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4. Beam Elements - Beam3D

Beam elements are a specialization of a volume element in which two directions, the beam cross section, may be assumed to be small with respect to the beam axis.

The Beam3D module is used to simulate 3D beam elements. Beam elements are one-dimensional elements in 3D space which support axial deformation, bending and torsion. In addition Beam3D supports the flexibility due to transverse shear deformation.

The methods associated with a Beam3D object are the following.

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4.1 Element Geometry

The basic beam element geometry is defined by the node coordinates of the beam reference axis. The beam section is defined by the node offsets of the beam centroidal axis, beam section properties and beam node normals. These beam section properties which are set using vfe_Beam3DSetPropPtr are illustrated below in Figure 4-2. Additional beam section properties may be set such as area, moments of inertia, torsional constant and shear center offsets. Other element quantities which may be set using this function are beam temperature and effective shear factor.

If the node offsets are zero, the beam centroidal axis is coincident with the beam reference axis. In general, large centroidal axis offset values, which are much greater than the beam section dimensions, should be avoided. By default the beam section is perpendicular to the tangent along the beam reference axis with the orientation of the section defined by a prescription specified by vfe_Beam3DSetLocalSystem. The user may optionally enter node normals to specifically define the orientation of the beam cross section. These user defined normals allow for beam section orientations which are not perpendicular to the beam reference axis and override the prescription for the node normals specified in vfe_Beam3DSetLocalSystem. If the both the node normal y and normal z are set using vfe_Beam3DSetPropPtr the beam section lies in the plane defined by the node normals. The node normal z is recomputed to be orthogonal to the normal y. If only the normal y is set then the normal z is computed to be orthogonal to the centroidal axis and the node normal y. Beam properties such as area, offsets, moments of inertia, shear center offsets, etc. are always measured in the plane perpendicular to the beam reference axis regardless of the direction of the beam node normals.

The element natural coordinate, r, is tangent to the the beam centroidal axis.


Figure 4-2, Geometry for 3 Node 3D Beam Element
The exact specification of the beam section which couples element and primitive material properties, is managed using the BeamProp module. The BeamProp module provides for general integrated beam sections vfe_BeamPropSetIntegrate as well as preintegrated beam sections input as general section area properties, vfe_BeamPropSetSection, or as a general matrix, vfe_BeamPropSetMatrix, relating centroidal axis strains and curvatures to stress and moment resultants. For general integrated and general area beam sections the BeamProp module allows a primitive material, such as defined by the LinMat module, to be specified.

Note that when using the general integrated beam section defined by vfe_BeamPropSetIntegrate, the actual distance of the beam section integration point from the centroidal axis is computed internally by multiplying the integration point coordinates input in vfe_BeamPropSetIntegrate by one-half of the thicknesses specified using vfe_Beam3DSetPropPtr.

Use the function vfe_Beam3DStrsAdapt to aid in computing element strain energy, strain energy error and other useful quantities to aid in solution error estimation and mesh adaptation.

Pin flags can be set at either of the beam's ends with vfe_Beam3DSetPins. Degrees of freedom marked with a pin flag are not transmitted to neighboring elements. Every degree of freedom marked with a pin flag creates an additional internal degree of freedom in the element. If large rotations are used then the degrees of freedom in the element must be updated using vfe_Beam3DUpdateDofs, otherwise updated degrees of freedom are simply the addition of the degrees of freedom at the beginning of the step and the incremental values. If pin flags are defined, the element degrees of freedom may be recovered using vfe_Beam3DSixDof.

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4.2 Function Descriptions

The currently available Beam3D functions are described in detail in this section.

Table of Contents , Beam3D

NAME

*vfe_Beam3DBegin - create an instance of a Beam3D object

C SPECIFICATION

vfe_Beam3D *vfe_Beam3DBegin ()

ARGUMENTS

None

FUNCTION RETURN VALUE

The function returns a pointer to the newly created Beam3D object. If the object creation fails, NULL is returned.

DESCRIPTION

Create an instance of a Beam3D object. Memory is allocated for the object private data and the pointer to the object is returned. Default topology is the 2-noded element with isoparametric technology.

