTTOR            Extensional and torsional
kext         Intrinsic extensional stiffness
ktor         Intrinsic torsional stiffness
dext         Intrinsic extensional damping coefficient
dtor         Intrinsic torsional damping coefficient

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is specified. SYS_ERROR_OPERATION is generated if an unallowed type is specified for 2D analysis.

DESCRIPTION

Define the type and magnitude of intrinsic stiffness. The type CONELAS_EXT ignores ktor and dtor. The type CONELAS_TOR ignores kext and dext. If the dimension of the element is 2D, then only a type of CONELAS_EXT is allowed.

Table of Contents , ConElas

NAME

vfe_ConElasSetPropPtr - set pointer to element nodal properties

C SPECIFICATION

void vfe_ConElasSetPropPtr (vfe_ConElas *conelas,
                            Vint type,
                            Vdouble *propptr)

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
type         Type of element property
             =VFE_PROP_VELOCITY         Velocity
propptr      Pointer to start of element nodal properties

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is specified.

DESCRIPTION

Set a pointer to the start of a specified type of element properties. Note that the properties are not copied by this function, only the pointer itself is copied. If a property pointer is not set the element assumes a default value. By default the velocity used in damping functions is 0.0. AQUI

Table of Contents , ConElas

NAME

vfe_ConElasSetLocalSystem - set element local system direction

C SPECIFICATION

void vfe_ConElasSetLocalSystem (vfe_ConElas *conelas,
                                Vint type,
                                Vdouble vec[],
                                Vdouble angle)

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
type         Local system convention
vec          Orientation vector data
angle        Angle to rotate y',z' axes about the element x'
             axis in degrees.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is input.

DESCRIPTION

Specify the convention to be used to construct the orientation of the element local x',y',z' coordinate system. This local system is computed for vector spring elements only at each node location to determine the local directions of the node degree of freedom.

For a description of element coordinate systems, type, and associated orientation vector data, please see
1.4 Element Coordinate Systems

Table of Contents , ConElas

NAME

vfe_ConElasDofMap - query element degree of freedom map

C SPECIFICATION

void vfe_ConElasDofMap (vfe_ConElas *conelas,
                        Vint analysistype,
                        Vint loc[], Vint tag[])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis

OUTPUT ARGUMENTS

loc          Vector of degree of freedom locations
tag          Vector of degree of freedom types

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for element degree of freedom map. The degree of freedom map consists of a location index, loc and type, tag for each degree of freedom used by the element.

The location index is a positive node index into the element connectivity indicating a nodal freedom. The tag indicates the type of the degree of freedom. Tag values are one of a set of enumerated types which indicate whether the degree of freedom is a translation or rotation. The length of the loc and tag vectors is equal to the number of element degrees of freedom. Use vfe_ConElasNumDof to return the number of element degrees of freedom.

Table of Contents , ConElas

NAME

vfe_ConElasNumDof - query number of element degrees of freedom

C SPECIFICATION

void vfe_ConElasNumDof (vfe_ConElas *conelas,
                        Vint analysistype,
                        Vint *nedofs)

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis

OUTPUT ARGUMENTS

nedofs       Number of element degrees of freedom

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for number of element degree of freedom nedofs. The number of degrees of freedom will generally be equal to the number of nodal degrees of freedom per node times the number of nodes. Use vfe_ConElasDofMap to return the location and type of each degree of freedom.

Table of Contents , ConElas

NAME

vfe_ConElasReact - reaction vector

C SPECIFICATION

void vfe_ConElasReact (vfe_ConElas *conelas,
                       Vdouble x[][3],
                       Vdouble u[],
                       Vdouble r[])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
x            Array of node locations.
u            Degree of freedom vector of displacements

OUTPUT ARGUMENTS

r            Degree of freedom reaction vector

ERRORS

SYS_ERROR_COMPUTE is generated if element geometry can not be defined.

DESCRIPTION

Compute the reaction vector, r, given the node coordinates, x, and the degree of freedom displacement vector, u. If damping is defined the nodal velocities are set with vfe_ConElasSetPropPtr.

Table of Contents , ConElas

NAME

vfe_ConElasReactStiff - reaction vector, stiffness matrix

C SPECIFICATION

void vfe_ConElasReactStiff (vfe_ConElas *conelas,
                            Vdouble x[][3],
                            Vdouble u[],
                            Vdouble kflag,
                            Vdouble r[],
                            Vdouble k[])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
x            Array of node locations.
u            Degree of freedom vector of displacements
kflag        Flag to compute stiffness matrix, k
             =SYS_OFF      Do not compute stiffness matrix
             =SYS_ON       Compute and return stiffness matrix

OUTPUT ARGUMENTS

r            Degree of freedom reaction vector
k            Degree of freedom stiffness matrix

ERRORS

SYS_ERROR_COMPUTE is generated if element geometry can not be defined.

DESCRIPTION

Compute the reaction vector, r, and optionally the stiffness matrix, k, given the node coordinates, x, and the degree of freedom displacement vector, u. The lower triangle of the stiffness matrix is returned. If damping is defined the nodal velocities are set with vfe_ConElasSetPropPtr.

Table of Contents , ConElas

NAME

vfe_ConElasReactStiffDamp - reaction vector, stiffness and damping matrices

C SPECIFICATION

void vfe_ConElasReactStiffDamp (vfe_ConElas *conelas,
                                Vdouble x[][3],
                                Vdouble u[],
                                Vdouble kflag,
                                Vdouble dflag,
                                Vdouble r[],
                                Vdouble k[],
                                Vdouble d[])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
x            Array of node locations.
u            Degree of freedom vector of displacements
kflag        Flag to compute stiffness matrix, k
             =SYS_OFF      Do not compute stiffness matrix
             =SYS_ON       Compute and return stiffness matrix
dflag        Flag to compute damping matrix, d
             =SYS_OFF      Do not compute damping matrix
             =SYS_ON       Compute and return damping matrix

OUTPUT ARGUMENTS

r            Degree of freedom reaction vector
k            Degree of freedom stiffness matrix
d            Degree of freedom damping matrix

ERRORS

SYS_ERROR_COMPUTE is generated if element geometry can not be defined.

DESCRIPTION

Compute the reaction vector, r, and optionally the stiffness matrix, k, and the damping matrix, d, given the node coordinates, x, and the degree of freedom displacement vector, u. If damping is defined the nodal velocities are set with vfe_ConElasSetPropPtr. The lower triangle of the stiffness matrix is returned.

