5. Truss Elements - Truss3D
Truss elements are a specialization of a beam element in which only axial forces are supported. Truss elements are one-dimensional structural members in 3D space, that are usually long and slender, which only transmit axial force. The Truss3D module is used to simulate 3D truss elements. The 3 node version of the truss is useful in modelling curved cable structures.
The methods associated with a Truss3D object are the following.
Begin and end an instance of an object, generic object functions
vfe_Truss3DBegin()
- create an instance of a Truss3D objectvfe_Truss3DEnd()
- destroy an instance of a Truss3D objectvfe_Truss3DError()
- return Truss3D object error flag
Attributes and Parameters
vfe_Truss3DSetHistPtr()
- set pointers to material historyvfe_Truss3DSetLocalSystem()
- set stress axes directionvfe_Truss3DSetObject()
- set attribute objectvfe_Truss3DSetParamd()
- set element formulation parametersvfe_Truss3DSetParami()
- set element formulation parametersvfe_Truss3DSetPropPtr()
- set pointer to element nodal propertiesvfe_Truss3DSetTopology()
- set input element topologyvfe_Truss3DDirCos()
- compute truss local direction cosines
Degree of Freedom and Integration Information
vfe_Truss3DDofMap()
- query element degree of freedom mapvfe_Truss3DNumDof()
- query number of element degrees of freedomvfe_Truss3DNumIntPnt()
- query number of element integration points
Structural analysis computations
vfe_Truss3DDistLoad()
- distributed load vector.vfe_Truss3DElemLoad()
- body force vectorvfe_Truss3DGeomStiff()
- geometric stiffness matrixvfe_Truss3DInitHist()
- initialize material historyvfe_Truss3DMass()
- consistent mass matrixvfe_Truss3DMassDiag()
- diagonal mass matrixvfe_Truss3DReact()
- reaction vectorvfe_Truss3DReactStiff()
- reaction vector, stiffness matrixvfe_Truss3DStiff()
- linear stiffness matrixvfe_Truss3DStrsAdapt()
- stress based error analysisvfe_Truss3DStrsStrn()
- stress and strain
Thermal analysis computations
vfe_Truss3DDistHeat()
- distributed heat loads.vfe_Truss3DElemHeat()
- body heat generationvfe_Truss3DCap()
- consistent capacitance matrixvfe_Truss3DCapDiag()
- diagonal capacitance matrixvfe_Truss3DPower()
- thermal powervfe_Truss3DPowerCond()
- thermal power, conductance matrixvfe_Truss3DCond()
- conductance matrixvfe_Truss3DHFlxAdapt()
- heat flux based error analysisvfe_Truss3DHFlxTGrd()
- heat flux and temperature gradient
Instance a Truss3D object using vfe_Truss3DBegin()
.
Once a Truss3D is instanced,
set the material function attribute object MatlFun using
vfe_Truss3DSetObject()
.
The current topology of the element is specified using
vfe_Truss3DSetTopology()
.
The area of the truss element is
specified using vfe_Truss3DSetPropPtr()
.
Query the element degree of freedom map using vfe_Truss3DDofMap()
and
vfe_Truss3DNumDof()
.
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_Truss3DSetHistPtr()
and vfe_Truss3DInitHist()
.
Since all element geometry is available directly to the element in terms
of node coordinates and areas,
the material function should point to a primitive material.
5.1. Element Geometry
The basic truss element geometry is defined by the node coordinates of the
truss axis and the cross section properties of the truss.
The truss section is defined by a cross sectional area. The cross section
is always assumed to be perpendicular to the truss axis.
The truss section properties which are set using vfe_Truss3DSetPropPtr()
are illustrated below in Figure 5-2.
Other element quantities which may be set using
this function are node temperature and reference temperature.
The x’ axis of the truss is always tangent to the axis
of the truss. The components of stress y’ and z’ in the plane
perpendicular to x’ are always zero as well as all shear stresses.
The element natural coordinate, r, is tangent to the
the truss centroidal axis.
Use the function
vfe_Truss3DStrsAdapt()
to aid in computing element strain energy, strain
energy error and other useful quantities to aid in solution error estimation
and mesh adaptation.