Destroy an instance of a Beam3D object using 

     void vfe_Beam3DEnd (vfe_Beam3D *beam3d)

Return the current value of a Beam3D object error flag using 

     Vint vfe_Beam3DError (vfe_Beam3D *beam3d)

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NAME

vfe_Beam3DSetHistPtr - set pointers to material history

C SPECIFICATION

void vfe_Beam3DSetHistPtr (vfe_Beam3D *beam3d,
                           Vdouble *oldhist, Vdouble *newhist)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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 total number of integration points in the element. The number of history variables depends on the underlying material model and may be queried using vfe_MatlFunNumHist. The total number of integration points is the product of the number of element integration points returned using vfe_Beam3DNumIntPnt and the number of history values returned using vfe_MatlFunNumHist. By default the pointers to the material history are NULL. If the number of history variables is zero, this function need not be called.

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NAME

vfe_Beam3DSetLocalSystem - set local coordinate system convention

C SPECIFICATION

void vfe_Beam3DSetLocalSystem (vfe_Beam3D *beam3d,
                               Vint type,
                               Vdouble vec[],
                               Vdouble angle)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
type         Local system convention
vec          Orientation vector data
angle        Angle to rotate beam y',z' axes about the beam 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 beam element local x',y',z' coordinate system with respect to the beam reference axis. This local system is computed at each integration point location on the beam 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 either vfe_Beam3DStrsStrn or vfe_Beam3DStressStrain, 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 tangent to the beam reference axis. The orientation of the y' and z' axes perpendicular to the beam reference 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

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NAME

vfe_Beam3DSetObject - set attribute object

C SPECIFICATION

void vfe_Beam3DSetObject (vfe_Beam3D *beam3d,
                          Vint objecttype,
                          Vobject *object)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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.

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NAME

vfe_Beam3DSetParamd - set element formulation parameters

C SPECIFICATION

void vfe_Beam3DSetParamd (vfe_Beam3D *beam3d,
                          Vint type,
                          Vdouble dparam)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
type         Type of formulation parameter to set
             =VFE_MAXPROJANG         Maximum nodal projection angle
             =VFE_ADDEDMASS          Additional mass/length
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_MAXPROJANG to set the maximum angle in degrees between the beam tangent at an element integration point and the beam tangent at a node. By default VFE_MAXPROJANG is set to 90. degrees.

Use VFE_ADDEDMASS to add non-structural mass/length to the beam element. By default VFE_ADDEDMASS is set to 0..

Table of Contents , Beam3D

NAME

vfe_Beam3DSetParami - set element formulation parameters

C SPECIFICATION

void vfe_Beam3DSetParami (vfe_Beam3D *beam3d,
                          Vint type,
                          Vint iparam)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
type         Type of formulation parameter to set
             =VFE_TECH               Element technology
             =VFE_LARGEROTATION      Toggle for large rotations
             =VFE_ROTINERTIA         Enable rotary inertias
             =VFE_TEMPMATLAVE        Average material temperature flag
iparam       Integer parameter value. 
             =VFE_TECH_ISOP          Mindlin isoparametric technology
             =VFE_TECH_KIRCHHOFF     Kirchhoff technology
             =VFE_TECH_ENHANCED      Enhanced technology
             =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 technology and formulation parameters.

The basic element technology is set with the VFE_TECH parameter. The Kirchhoff technology assumes a cubic variation of displacement transverse to the beam axis and is only available in a pre-integrated formulation and a two node topology. By default VFE_TECH is set to VFE_TECH_ISOP.

Toggle large rotations using VFE_LARGEROTATION. By default VFE_LARGEROTATION is set to SYS_OFF.

The addition of rotary inertias to the element mass matrix is set with the VFE_ROTINERTIA parameter. By default VFE_ROTINERTIA is set to SYS_OFF.

The parameter VFE_TEMPMATLAVG toggles the method for computing the temperature used for evaluating temperature dependent material properties. If enabled, the temperature used for temperature dependent material properties is the average of the element node point temperatures. If disabled, the temperature is isoparametrically interpolated from the node point temperatures at each element integration point. By default VFE_TEMPMATLAVG is set to SYS_ON.