Table of Contents , ConElas

NAME

vfe_ConElasStiff - linear stiffness matrix

C SPECIFICATION

void vfe_ConElasStiff (vfe_ConElas *conelas,
                       Vdouble x[][3],
                       Vdouble kl[])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
x            Array of node locations.

OUTPUT ARGUMENTS

kl           Degree of freedom stiffness matrix

ERRORS

SYS_ERROR_COMPUTE is generated if element geometry can not be defined.

DESCRIPTION

Compute the linear stiffness matrix, kl, given the node coordinates, x. The lower triangle of the stiffness matrix is returned.

Table of Contents , ConElas

NAME

vfe_ConElasStiffDamp - linear stiffness and damping matrices

C SPECIFICATION

void vfe_ConElasStiffDamp (vfe_ConElas *conelas,
                           Vdouble x[][3],
                           Vdouble kl[],
                           Vdouble dl[])

INPUT ARGUMENTS

conelas      Pointer to ConElas object.
x            Array of node locations.

OUTPUT ARGUMENTS

kl           Degree of freedom stiffness matrix
dl           Degree of freedom damping matrix

ERRORS

SYS_ERROR_COMPUTE is generated if element geometry can not be defined.

DESCRIPTION

Compute the linear stiffness matrix, kl, given the node coordinates, x. The lower triangle of the stiffness matrix is returned.

Table of Contents

6.3 Concentrated and Degree of Freedom Masses - ConMass

The ConMass module is used to simulate concentrated mass and degree of freedom masses. Mass matrix coefficients may be entered explicitly at specified degrees of freedom at each of two points. This feature is sometimes referred to as a degree of freedom or "scalar" mass. A variety of other concentrated mass types are available.

The methods associated with a ConMass object are the following.

Instance a ConMass object using vfe_ConMassBegin. Once a ConMass is instanced, define the mass type and dimension using vfe_ConMassDef. If the mass is defined to exist in 3D space, then all 3 translations and 3 rotations may exist in the element degree of freedom map. If the mass is defined to exist in 2D space, then only the x and y translations and z rotation may appear in the element degree of freedom map. Use vfe_ConMassSetDofLink to define scalar masses similar to NASTRAN like CMASSx elements. Use vfe_ConMassSetMatrix to define the components of a complete symmetric mass matrix at a point similar to NASTRAN like CONM1 elements. Use vfe_ConMassSetPrinc to define a concentrated mass as a translational mass and a rotary inertia tensor similar to NASTRAN like CONM2 elements. Use vfe_ConMassSetTrans to define a single concentrated translational mass at a point.

The degree of freedom configuration for the element may be returned using vfe_ConMassNumDof and vfe_ConMassDofMap.

Unlike other, more general, finite elements, these elements do not require a material function interface using the MatlFun object. Element consistent and diagonal mass are computed using vfe_ConMassMass and vfe_ConMassMassDiag.

Table of Contents

6.4 Function Descriptions

The currently available ConMass functions are described in detail in this section.

Table of Contents , ConMass

NAME

*vfe_ConMassBegin - create an instance of a ConMass object

C SPECIFICATION

vfe_ConMass *vfe_ConMassBegin ()

ARGUMENTS

None

FUNCTION RETURN VALUE

The function returns a pointer to the newly created ConMass object. If the object creation fails, NULL is returned.

DESCRIPTION

Create an instance of a ConMass object. Memory is allocated for the object private data and the pointer to the object is returned.

Destroy an instance of a ConMass object using 

     void vfe_ConMassEnd (vfe_ConMass *conmass)

Return the current value of a ConMass object error flag using 

     Vint vfe_ConMassError (vfe_ConMass *conmass)

Table of Contents , ConMass

NAME

vfe_ConMassDef - define mass type and dimension

C SPECIFICATION

void vfe_ConMassDef (vfe_ConMass *conmass,
                     Vint type,
                     Vint dime)

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
type         Mass type
             =CONMASS_DOFLINK           Degree of freedom link
             =CONMASS_TRANS             Translational mass
             =CONMASS_PRINC             Translational mass, rotary inertia
             =CONMASS_MATRIX            Symmetric mass matrix
dime         Mass dimension
             =VFE_2D       2D analysis
             =VFE_3D       3D analysis

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type or dime is specified.

DESCRIPTION

Define the type and dimension of the mass to be specified. The type CONMASS_DOFLINK requires a call to vfe_ConMassSetDofLink, CONMASS_TRANS requires a call to vfe_ConMassSetTrans, CONMASS_PRINC requires a call to vfe_ConMassSetPrinc and CONMASS_MATRIX requires a call to vfe_ConMassSetMatrix, By default type is CONMASS_DOFLINK and dime is VFE_3D.

Inquire of a defined type and dime as output arguments using 

     void vfe_ConMassInq (vfe_ConMass *conmass,
                          Vint *type,
                          Vint *dime)

Table of Contents , ConMass

NAME

vfe_ConMassSetParami - set integer parameters

C SPECIFICATION

void vfe_ConMassSetParami (vfe_ConMass *conmass,
                           Vint type,
                           Vint iparam)

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
type         Type of formulation parameter to set
             =VFE_ROTINERTIA         Enable rotary inertias
iparam       Integer parameter value.
             =SYS_OFF                Disable
             =SYS_ON                 Enable

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is specified.

DESCRIPTION

Set element formulation parameters. The inclusion of rotary inertias to the element mass matrix is set with the VFE_ROTINERTIA parameter. By default VFE_ROTINERTIA is set to SYS_OFF.

Table of Contents , ConMass

NAME

vfe_ConMassSetDofLink - set degree of freedom link properties

C SPECIFICATION

void vfe_ConMassSetDofLink (vfe_ConMass *conmass,
                            Vint tag1,
                            Vint tag2,
                            Vdouble kl[3])

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
tag1         First degree of freedom type
tag2         Second degree of freedom type
kl           Lower triangle of symmetric mass matrix

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper tag1 or tag2 is specified.

DESCRIPTION

Define a general mass symmetric matrix connecting a degree of freedom at each of two points. If the dimension of the element is 2D, then tag1 and tag2 must be one of SYS_DOF_TX, SYS_DOF_TY, or SYS_DOF_RZ, otherwise any translational or rotational degree of freedom type is allowed.

Table of Contents , ConMass

NAME

vfe_ConMassSetLocalSystem - set local inertia tensor system

C SPECIFICATION

void vfe_ConMassSetLocalSystem (vfe_ConMass *conmass,
                                Vint type,
                                Vdouble vec[],
                                Vdouble angle)

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
type         Local system convention
vec          Orientation vector data
angle        Angle to rotate y',z' axes about the element x'
             axis in degrees.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is input.