The function vfe_Truss3DHFlxAdapt()
performs a similar
computation for heat transfer analysis.
5.2. Function Descriptions
The currently available Truss3D functions are described in detail in this section.
-
vfe_Truss3D *vfe_Truss3DBegin(void)
create an instance of a Truss3D object
Create an instance of a Truss3D object. Memory is allocated for the object private data and the pointer to the object is returned. Default topology is the 2-noded truss.
Destroy an instance of a Truss3D object using
void vfe_Truss3DEnd (vfe_Truss3D *truss3d)
Return the current value of a Truss3D object error flag using
Vint vfe_Truss3DError (vfe_Truss3D *truss3d)
- Returns:
The function returns a pointer to the newly created Truss3D object. If the object creation fails, NULL is returned.
-
void vfe_Truss3DEnd(vfe_Truss3D *p)
destroy an instance of a Truss3D object
-
Vint vfe_Truss3DError(vfe_Truss3D *p)
return the current value of a Truss3D object error
-
void vfe_Truss3DSetObject(vfe_Truss3D *p, Vint objecttype, Vobject *object)
set attribute object
Set a pointer to an attribute object. Users must supply a MatlFun object prior to computing any quantity that requires a material model definition.
- Errors
SYS_ERROR_OBJECTTYPE
is generated if an improper objecttype is specified.
- Parameters:
p – Pointer to Truss3D object.
objecttype – The object type identifier
x=VFE_MATLFUN MatlFun object
object – Pointer to the object to be set.
-
void vfe_Truss3DSetParami(vfe_Truss3D *p, Vint type, Vint iparam)
set element formulation parameters
Set element formulation parameters. Set element strain type using
VFE_STRAINTYPE
with a value of eitherVFE_LARGESTRAIN
to enable large strain orVFE_SMALLSTRAIN
to enable small strains. By defaultVFE_STRAINTYPE
is set toVFE_SMALLSTRAIN
. If a small strain material is used underVFE_LARGESTRAIN
then it is assumed that the material law relates the Green-Lagrange strain tensor with the second second Piola-Kirchhoff stress tensor. Otherwise, the material law relates the deformation gradient with the Cauchy stress.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 defaultVFE_TEMPMATLAVG
is set toSYS_ON
.- Errors
SYS_ERROR_ENUM
is generated if an improper type is specified.SYS_ERROR_VALUE
is generated if an improper iparam is specified.
- Parameters:
p – Pointer to Truss3D object.
type – Type of formulation parameter to set
x=VFE_STRAINTYPE Element strain type =VFE_TEMPMATLAVE Average material temperature flag
iparam – Integer parameter value.
x=VFE_SMALLSTRAIN Small strain =VFE_LARGESTRAIN Large strain
-
void vfe_Truss3DSetParamd(vfe_Truss3D *p, Vint type, Vdouble dparam)
set element formulation parameters
Set element formulation parameters. Use
VFE_MAXPROJANG
to set the maximum angle in degrees between the truss tangent at an element integration point and the truss tangent at a node. By defaultVFE_MAXPROJANG
is set to 90. degrees.Use
VFE_ADDEDMASS
to add non-structural mass/length to the truss element. By defaultVFE_ADDEDMASS
is set to 0..- Errors
SYS_ERROR_ENUM
is generated if an improper type is specified.SYS_ERROR_VALUE
is generated if an improper dparam is specified.
- Parameters:
p – Pointer to Truss3D object.
type – Type of formulation parameter to set
x=VFE_MAXPROJANG Maximum nodal projection angle =VFE_ADDEDMASS Additional mass/length
dparam – Double precision parameter value.
-
void vfe_Truss3DSetTopology(vfe_Truss3D *p, Vint maxi)
set element topology
Specify the topology of a 3D truss element. If maxi is set to 3 then a quadratic element form is assumed. The default topology is maxi = 0.
- Errors
SYS_ERROR_VALUE
is generated if an improper maxi is specified.
- Parameters:
p – Pointer to Truss3D object.
maxi – The number of points along the i direction. If maxi = 0 then the linear Serendipity element form is assumed.