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NAME

vfe_Beam3DSetPropPtr - set pointer to element nodal properties

C SPECIFICATION

void vfe_Beam3DSetPropPtr (vfe_Beam3D *beam3d,
                           Vint type,
                           Vdouble *propptr)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
type         Type of element property
             =VFE_PROP_TEMPERATURE      Temperatures
             =VFE_PROP_TEMPREF          Reference temperatures
             =VFE_PROP_THICKNESSY       Thicknesses in y'
             =VFE_PROP_THICKNESSZ       Thicknesses in z'
             =VFE_PROP_OFFSETY          Offsets in y'
             =VFE_PROP_OFFSETZ          Offsets in z'
             =VFE_PROP_NORMALY          Normals in y'
             =VFE_PROP_NORMALZ          Normals in z'
             =VFE_PROP_AREA             Areas
             =VFE_PROP_IYY              Moments of inertia about y'
             =VFE_PROP_IZZ              Moments of inertia about z'
             =VFE_PROP_IYZ              Products of inertia
             =VFE_PROP_J                Torsional constants
             =VFE_PROP_KSY              Effective shear factor in y'
             =VFE_PROP_KSZ              Effective shear factor in z'
             =VFE_PROP_DSY              Shear center offsets in y'
             =VFE_PROP_DSZ              Shear center offsets in z'
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 nodal 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 for the associated property. By default the temperature is 0., the thicknesses are 2., the offsets are 0., the area is 4., and the effective shear factors are 5/6. By default the reference temperature is 0.

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NAME

vfe_Beam3DSetTopology - set element topology

C SPECIFICATION

void vfe_Beam3DSetTopology (vfe_Beam3D *beam3d,
                            Vint maxi)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
maxi         The number of points along the i direction.
             If maxi = 0 then the linear Serendipity
             element form of the specified shape is assumed.

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_VALUE is generated if an improper maxi is specified.

DESCRIPTION

Specify the topology of a 3D beam element. If maxi is set to 3 then a quadratic element form is assumed.

Table of Contents , Beam3D

NAME

vfe_Beam3DDofMap - query element degree of freedom map

C SPECIFICATION

void vfe_Beam3DDofMap (vfe_Beam3D *beam3d,
                       Vint analysistype,
                       Vint loc[], Vint tag[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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.

The length of the loc and tag vectors is equal to the number of element degrees of freedom. Use vfe_Beam3DNumDof to return the number of element degrees of freedom.

Table of Contents , Beam3D

NAME

vfe_Beam3DNumDof - query number of element degrees of freedom

C SPECIFICATION

void vfe_Beam3DNumDof (vfe_Beam3D *beam3d,
                       Vint analysistype,
                       Vint *nedofs)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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_Beam3DDofMap to return the location and type of each degree of freedom.

Table of Contents , Beam3D

NAME

vfe_Beam3DNumIntPnt - query number of element integration points

C SPECIFICATION

void vfe_Beam3DNumIntPnt (vfe_Beam3D *beam3d,
                          Vint analysistype,
                          Vint *nepnts)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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.

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NAME

vfe_Beam3DSetPins - set pin flags

C SPECIFICATION

void vfe_Beam3DSetPins (vfe_Beam3D *beam3d,
                        Vint npins1,
                        Vint tags1[],
                        Vint npins2,
                        Vint tags2[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
npins1       Number of pin flags set on first node
tags1        List of npins1 degrees of freedom pinned on first node
npins1       Number of pin flags set on second node
tags1        List of npins1 degrees of freedom pinned on second node

OUTPUT ARGUMENTS

None

ERRORS

SYS_ERROR_ENUM is generated if an improper tags1 or tags2 contains entries other than SYS_DOF_TX, SYS_DOF_TY, SYS_DOF_TZ, SYS_DOF_RX, SYS_DOF_RY, or SYS_DOF_RZ.

DESCRIPTION

Sets pin flags at either end of the beam. If a linear beam then the second node is node 2; if a quadratic beam then the second node is the third beam.

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NAME

vfe_Beam3DSixDof - gather nodal displacements and rotations

C SPECIFICATION

void vfe_Beam3DSixDof (vfe_Beam3D *beam3d,
                       Vdouble x[][3],
                       Vdouble u[],
                       Vdouble sixdof[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of point locations defining beam surface.
u            The element degrees of freedom

OUTPUT ARGUMENTS

sixdof       Global displacements and rotations for each node

ERRORS

None

DESCRIPTION

Gathers the nodal displacements and rotations for the element. This function is needed in case pin flags are set. In this case the incoming degrees of freedom are usually those shared with all elements connected through the node. The element's displacement and rotation degrees of freedom require an internal transformation performed by this function.