DESCRIPTION

Specify the local coordinate system of the inertia tensor. The default is SYS_ELEMSYS_GLOBAL.

For a description of element coordinate systems, type, and associated orientation vector data, please see
1.4 Element Coordinate Systems

Table of Contents , ConMass

NAME

vfe_ConMassSetTrans - set single translational mass

C SPECIFICATION

void vfe_ConMassSetTrans (vfe_ConMass *conmass,
                          Vdouble mass)

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
mass         Single translational mass

OUTPUT ARGUMENTS

None

DESCRIPTION

Define a single translational mass. This mass value is inserted as the diagonal translational mass for all appropriate translational degrees of freedom.

Table of Contents , ConMass

NAME

vfe_ConMassSetPrinc - set translational mass and rotary inertia

C SPECIFICATION

void vfe_ConMassSetPrinc (vfe_ConMass *conmass,
                          Vdouble mass,
                          Vdouble rotary[3],
                          Vdouble tm[3][3],
                          Vdouble offset[3]);

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
mass         Single translational mass
rotary       Principal values of rotary inertia.
tm           Orientation of principal axes of rotary inertia tensor
offset       Offset of the center of gravity of the mass.

OUTPUT ARGUMENTS

None

DESCRIPTION

Define a concentrated mass matrix at a point as a single translational mass and the principal moments of rotary inertia, rotary. The orientation of the principal axes is specified with the direction cosine matrix, tm. The center of gravity of the mass may be offset from its attachment point.

Table of Contents , ConMass

NAME

vfe_ConMassSetMatrix - set symmetric mass matrix at a point

C SPECIFICATION

void vfe_ConMassSetMatrix (vfe_ConMass *conmass,
                           Vdouble a[21])

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
a            Complete lower triangle of symmetric mass matrix at a node

OUTPUT ARGUMENTS

None

DESCRIPTION

Define a concentrated mass matrix at a point as a complete symmetric mass matrix. The mass matrix entries are dependent upon the dimension of the element. In 3D the entries of a are as follows in which the order of the degrees of freedom at the point is SYS_DOF_TX, SYS_DOF_TY, SYS_DOF_TZ, SYS_DOF_RX, SYS_DOF_RY, SYS_DOF_RZ. 
        -                                     -
        | a[ 0] a[ 1] a[ 3] a[ 6] a[10] a[15] |
        | a[ 1] a[ 2] a[ 4] a[ 7] a[11] a[16] |
    M = | a[ 3] a[ 4] a[ 5] a[ 8] a[12] a[17] |
        | a[ 6] a[ 7] a[ 8] a[ 9] a[13] a[18] |
        | a[10] a[11] a[12] a[13] a[14] a[19] |
        | a[15] a[16] a[17] a[18] a[19] a[20] |
        -                                     -

In 2D the entries of a are as follows in which the order of the degrees of freedom at the point is SYS_DOF_TX, SYS_DOF_TY, SYS_DOF_RZ. 

        -                   -
        | a[ 0] a[ 1] a[ 3] |
    M = | a[ 1] a[ 2] a[ 4] |
        | a[ 3] a[ 4] a[ 5] |
        -                   -

Table of Contents , ConMass

NAME

vfe_ConMassSetOffset - set offset of center of mass

C SPECIFICATION

void vfe_ConMassSetOffset (vfe_ConMass *conmass,
                           Vdouble offset[3])

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
offset       Offset of center of mass in global coordinates

OUTPUT ARGUMENTS

None

DESCRIPTION

Define an offset of the center of mass in global coordinates.

Table of Contents , ConMass

NAME

vfe_ConMassDofMap - query element degree of freedom map

C SPECIFICATION

void vfe_ConMassDofMap (vfe_ConMass *conmass,
                        Vint analysistype,
                        Vint loc[], Vint tag[])

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis
             =VFE_ANALYSIS_THERMAL    Thermal analysis

OUTPUT ARGUMENTS

loc          Vector of degree of freedom locations
tag          Vector of degree of freedom types

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for element degree of freedom map. The degree of freedom map consists of a location index, loc and type, tag for each degree of freedom used by the element.

The location index is a positive node index into the element connectivity indicating a nodal freedom. The tag indicates the type of the degree of freedom. Tag values are one of a set of enumerated types which indicate whether the degree of freedom is a translation or rotation. The length of the loc and tag vectors is equal to the number of element degrees of freedom. Use vfe_ConMassNumDof to return the number of element degrees of freedom.

Table of Contents , ConMass

NAME

vfe_ConMassNumDof - query number of element degrees of freedom

C SPECIFICATION

void vfe_ConMassNumDof (vfe_ConMass *conmass,
                        Vint analysistype,
                        Vint *nedofs)

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis
             =VFE_ANALYSIS_THERMAL    Thermal analysis

OUTPUT ARGUMENTS

nedofs       Number of element degrees of freedom

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for number of element degree of freedom nedofs. The number of degrees of freedom will generally be equal to the number of nodal degrees of freedom per node times the number of nodes. Use vfe_ConMassDofMap to return the location and type of each degree of freedom.

Table of Contents , ConMass

NAME

vfe_ConMassElemLoad - body force vector

C SPECIFICATION

void vfe_ConMassElemLoad (vfe_ConMass *conmass,
                          Vdouble x[][3],
                          Vdouble q[][3],
                          Vdouble f[],

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
x            Array of node locations.
q            Array of node accelerations

OUTPUT ARGUMENTS

f            Degree of freedom vector of consistent loads.

DESCRIPTION

Compute the consistent degree of freedom body loads given acceleration load vector, q on an element. The vector q contains an acceleration vector for for each node in the element. The output array of consistent degree of freedom loads, f, contains loads for all degrees of freedom in the element. The input element loads are in the units of force per unit mass.

Table of Contents , ConMass

NAME

vfe_ConMassMass - consistent mass matrix

C SPECIFICATION

void vfe_ConMassMass (vfe_ConMass *conmass,
                      Vdouble x[][3],
                      Vdouble m[])

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
x            Array of node locations.

OUTPUT ARGUMENTS

m            Consistent mass matrix

DESCRIPTION

Compute the consistent mass matrix, m. The lower triangle of the consistent mass is returned. Use vfe_ConMassMassDiag to compute diagonal mass.

Table of Contents , ConMass

NAME

vfe_ConMassMassDiag - diagonal mass matrix

C SPECIFICATION

void vfe_ConMassMassDiag (vfe_ConMass *conmass,
                          Vdouble x[][3],
                          Vdouble md[])

INPUT ARGUMENTS

conmass      Pointer to ConMass object.
x            Array of node locations.