-
void vfe_Truss3DSetPropPtr(vfe_Truss3D *p, Vint type, Vdouble *propptr)
set pointer to element nodal properties
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. Element nodal properties must be defined as an array of Vdouble, as they should be defined for all nodes. If a property pointer is not set the element assumes a default value. for the associated property. By default the area is 1., the temperature is 0. and the reference temperature is 0. If a pre-stress is set it is added to the computed stress resulting from the material model.
- Errors
SYS_ERROR_ENUM
is generated if an improper type is specified.
- Parameters:
p – Pointer to Truss3D object.
type – Type of element property
x=VFE_PROP_AREA Areas =VFE_PROP_TEMPERATURE Temperatures =VFE_PROP_TEMPREF Reference temperatures =VFE_PROP_PRESTRESS Prestresses
propptr – Pointer to start of element nodal properties
-
void vfe_Truss3DStiff(vfe_Truss3D *p, Vdouble x[][3], Vdouble kl[])
linear stiffness matrix
Compute the linear stiffness matrix, kl, given the node coordinates, x. The lower triangle of the stiffness matrix is returned.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
kl – [out] Degree of freedom stiffness matrix
-
void vfe_Truss3DStrsStrn(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble strs[], Vdouble strn[])
stress and strain
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 truss local system. The x’ axis of the system is along the axis of the element. The convention used to generate local coordinate systems is specified using
vfe_Truss3DSetLocalSystem()
. The orientation of the y’ and z’ axes is in some sense arbitrary since there is only non-zero stress along the x’ axis. The stress and strain values are ordered first by the 6 tensor components followed by the the number of element nodes.- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of displacements
strs – [out] Array of nodal stresses
strn – [out] Array of nodal strains
-
void vfe_Truss3DReact(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble r[])
reaction vector
Compute the reaction vector, r, given the node coordinates, x, and the degree of freedom displacement vector, u.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of displacements
r – [out] Degree of freedom reaction vector
-
void vfe_Truss3DReactStiff(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vint kflag, Vdouble r[], Vdouble k[])
reaction vector, 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.
- Parameters:
p – Pointer to Truss3D 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
r – [out] Degree of freedom reaction vector
k – [out] Degree of freedom stiffness matrix
-
void vfe_Truss3DInitHist(vfe_Truss3D *p)
initialize material history
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.
- Errors
SYS_ERROR_NULLOBJECT
is generated if a MatlFun attribute object has not been set.
- Parameters:
p – Pointer to Truss3D object.
-
void vfe_Truss3DNumDof(vfe_Truss3D *p, Vint analysistype, Vint *nedofs)
query number of element degrees of freedom
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_Truss3DDofMap()
to return the location and type of each degree of freedom.- Errors
SYS_ERROR_ENUM
is generated if an improper analysistype is specified.
- Parameters:
p – Pointer to Truss3D object.
analysistype – The type of analysis
x=VFE_ANALYSIS_STRUCTURAL Structural analysis =VFE_ANALYSIS_THERMAL Thermal analysis
nedofs – [out] Number of element degrees of freedom
-
void vfe_Truss3DNumIntPnt(vfe_Truss3D *p, Vint analysistype, Vint *nepnts)
query number of element integration points
Query for number of element integration points nepnts.
- Errors
SYS_ERROR_ENUM
is generated if an improper analysistype is specified.
- Parameters:
p – Pointer to Truss3D object.
analysistype – The type of analysis
x=VFE_ANALYSIS_STRUCTURAL Structural analysis =VFE_ANALYSIS_THERMAL Thermal analysis
nepnts – [out] Number of element integration points
-
void vfe_Truss3DDofMap(vfe_Truss3D *p, Vint analysistype, Vint loc[], Vint tag[])
query element degree of freedom map
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, temperature, etc.
The length of the loc and tag vectors is equal to the number of element degrees of freedom. Use
vfe_Truss3DNumDof()
to return the number of element degrees of freedom.- Errors
SYS_ERROR_ENUM
is generated if an improper analysistype is specified.