Table of Contents , Beam3D

NAME

vfe_Beam3DDirCos - compute beam local direction cosines

C SPECIFICATION

void vfe_Beam3DDirCos (vfe_Beam3D *beam3d,
                       Vdouble x[][3],
                       Vdouble u[],
                       Vdouble tm[][3][3])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of point locations defining beam surface.
u            The element degrees of freedom

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 either vfe_Beam3DStrsStrn or vfe_Beam3DStressStrain 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_Beam3DSetLocalSystem or alternatively the normals in the beam y' and z' directions using vfe_Beam3DSetPropPtr.

The element degrees of freedom, u, are only required if large rotations have been enabled. Otherwise this argument is ignored.

Table of Contents , Beam3D

NAME

vfe_Beam3DDistLoad - distributed load vector

C SPECIFICATION

void vfe_Beam3DDistLoad (vfe_Beam3D *beam3d,
                         Vdouble x[][3],
                         Vint enttype,
                         Vint no,
                         Vint loadtype,
                         Vdouble q[],
                         Vdouble f[],

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of node locations.
enttype      Entity type on which load is applied
             =SYS_EDGE     Element edge
no           Element edge number, currently unused and ignored.
loadtype     Distributed load type
             =VFE_DISTLOAD_TRAC      Load directed along vector
q            Vector of distributed load values

OUTPUT ARGUMENTS

f            Degree of freedom vector of consistent loads.

ERRORS

SYS_ERROR_ENUM is generated if an improper enttype or loadtype is specified. SYS_ERROR_OPERATION is generated if an invalid combination of enttype and loadtype is specified. SYS_ERROR_VALUE is generated if an improper no is specified. SYS_ERROR_COMPUTE is generated if a zero edge Jacobian is computed.

DESCRIPTION

Compute the consistent degree of freedom loads given a distributed load, q along a 3D beam element edge. The vector q contains values for the load type for each node in the element. If the loadtype is VFE_DISTLOAD_TRAC then q contains a vector traction at each element node. If the traction is applied to an edge the units are force/length. at each element node. Note that the input array of node locations, x, contains the coordinate locations for all nodes in the element. Correspondingly the output array of consistent degree of freedom loads, f, contains loads for all degrees of freedom in the element. The distributed loads for edges are in units of force per unit length.

Table of Contents , Beam3D

NAME

vfe_Beam3DElemLoad - body force vector

C SPECIFICATION

void vfe_Beam3DElemLoad (vfe_Beam3D *beam3d,
                         Vdouble x[][3],
                         Vdouble q[][3],
                         Vdouble f[],

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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 zero 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 , Beam3D

NAME

vfe_Beam3DGeomStiff - geometric stiffness matrix

C SPECIFICATION

void vfe_Beam3DGeomStiff (vfe_Beam3D *beam3d,
                          Vdouble x[][3],
                          Vdouble u[],
                          Vdouble kg[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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 , Beam3D

NAME

vfe_Beam3DInitHist - initialize material history

C SPECIFICATION

void vfe_Beam3DInitHist (vfe_Beam3D *beam3d)

INPUT ARGUMENTS

beam3d      Pointer to Beam3D 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 , Beam3D

NAME

vfe_Beam3DMass - consistent mass matrix

C SPECIFICATION

void vfe_Beam3DMass (vfe_Beam3D *beam3d,
                     Vdouble x[][3],
                     Vdouble m[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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_Beam3DMassDiag to compute a diagonal mass matrix.

Table of Contents , Beam3D

NAME

vfe_Beam3DMassDiag - diagonal mass matrix

C SPECIFICATION

void vfe_Beam3DMassDiag (vfe_Beam3D *beam3d,
                         Vdouble x[][3],
                         Vdouble md[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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_Beam3DMass to compute a consistent mass matrix.

Table of Contents , Beam3D

NAME

vfe_Beam3DReact - reaction vector

C SPECIFICATION

void vfe_Beam3DReact (vfe_Beam3D *beam3d,
                      Vdouble x[][3],
                      Vdouble u[],
                      Vdouble r[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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 , Beam3D

NAME

vfe_Beam3DReactStiff - reaction vector, stiffness matrix

C SPECIFICATION

void vfe_Beam3DReactStiff (vfe_Beam3D *beam3d,
                           Vdouble x[][3],
                           Vdouble u[],
                           Vdouble kflag,
                           Vdouble r[],
                           Vdouble k[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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 , Beam3D

NAME

vfe_Beam3DStiff - linear stiffness matrix

C SPECIFICATION

void vfe_Beam3DStiff (vfe_Beam3D *beam3d,
                      Vdouble x[][3],
                      Vdouble kl[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D 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 , Beam3D