OUTPUT ARGUMENTS

md           Diagonal mass matrix

DESCRIPTION

Compute the diagonal mass matrix, md. Use vfe_ConMassMass to compute consistent mass.

Table of Contents

6.5 Bulk Elements - Bulk

The Bulk module is used to represent a volumetric mass or heat capacitance at a single point.

The methods associated with a Bulk object are the following.

Instance a Bulk object using vfe_BulkBegin. Once a Bulk is instanced, define the bulk dimension using vfe_BulkDef. In structural analysis, if the bulk mass is defined in 2D space, then only x and y translations appear in the element degree of freedom map. If the bulk mass is defined in 3D space, then x, y and z translations appear in the element degree of freedom map. The bulk mass does not contain any rotary inertia. In thermal analysis, the bulk capacitance will always have the temperature appear in the element degree of freedom map.

The Bulk module accesses material density and specific heat through a MatlFun interface to a primitive material. Use vfe_BulkSetObject to set the MatlFun object. The bulk element temperature and volume are set using vfe_BulkSetPropPtr. Query the element degree of freedom map using vfe_BulkDofMap and vfe_BulkNumDof.

For structural analysis the bulk element supports the computation of body forces and consistent and diagonal mass using vfe_BulkElemLoad, vfe_BulkMass and vfe_BulkMassDiag. For thermal analysis the bulk element supports the computation of body heat generation and consistent and diagonal capacitance using vfe_BulkElemHeat, vfe_BulkCap and vfe_BulkCapDiag. Note that the coordinate location of the bulk element is immaterial. The functions for the computation of body loads, mass and capacitance have the coordinates in their input argument lists only for consistency with the argument lists of the analogous functions for all other element types such as Solid3D, etc.

Table of Contents

6.6 Function Descriptions

The currently available Bulk functions are described in detail in this section.

Table of Contents , Bulk

NAME

*vfe_BulkBegin - create an instance of a Bulk object

C SPECIFICATION

vfe_Bulk *vfe_BulkBegin ()

ARGUMENTS

None

FUNCTION RETURN VALUE

The function returns a pointer to the newly created Bulk object. If the object creation fails, NULL is returned.

DESCRIPTION

Create an instance of a Bulk object. Memory is allocated for the object private data and the pointer to the object is returned.

Destroy an instance of a Bulk object using 

     void vfe_BulkEnd (vfe_Bulk *bulk)

Return the current value of a Bulk object error flag using 

     Vint vfe_BulkError (vfe_Bulk *bulk)

Table of Contents , Bulk

NAME

vfe_BulkDef - define bulk dimension

C SPECIFICATION

void vfe_BulkDef (vfe_Bulk *bulk,
                  Vint dime)

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
dime         Bulk dimension
             =VFE_2D       2D analysis
             =VFE_3D       3D analysis

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper dime is specified.

DESCRIPTION

Define the dimension of the bulk element.

Inquire of a defined dime as an output argument using 

     void vfe_BulkInq (vfe_Bulk *bulk,
                       Vint *dime)

Table of Contents , Bulk

NAME

vfe_BulkSetObject - set attribute object

C SPECIFICATION

void vfe_BulkSetObject (vfe_Bulk *bulk,
                        Vint objecttype,
                        Vobject *object)

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
objecttype   The object type identifier
             =VFE_MATLFUN            MatlFun object
object       Pointer to the object to be set.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OBJECTTYPE is generated if an improper objecttype is specified.

DESCRIPTION

Set a pointer to an attribute object. Users must supply a MatlFun object prior to computing any quantity that requires a material model definition.

Table of Contents , Bulk

NAME

vfe_BulkSetPropPtr - set pointer to element nodal properties

C SPECIFICATION

void vfe_BulkSetPropPtr (vfe_Bulk *bulk,
                         Vint type,
                         Vdouble *propptr)

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
type         Type of element property
             =VFE_PROP_TEMPERATURE      Temperatures
             =VFE_PROP_VOLUME           Volume
propptr      Pointer to start of element nodal properties

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is specified.

DESCRIPTION

Set a pointer to the start of a specified type of element properties. Note that the properties are not copied by this function, only the pointer itself is copied. If a property pointer is not set the element assumes a default value. By default the temperature is 0. and the volume is 1.

Table of Contents , Bulk

NAME

vfe_BulkDofMap - query element degree of freedom map

C SPECIFICATION

void vfe_BulkDofMap (vfe_Bulk *bulk,
                     Vint analysistype,
                     Vint loc[], Vint tag[])

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis
             =VFE_ANALYSIS_THERMAL    Thermal analysis

OUTPUT ARGUMENTS

loc          Vector of degree of freedom locations
tag          Vector of degree of freedom types

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for element degree of freedom map. The degree of freedom map consists of a location index, loc and type, tag for each degree of freedom used by the element.

The location index is a positive node index into the element connectivity indicating a nodal freedom. The tag indicates the type of the degree of freedom. Tag values are one of a set of enumerated types which indicate whether the degree of freedom is a translation, temperature, etc.

The length of the loc and tag vectors is equal to the number of element degrees of freedom. Use vfe_BulkNumDof to return the number of element degrees of freedom.

Table of Contents , Bulk

NAME

vfe_BulkNumDof - query number of element degrees of freedom

C SPECIFICATION

void vfe_BulkNumDof (vfe_Bulk *bulk,
                     Vint analysistype,
                     Vint *nedofs)

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis
             =VFE_ANALYSIS_THERMAL    Thermal analysis

OUTPUT ARGUMENTS

nedofs       Number of element degrees of freedom

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for number of element degrees of freedom nedofs. For structural analysis, nedofs is 2 for 2D space and 3 for 3D space. For thermal analysis, nedofs is 1. Use vfe_BulkDofMap to return the location and type of each degree of freedom.

Table of Contents , Bulk

NAME

vfe_BulkElemLoad - body force vector

C SPECIFICATION

void vfe_BulkElemLoad (vfe_Bulk *bulk,
                       Vdouble x[][3],
                       Vdouble q[][3],
                       Vdouble f[],

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
x            Array of node locations.
q            Array of node accelerations

OUTPUT ARGUMENTS

f            Degree of freedom vector of consistent loads.

ERRORS

SYS_ERROR_COMPUTE is generated if a non-positive Jacobian is computed.

DESCRIPTION

Compute the consistent degree of freedom body loads given acceleration load vector, q on an element. The vector q contains an acceleration vector for for each node in the element. The output array of consistent degree of freedom loads, f, contains loads for all degrees of freedom in the element. The input element loads are in the units of force per unit mass. Note that the computation of consistent loads uses the material density.