- Parameters:
p – Pointer to Truss3D object.
analysistype – The type of analysis
x=VFE_ANALYSIS_STRUCTURAL Structural analysis =VFE_ANALYSIS_THERMAL Thermal analysis
loc – [out] Vector of degree of freedom locations
tag – [out] Vector of degree of freedom types
-
void vfe_Truss3DSetHistPtr(vfe_Truss3D *p, Vdouble *oldhist, Vdouble *newhist)
set pointers to material history
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 usingvfe_Truss3DNumIntPnt()
. By default the pointers to the material history are NULL. If the number of history variables is zero, this function need not be called.- Parameters:
p – Pointer to Truss3D object.
oldhist – Pointer to start of material history at previous step
newhist – Pointer to start of material history at current step
-
void vfe_Truss3DMass(vfe_Truss3D *p, Vdouble x[][3], Vdouble m[])
consistent mass matrix
Compute the consistent mass matrix, m, given the node coordinates, x. The lower triangle of the consistent mass is returned. Use
vfe_Truss3DMassDiag()
to compute a diagonal 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
m – [out] Degree of freedom consistent mass matrix
-
void vfe_Truss3DMassDiag(vfe_Truss3D *p, Vdouble x[][3], Vdouble md[])
diagonal mass matrix
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_Truss3DMass()
to compute a 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
md – [out] Degree of freedom diagonal mass vector
-
void vfe_Truss3DGeomStiff(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble kg[])
geometric stiffness matrix
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.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of displacements
kg – [out] Degree of freedom geometric stiffness matrix
-
void vfe_Truss3DDistLoad(vfe_Truss3D *p, Vdouble x[][3], Vint enttype, Vint no, Vint loadtype, Vdouble q[], Vdouble f[])
distributed load vector
Compute the consistent degree of freedom loads given a distributed load, q on a 3D truss 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. If the loadtype isVFE_DISTLOAD_TANGFORCE
then q contains a scalar force/length at each element node.- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
enttype – Entity type on which load is applied
=SYS_EDGE Element edge
no – Element edge number
loadtype – Distributed load type
x=VFE_DISTLOAD_TRAC Load directed along vector =VFE_DISTLOAD_TANGFORCE Load directed along element edge
q – Vector of distributed load values
f – [out] Degree of freedom vector of consistent loads.
-
void vfe_Truss3DElemLoad(vfe_Truss3D *p, Vdouble x[][3], Vdouble q[][3], Vdouble f[])
body force vector
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.
- Errors
SYS_ERROR_COMPUTE
is generated if a non-positive Jacobian is computed.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
q – Array of node accelerations
f – [out] Degree of freedom vector of consistent loads.
-
void vfe_Truss3DDistHeat(vfe_Truss3D *p, Vdouble x[][3], Vint enttype, Vint no, Vdouble q[], Vdouble f[])
distributed heat loads
Compute the consistent degree of freedom loads given a distributed heat load, q along a 3D truss element edge. The vector q contains values for the heat flux for each node in the element. The distributed loads are in units of heat flux per unit length.
- Errors
SYS_ERROR_ENUM
is generated if an improper enttype 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
enttype – Entity type on which load is applied
=SYS_EDGE Element edge
no – Element edge number
q – Vector of distributed load values
f – [out] Degree of freedom vector of consistent loads.
-
void vfe_Truss3DElemHeat(vfe_Truss3D *p, Vdouble x[][3], Vdouble q[], Vdouble f[])
body heat generation
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.
- Errors
SYS_ERROR_COMPUTE
is generated if a non-positive Jacobian is computed.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
q – Array of node heat fluxes
f – [out] Degree of freedom vector of consistent loads.