NAME

vfe_Beam3DStrsAdapt - stress based error analysis

C SPECIFICATION

void vfe_Beam3DStrsAdapt (vfe_Beam3D *beam3d,
                          Vdouble x[][3],
                          Vdouble u[],
                          Vdouble strss[],
                          Vdouble *setot,
                          Vdouble *seerr,
                          Vdouble *h,
                          Vdouble *p,
                          Vdouble *d)

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of node locations.
u            Degree of freedom vector of displacements
strss        Array of recovered nodal stresses

OUTPUT ARGUMENTS

setot        Total strain energy
seerr        Strain energy error
h            Characteristic length
p            Effective polynomial order
d            Dimension

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 element total strain energy, setot, and strain energy error, seerr, given the element displacements, u, and an estimate of the exact nodal stress resultants, strss. In addition useful quantities such as the characteristic length, effective polynomial order and dimension of the element are returned. The element dimension, d, is 1. These quantities are useful for computing new characteristic element length for mesh adaptation.

Table of Contents , Beam3D

NAME

vfe_Beam3DStrsStrn - resultant stress and strain/curvature

C SPECIFICATION

void vfe_Beam3DStrsStrn (vfe_Beam3D *beam3d,
                         Vdouble x[][3],
                         Vdouble u[],
                         Vdouble strs[], Vdouble strn[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of node locations.
u            Degree of freedom vector of displacements

OUTPUT ARGUMENTS

strs         Array of nodal stress resultant
strn         Array of nodal strains/curvatures

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 stress resultants and strains, strs and strn, given the node coordinates, x, and the degree of freedom displacement vector, u.

The stress resultants and strains/curvatures are computed in the beam local coordinate system. The convention used to generate local coordinate systems is specified using vfe_Beam3DSetLocalSystem or alternatively setting normal directions using vfe_Beam3DSetPropPtr. The actual direction cosine matrices of the beam local systems at the element output locations may be returned using vfe_Beam3DDirCos.

The strs is composed of 6 stress resultants and the strn is composed of 6 associated midsurface strains, twists and curvatures at each output location. The stress and strain values are ordered first by the 6 stress resultant or strain components followed by the the number of element nodes. For example, for a 2 node beam element a total of 6*2 = 12 stress resultant values will be returned in strs and 12 strain values returned in strn.

Table of Contents , Beam3D

NAME

vfe_Beam3DStressStrain - three-dimensional stress and strain

C SPECIFICATION

void vfe_Beam3DStressStrain (vfe_Beam3D *beam3d,
                             Vdouble x[][3],
                             Vdouble u[],
                             Vdouble strs[], Vdouble strn[],
                             Vdouble stress[], Vdouble strain[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of node locations.
u            Degree of freedom vector of displacements

OUTPUT ARGUMENTS

strs         Array of nodal stress resultant
strn         Array of nodal strains/curvatures
stress       Array of nodal three dimensional stresses at recovery points
strain       Array of nodal three dimensional strains at recovery points

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 stress resultants and strains, strs and strn, and the three-dimensional stresses and strains, stress and strain, given the node coordinates, x, and the degree of freedom displacement vector, u.

The stress resultants and strains/curvatures are the same as those obtained with vfe_Beam3DStrsStrn, and the same remarks regarding local coordinate systems apply.

The three-dimensional stresses and strains are computed at a series of points in the beam's cross section. The number of cross sectional points is obtained using vfe_MatlFunNumStressStrain and depend on the type of cross section used. See BeamProp for more details on each cross section type.

Table of Contents , Beam3D

NAME

vfe_Beam3DUpdateDofs - update dofs for large-rotation problems

C SPECIFICATION

void vfe_Beam3DUpdateDofs (vfe_Beam3D *beam3d,
                           Vdouble x[][3],
                           Vdouble un[],
                           Vdouble uinc[],
                           Vdouble un1[])

INPUT ARGUMENTS

beam3d       Pointer to Beam3D object.
x            Array of point locations defining beam surface.
un           Dofs at the beginning of the step
uinc         Incremental dofs computed at the step

OUTPUT ARGUMENTS

un1          Dofs at the end of the step

ERRORS

None

DESCRIPTION

Compute the updated degrees of freedom at the end of a step given the initial and incremental values. For linear analysis the updated dofs are simply the sum of the un and uinc; however, if large rotations are used, the rotation dofs at the end of the step require special treatment.