Table of Contents , Bulk

NAME

vfe_BulkMass - consistent mass matrix

C SPECIFICATION

void vfe_BulkMass (vfe_Bulk *bulk,
                   Vdouble x[][3],
                   Vdouble m[])

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
x            Array of node locations.

OUTPUT ARGUMENTS

m            Degree of freedom consistent mass matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set.

DESCRIPTION

Compute the consistent mass matrix, m, given the node coordinates, x. The lower triangle of the consistent mass is returned. Use vfe_BulkMassDiag to compute a diagonal mass matrix.

Table of Contents , Bulk

NAME

vfe_BulkMassDiag - diagonal mass matrix

C SPECIFICATION

void vfe_BulkMassDiag (vfe_Bulk *bulk,
                       Vdouble x[][3],
                       Vdouble md[])

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
x            Array of node locations.

OUTPUT ARGUMENTS

md           Degree of freedom diagonal mass vector

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set.

DESCRIPTION

Compute the diagonal mass matrix, md, given the node coordinates, x. The diagonal mass is returned as a degree of freedom length vector. Use vfe_BulkMass to compute a consistent mass matrix.

Table of Contents , Bulk

NAME

vfe_BulkElemHeat - body heat generation

C SPECIFICATION

void vfe_BulkElemHeat (vfe_Bulk *bulk,
                       Vdouble x[][3],
                       Vdouble q[],
                       Vdouble f[],

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
x            Array of node locations.
q            Array of node heat fluxes

OUTPUT ARGUMENTS

f            Degree of freedom vector of consistent loads.

ERRORS

SYS_ERROR_COMPUTE is generated if a non-positive Jacobian is computed.

DESCRIPTION

Compute the consistent degree of freedom body heat generation given nodal heat generation vector, q on an element. The vector q contains heat generation per volume for each node in the element. The output array of consistent degree of freedom loads, f, contains the heat generation in the element. The input element loads are in the units of power per unit volume.

Table of Contents , Bulk

NAME

vfe_BulkCap - consistent capacitance matrix

C SPECIFICATION

void vfe_BulkCap (vfe_Bulk *bulk,
                  Vdouble x[][3],
                  Vdouble u[],
                  Vdouble c[])

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
x            Array of node locations.
u            Degree of freedom vector of temperatures

OUTPUT ARGUMENTS

c            Degree of freedom consistent capacitance matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed.

DESCRIPTION

Compute the consistent capacitance matrix, c, given the node coordinates, x, and temperatures, u. The lower triangle of the consistent capacitance is returned. Use vfe_BulkCapDiag to compute a diagonal capacitance matrix. This calculation requires material density and specific heat.

Table of Contents , Bulk

NAME

vfe_BulkCapDiag - diagonal capacitance matrix

C SPECIFICATION

void vfe_BulkCapDiag (vfe_Bulk *bulk,
                      Vdouble x[][3],
                      Vdouble u[],
                      Vdouble cd[])

INPUT ARGUMENTS

bulk         Pointer to Bulk object.
x            Array of node locations.
u            Degree of freedom vector of temperatures

OUTPUT ARGUMENTS

cd           Degree of freedom diagonal capacitance matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set.

DESCRIPTION

Compute the diagonal capacitance matrix, cd, given the node coordinates, x, and temperatures, u. The diagonal capacitance is returned as a degree of freedom length vector. Use vfe_BulkCap to compute a consistent capacitance matrix. This calculation requires material density and specific heat.

Table of Contents

6.7 Springs - Spring

The Spring module is used to model specialized elastic connections such as spot welds and flexible joints. In their simplest form, springs act like connectors between two end points. The Spring module generalizes this concept to allow for each end point connection to be distributed over an element surface.

The methods associated with a Spring object are the following.

Instance a Spring object using vfe_SpringBegin. Once a Spring object is instanced, define the spring type using vfe_SpringDef. Currently options exist for spot welds, and generalized springs. The spot weld is similar to the NASTRAN CWELD element and is specified using vfe_SpringSetWeld. The generalized spring is similar to the NASTRAN CBUSH element and is specified using vfe_SpringSetBush.

Set the material function attribute object MatlFun using vfe_SpringSetObject. Query the element degree of freedom map using vfe_SpringDofMap and vfe_SpringNumDof.

If the element is to support a material model, such as a plastic material model, which requires a material history then the user must manage the material history information using vfe_SpringSetHistPtr and vfe_SpringInitHist. Since all element geometry is available directly to the element the material function should point to a primitive material.

Table of Contents

6.8 Element Geometry

The basic spring element connection is between two end points, A and B. The Spring module allows for the motion of an end point to be represented by the motion of a single node or the motion of an element face at a point. The three possibilities become node to node, node to element face and element face to element face. Therefore the nodal connections of a spring may range from two nodes to the set of nodes on two element faces. If the connection is node to node the end point coordinates A and B are entered using vfe_SpringSetPntPnt. If the connection is node to element face the end point coordinates A and B and the topology of the element face to be connected to point B are entered using vfe_SpringSetPntSurf. If the connection is element face to element face the end point coordinates A and B and the topologies of the associated element faces are entered using vfe_SpringSetSurfSurf. The topologies of the two element faces need not be the same.

Options exist for the Spring module to alter the end point coordinates under certain conditions. One option specifies that the end point coordinates will be projected to the associated node or element face. This option is set using vfe_SpringSetParami with type VIS_ENDPROJECT. An additional end point alteration may occur in the case of the weld type spring if the length/diameter ratio exceeds certain bounds. These limits are specified using vfe_SpringSetParamd with the types VFE_MINRATIO and VFE_MAXRATIO. The element coordinate system x',y',z' is constructed so that the x' coordinate system is directed from end point A to B in their final adjusted locations. The orientation of the y' and z' axes is determined using vfe_SpringSetLocalSystem.

The link type spring is the simplest: it connects two nodes with a simple spring constant. The force along the direction defined by the two nodes depends on the relative change in distance between the nodes.

The weld type spring is characterized by a specialized beam connection characterized by a radius and a length from end point A to B. The computed stress and strain are the same as an equivalent beam element connected to points A and B. A MatlFun of a primitive material must be set using vfe_SpringSetObject. The weld type spring geometry is illustrated below in Figure 6-1.


Figure 6-1, Geometry for a Weld type Point to Surface Spring
The generalized bush type spring is characterized by a spring location S and a set of 6 stiffness coefficients and 6 stress and 6 strain recovery coefficients. Each of the stiffness coefficients relates the relative displacement of the 3 translations and 3 rotations of the end points of the spring in the spring element local system to the element forces. The stress is reported as the element force times the associated stress recovery coefficient. The strain is reported as the element relative displacement times the associated strain recovery coefficient. A MatlFun is not required. The generalized (bush) type spring geometry is illustrated below in Figure 6-2.