-
void vfe_Truss3DPower(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble r[])
thermal power vector
Compute the power vector, r, given the node coordinates, x, and the degree of freedom temperature vector, u.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of temperatures
r – [out] Degree of freedom power vector
-
void vfe_Truss3DPowerCond(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vint kflag, Vdouble r[], Vdouble k[])
thermal power, conductance matrix
Compute the power vector, r, and optionally the conductance matrix, k, given the node coordinates, x, and the degree of freedom temperature vector, u. The lower triangle of the conductance matrix is returned.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of temperatures
kflag – Flag to compute conductance matrix, k
=SYS_OFF Do not compute conductance matrix =SYS_ON Compute and return conductance matrix
r – [out] Degree of freedom power vector
k – [out] Degree of freedom conductance matrix
-
void vfe_Truss3DCond(vfe_Truss3D *p, Vdouble x[][3], Vdouble kl[])
thermal conductance matrix
Compute the linear conductance matrix, kl, given the node coordinates, x. The lower triangle of the conductance matrix is returned.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
kl – [out] Degree of freedom conductance matrix
-
void vfe_Truss3DHFlxTGrd(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble hflx[], Vdouble tgrd[])
heat flux and thermal gradient
Compute nodal heat fluxes and temperature gradients, hflx and tgrd, given the node coordinates, x, and the degree of freedom temperature vector, u. The flux and gradients are computed in the truss local system. The x’ axis of the system is along the axis of the element. The convention used to generate local coordinate systems is specified using
vfe_Truss3DSetLocalSystem()
. The orientation of the y’ and z’ axes is in some sense arbitrary since there is only non-zero flux along the x’ axis.The flux and gradient values are ordered first by the 3 vectoral components followed by the number of element nodes.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of temperatures
hflx – [out] Array of nodal heat fluxes
tgrd – [out] Array of nodal temperature gradients
-
void vfe_Truss3DCap(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble c[])
consistent capacitance matrix
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_Truss3DCapDiag()
to compute a diagonal capacitance matrix. This calculation requires material density and specific heat.- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of temperatures
c – [out] Degree of freedom consistent capacitance matrix
-
void vfe_Truss3DCapDiag(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble cd[])
diagonal capacitance matrix
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_Truss3DCap()
to compute a consistent capacitance matrix. This calculation requires material density and specific heat.- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of temperatures
cd – [out] Degree of freedom diagonal capacitance matrix
-
void vfe_Truss3DDirCos(vfe_Truss3D *p, Vdouble x[][3], Vdouble tm[][3][3])
compute truss local direction cosines
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_Truss3DStrsStrn()
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:The local coordinate system is determined by the local system convention set usingtm[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
vfe_Truss3DSetLocalSystem()
.- Parameters:
p – Pointer to Truss3D object.
x – Array of point locations defining truss axis
tm – [out] Array of direction cosine matrices at the element nodes.
-
void vfe_Truss3DSetLocalSystem(vfe_Truss3D *p, Vint type, Vdouble vec[], Vdouble angle)
set local coordinate system convention
Specify the convention to be used to construct the orientation of the element local x’,y’,z’ coordinate system with respect to the truss axis. This local system is computed at each integration point location on the truss 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_Truss3DStrsStrn()
, 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 truss axis. The orientation of the y’ and z’ axes perpendicular to the truss 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 Element Coordinate Systems
- Errors
SYS_ERROR_ENUM
is generated if an improper type is input.
- Parameters:
p – Pointer to Truss3D object.
type – Local system convention
vec – Orientation vector data
angle – Angle to rotate truss y’,z’ axes about the truss x’ axis in degrees.
-
void vfe_Truss3DStrsAdapt(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble strss[], Vdouble *setot, Vdouble *seerr, Vdouble *hsize, Vdouble *order, Vdouble *d)
stress based error analysis
Compute the element total strain energy, setot, and strain energy error, seerr, given the element displacements, u, and an estimate of the exact nodal stresses, 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.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of displacements
strss – Array of recovered nodal stresses
setot – [out] Total strain energy
seerr – [out] Strain energy error
hsize – [out] Characteristic length
order – [out] Effective polynomial order
d – [out] Dimension
-
void vfe_Truss3DHFlxAdapt(vfe_Truss3D *p, Vdouble x[][3], Vdouble u[], Vdouble hflxs[], Vdouble *hetot, Vdouble *heerr, Vdouble *hsize, Vdouble *order, Vdouble *d)
heat flux based error analysis
Compute the element total heat energy, hetot, and heat energy error, heerr, given the element temperatures, u, and an estimate of the exact nodal heat flux, hflxs. 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.
- 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.
- Parameters:
p – Pointer to Truss3D object.
x – Array of node locations.
u – Degree of freedom vector of temperatures
hflxs – Array of recovered nodal heat flux
hetot – [out] Total heat energy
heerr – [out] Heat energy error
hsize – [out] Characteristic length
order – [out] Effective polynomial order
d – [out] Dimension