Figure 6-2, Geometry for a Bush type Point to Surface Spring
The nodal freedoms used by spring elements depend upon the spring element type and the end point connection. If the motion of an end point is connected to an element face, only the translational freedoms of the element face nodes are used to compute the motion of the connected end point.

Table of Contents

6.9 Function Descriptions

The currently available Spring functions are described in detail in this section.

Table of Contents , Spring

NAME

*vfe_SpringBegin - create an instance of a Spring object

C SPECIFICATION

vfe_Spring *vfe_SpringBegin ()

ARGUMENTS

None

FUNCTION RETURN VALUE

The function returns a pointer to the newly created Spring object. If the object creation fails, NULL is returned.

DESCRIPTION

Create an instance of a Spring object. Memory is allocated for the object private data and the pointer to the object is returned.

Destroy an instance of a Spring object using 

     void vfe_SpringEnd (vfe_Spring *spring)

Return the current value of a Spring object error flag using 

     Vint vfe_SpringError (vfe_Spring *spring)

Table of Contents , Spring

NAME

vfe_SpringDef - specify spring type

C SPECIFICATION

void vfe_SpringDef (vfe_Spring *spring,
                    Vint type,
                    Vint contype)

INPUT ARGUMENTS

spring       Pointer to Spring object.
type         Spring type
             =SPRING_WELD               Weld type spring
             =SPRING_BUSH               Bush type spring
             =SPRING_LINK               Link type spring
contype       End point A and B connection type
             =SPRING_PNTPNT             Point to point connection
             =SPRING_PNTSURF            Point to surface connection
             =SPRING_SURFSURF           Surface to surface connection
             =SPRING_NONE               Coordinate connection

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type or contype are specified.

DESCRIPTION

Define the type of spring to be specified. SPRING_WELD requires a call to vfe_SpringSetWeld, SPRING_BUSH requires a call to vfe_SpringSetBush, SPRING_LINK requires a call to vfe_SpringSetLink, Specify the connection type to be made at end point A and B. SPRING_PNTPNT requires a call to vfe_SpringSetPntPnt, SPRING_PNTSURF requires a call to vfe_SpringSetPntSurf, SPRING_SURFSURF requires a call to vfe_SpringSetSurfSurf. SPRING_NONE does not required any additional call, as the direction is specified by the coordinates passed to the element routines. This is only valid for type=SPRING_LINK.

Inquire of the defined type and contype as output arguments using 

     void vfe_SpringInq (vfe_Spring *spring,
                         Vint *type,
                         Vint *contype)

Table of Contents , Spring

NAME

vfe_SpringSetHistPtr - set pointers to material history

C SPECIFICATION

void vfe_SpringSetHistPtr (vfe_Spring *spring,
                           Vdouble *oldhist, Vdouble *newhist)

INPUT ARGUMENTS

spring       Pointer to Spring object.
oldhist      Pointer to start of material history at previous step
newhist      Pointer to start of material history at current step

OUTPUT ARGUMENTS

None

DESCRIPTION

Set pointers to the start of the material history data at the previous step, oldhist and the current step newhist. This function is required when an underlying material model such as plasticity is used. Note that the material history data is not copied by this function, only the pointers themselves are copied. The number of double precision values required for the material history at a step is the number of history variables at an integration point times the number of element integration points. The number of history variables depends on the underlying material model and may be queried using vfe_MatlFunNumHist. The number of element integration points is returned using vfe_SpringNumIntPnt. By default the pointers to the material history are NULL. If the number of history variables is zero, this function need not be called.

Table of Contents , Spring

NAME

vfe_SpringSetLocalSystem - set local coordinate system convention

C SPECIFICATION

void vfe_SpringSetLocalSystem (vfe_Spring *spring,
                               Vint type,
                               Vdouble vec[],
                               Vdouble angle)

INPUT ARGUMENTS

spring       Pointer to Spring object.
type         Local system convention
vec          Orientation vector data
angle        Angle to rotate y',z' axes about the element x'
             axis in degrees.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is input.

DESCRIPTION

Specify the convention to be used to construct the orientation of the element local x',y',z' coordinate system with respect to the spring axis. This local system is computed at each integration point location on the element axis and is assumed to be the coordinate system in which the material properties of the element at the integration point are expressed. For stress and strain computation for output using vfe_SpringStrsStrn, the local coordinate system is evaluated at each output location and is the coordinate system in which the output stresses and strains at the output location are expressed.

The x' axis is always constructed to be directed from the first to the second spring end point. The orientation of the y' and z' axes perpendicular to the element x' axis is determined by type. The vec array is only used if the specified type requires position or direction vectors. An additional rotation of the y',z' axes about the x' axis can be specified with angle. By default the local system convention is SYS_ELEMSYS_STANDARD with angle set to 0.

For a description of element coordinate systems, type, and associated orientation vector data, please see
1.4 Element Coordinate Systems

Table of Contents , Spring

NAME

vfe_SpringSetObject - set attribute object

C SPECIFICATION

void vfe_SpringSetObject (vfe_Spring *spring,
                          Vint objecttype,
                          Vobject *object)

INPUT ARGUMENTS

spring       Pointer to Spring object.
objecttype   The object type identifier
             =VFE_MATLFUN            MatlFun object
object       Pointer to the object to be set.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OBJECTTYPE is generated if an improper objecttype is specified.

DESCRIPTION

Set a pointer to an attribute object. Users must supply a MatlFun object prior to computing any quantity that requires a material model definition. The bush type spring does not require a MatlFun object.

Table of Contents , Spring

NAME

vfe_SpringSetParamd - set element formulation parameters

C SPECIFICATION

void vfe_SpringSetParamd (vfe_Spring *spring,
                          Vint type,
                          Vdouble dparam)

INPUT ARGUMENTS

spring       Pointer to Spring object.
type         Type of formulation parameter to set
             =VFE_MINRATIO           Minimum length/diameter ratio
             =VFE_MAXRATIO           Maximum length/diameter ratio
dparam       Double precision parameter value.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is specified. SYS_ERROR_VALUE is generated if an improper dparam is specified.

DESCRIPTION

Set element formulation parameters.

Use VFE_MINRATIO and VFE_MAXRATIO to set the minimum and maximum length/diameter ratios for the weld type spring. By default VFE_MINRATIO is .2 and VFE_MAXRATIO is 5.

Table of Contents , Spring

NAME

vfe_SpringSetParami - set element formulation parameters

C SPECIFICATION

void vfe_SpringSetParami (vfe_Spring *spring,
                          Vint type,
                          Vint iparam)

INPUT ARGUMENTS

spring       Pointer to Spring object.
type         Type of formulation parameter to set
             =VFE_ENDPROJECT         Project end point
iparam       Integer parameter value. 
             =SYS_OFF                Disable
             =SYS_ON                 Enable

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper type is specified. SYS_ERROR_VALUE is generated if an improper iparam is specified.

DESCRIPTION

Set element formulation parameters.

Use VFE_ENDPROJECT to specify that an end point coordinate is to be projected to its connected node location or to the surface of its connected element face. By default VFE_ENDPROJECT is set to SYS_ON.

Table of Contents , Spring

NAME

vfe_SpringSetBush - set generalized spring properties

C SPECIFICATION

void vfe_SpringSetBush (vfe_Spring *spring,
                        Vdouble xs[3],
                        Vdouble ks[6],
                        Vdouble sc[6],
                        Vdouble ec[6])

INPUT ARGUMENTS

spring       Pointer to Spring object.
xs           Location of spring
ks           Stiffness coefficients
sc           Stress recovery coefficients
ec           Strain recovery coefficients

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OPERATION is generated if the spring type is not SPRING_BUSH.

DESCRIPTION

Set the location, xs, of the discrete spring, the spring stiffnesses, ks, and stress and strain recovery coefficients sc and ec.

Table of Contents , Spring

NAME

vfe_SpringSetLink - set link properties

C SPECIFICATION

void vfe_SpringSetLink (vfe_Spring *spring,
                        Vdouble stiff)

INPUT ARGUMENTS

spring       Pointer to Spring object.
stiff        Spring stiffness

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OPERATION is generated if the spring type is not SPRING_LINK.

DESCRIPTION

Set the stiffness, stiff, of the spring.

Table of Contents , Spring

NAME

vfe_SpringSetWeld - set spot weld properties

C SPECIFICATION

void vfe_SpringSetWeld (vfe_Spring *spring,
                        Vdouble r)

INPUT ARGUMENTS

spring       Pointer to Spring object.
r            Radius of spot weld

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OPERATION is generated if the spring type is not SPRING_WELD.

DESCRIPTION

Set the radius, r, of the spot weld.

Table of Contents , Spring

NAME

vfe_SpringSetPntPnt - set point to point connection

C SPECIFICATION

void vfe_SpringSetPntPnt (vfe_Spring *spring,
                          Vdouble xa[3],
                          Vdouble xb[3])

INPUT ARGUMENTS

spring       Pointer to Spring object.
xa           Location of end point A
xb           Location of end point B

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OPERATION is generated if the connection type is not SPRING_PNTPNT.

DESCRIPTION

Set the locations of the end points, xa and xb.

Table of Contents , Spring

NAME

vfe_SpringSetPntSurf - set point to surface connection

C SPECIFICATION

void vfe_SpringSetPntSurf (vfe_Spring *spring,
                           Vdouble xa[3],
                           Vdouble xb[3],
                           Vint shapeb,
                           Vint maxib,
                           Vint maxjb)

INPUT ARGUMENTS

spring       Pointer to Spring object.
xa           Location of end point A
xb           Location of end point B
shapeb       The shape for the element face connected to B
             =SYS_SHAPETRI           Triangle
             =SYS_SHAPEQUAD          Quadrilateral
maxib        The number of points along the i direction.
maxjb        The number of points along the j direction.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OPERATION is generated if the connection type is not SPRING_PNTPNT.

DESCRIPTION

Set the locations of the end points, xa and xb and the topology of the element face to be connected to end point B.

Table of Contents , Spring

NAME

vfe_SpringSetSurfSurf - set surface to surface connection

C SPECIFICATION

void vfe_SpringSetSurfSurf (vfe_Spring *spring,
                            Vdouble xa[3],
                            Vint shapea,
                            Vint maxia,
                            Vint maxja,
                            Vdouble xb[3],
                            Vint shapeb,
                            Vint maxib,
                            Vint maxjb)

INPUT ARGUMENTS

spring       Pointer to Spring object.
xa           Location of end point A
shapea       The shape for the element face connected to A
             =SYS_SHAPETRI           Triangle
             =SYS_SHAPEQUAD          Quadrilateral
maxia        The number of points along the i direction.
maxja        The number of points along the j direction.
xb           Location of end point B
shapeb       The shape for the element face connected to B
             =SYS_SHAPETRI           Triangle
             =SYS_SHAPEQUAD          Quadrilateral
maxib        The number of points along the i direction.
maxjb        The number of points along the j direction.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_OPERATION is generated if the connection type is not SPRING_PNTPNT.

DESCRIPTION

Set the locations of the end points, xa and xb and the topology of the element faces to be connected to end points A and B.

Table of Contents , Spring

NAME

vfe_SpringDofMap - query element degree of freedom map

C SPECIFICATION

void vfe_SpringDofMap (vfe_Spring *spring,
                       Vint analysistype,
                       Vint loc[], Vint tag[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis

OUTPUT ARGUMENTS

loc          Vector of degree of freedom locations
tag          Vector of degree of freedom types

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for element degree of freedom map. The degree of freedom map consists of a location index, loc and type, tag for each degree of freedom used by the element.

The location index is either a positive node index into the element connectivity indicating a nodal freedom or a zero value indicating an elemental degree of freedom. The tag indicates the type of the degree of freedom. Tag values are one of a set of enumerated types which indicate whether the degree of freedom is a translation or rotation, etc.

The length of the loc and tag vectors is equal to the number of element degrees of freedom. Use vfe_SpringNumDof to return the number of element degrees of freedom.

Table of Contents , Spring

NAME

vfe_SpringNumDof - query number of element degrees of freedom

C SPECIFICATION

void vfe_SpringNumDof (vfe_Spring *spring,
                       Vint analysistype,
                       Vint *nedofs)

INPUT ARGUMENTS

spring       Pointer to Spring object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis

OUTPUT ARGUMENTS

nedofs       Number of element degrees of freedom

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for number of element degree of freedom nedofs. The number of degrees of freedom will generally be equal to the number of nodal degrees of freedom per node times the number of nodes plus the number of elemental degrees of freedom. Use vfe_SpringDofMap to return the location and type of each degree of freedom.

Table of Contents , Spring

NAME

vfe_SpringNumIntPnt - query number of element integration points

C SPECIFICATION

void vfe_SpringNumIntPnt (vfe_Spring *spring,
                          Vint analysistype,
                          Vint *nepnts)

INPUT ARGUMENTS

spring       Pointer to Spring object.
analysistype The type of analysis
             =VFE_ANALYSIS_STRUCTURAL Structural analysis

OUTPUT ARGUMENTS

nepnts       Number of element integration points

ERRORS

SYS_ERROR_ENUM is generated if an improper analysistype is specified.

DESCRIPTION

Query for number of element integration points nepnts.

Table of Contents , Spring

NAME

vfe_SpringDirCos - compute spring local direction cosines

C SPECIFICATION

void vfe_SpringDirCos (vfe_Spring *spring,
                       Vdouble x[][3],
                       Vdouble tm[][3][3])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of point locations defining spring axis

OUTPUT ARGUMENTS

tm           Array of direction cosine matrices at the element nodes.

DESCRIPTION

Compute the direction cosine matrices of the element local coordinate system. For stress and strain computation the local coordinate system at each stress output location is the coordinate system in which the output stresses and strains at the location using vfe_SpringStrsStrn are expressed. Given that X',Y' and Z' are three orthonormal vectors indicating the direction of the local coordinate axes in the global coordinate system (x,y,z), then the direction cosine matrix, tm for this local coordinate system is defined as: 
     tm[0][0] = X'x  tm[0][1] = X'y  tm[0][2] = X'z
     tm[1][0] = Y'x  tm[1][1] = Y'y  tm[1][2] = Y'z
     tm[2][0] = Z'x  tm[2][1] = Z'y  tm[2][2] = Z'z

The local coordinate system is determined by the local system convention set using vfe_SpringSetLocalSystem.

Table of Contents , Spring

NAME

vfe_SpringGeomStiff - geometric stiffness matrix

C SPECIFICATION

void vfe_SpringGeomStiff (vfe_Spring *spring,
                          Vdouble x[][3],
                          Vdouble u[],
                          Vdouble kg[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.
u            Degree of freedom vector of displacements

OUTPUT ARGUMENTS

kg           Degree of freedom geometric stiffness matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute the geometric stiffness matrix, kg, given the node coordinates, x, and the degree of freedom displacement vector, u. The lower triangle of the geometric stiffness is returned.

Table of Contents , Spring

NAME

vfe_SpringInitHist - initialize material history

C SPECIFICATION

void vfe_SpringInitHist (vfe_Spring *spring)

INPUT ARGUMENTS

spring       Pointer to Spring object.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set.

DESCRIPTION

Initialize the values of the history variables used in the underlying element or primitive material model for the element. This operation should be performed once for each element (at the first load or time step for example) to initialize the old history variables to reflect the initial configuration condition. If the number of history variables is zero, this function need not be called.

Table of Contents , Spring

NAME

vfe_SpringMass - consistent mass matrix

C SPECIFICATION

void vfe_SpringMass (vfe_Spring *spring,
                     Vdouble x[][3],
                     Vdouble m[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.

OUTPUT ARGUMENTS

m            Degree of freedom consistent mass matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute the consistent mass matrix, m, given the node coordinates, x. The lower triangle of the consistent mass is returned. Use vfe_SpringMassDiag to compute a diagonal mass matrix.

Table of Contents , Spring

NAME

vfe_SpringMassDiag - diagonal mass matrix

C SPECIFICATION

void vfe_SpringMassDiag (vfe_Spring *spring,
                         Vdouble x[][3],
                         Vdouble md[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.

OUTPUT ARGUMENTS

md           Degree of freedom diagonal mass vector

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute the diagonal mass matrix, md, given the node coordinates, x. The diagonal mass is returned as a degree of freedom length vector. Use vfe_SpringMass to compute a consistent mass matrix.

Table of Contents , Spring

NAME

vfe_SpringReact - reaction vector

C SPECIFICATION

void vfe_SpringReact (vfe_Spring *spring,
                      Vdouble x[][3],
                      Vdouble u[],
                      Vdouble r[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.
u            Degree of freedom vector of displacements

OUTPUT ARGUMENTS

r            Degree of freedom reaction vector

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute the reaction vector, r, given the node coordinates, x, and the degree of freedom displacement vector, u.

Table of Contents , Spring

NAME

vfe_SpringReactStiff - reaction vector, stiffness matrix

C SPECIFICATION

void vfe_SpringReactStiff (vfe_Spring *spring,
                           Vdouble x[][3],
                           Vdouble u[],
                           Vdouble kflag,
                           Vdouble r[],
                           Vdouble k[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.
u            Degree of freedom vector of displacements
kflag        Flag to compute stiffness matrix, k
             =SYS_OFF      Do not compute stiffness matrix
             =SYS_ON       Compute and return stiffness matrix

OUTPUT ARGUMENTS

r            Degree of freedom reaction vector
k            Degree of freedom stiffness matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute the reaction vector, r, and optionally the stiffness matrix, k, given the node coordinates, x, and the degree of freedom displacement vector, u. The lower triangle of the stiffness matrix is returned.

Table of Contents , Spring

NAME

vfe_SpringStiff - linear stiffness matrix

C SPECIFICATION

void vfe_SpringStiff (vfe_Spring *spring,
                      Vdouble x[][3],
                      Vdouble kl[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.

OUTPUT ARGUMENTS

kl           Degree of freedom stiffness matrix

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute the linear stiffness matrix, kl, given the node coordinates, x. The lower triangle of the stiffness matrix is returned.

Table of Contents , Spring

NAME

vfe_SpringStrsStrn - stress and strain

C SPECIFICATION

void vfe_SpringStrsStrn (vfe_Spring *spring,
                         Vdouble x[][3],
                         Vdouble u[],
                         Vdouble strs[], Vdouble strn[])

INPUT ARGUMENTS

spring       Pointer to Spring object.
x            Array of node locations.
u            Degree of freedom vector of displacements

OUTPUT ARGUMENTS

strs         Array of nodal stresses
strn         Array of nodal strains

ERRORS

SYS_ERROR_NULLOBJECT is generated if a MatlFun attribute object has not been set. SYS_ERROR_COMPUTE is generated if a negative Jacobian transformation is computed or the maximum nodal projection angle is exceeded.

DESCRIPTION

Compute nodal stresses and strains, strs and strn, given the node coordinates, x, and the degree of freedom displacement vector, u. The stresses and strains are computed in the element local system at end points A and B. The values at end A are then output at all nodes connected to end point A. Similarly for end point B, the values at end B are then output at all nodes connected to end point B. The stress and strain values are ordered first by the 6 components followed by the the number of element nodes.