Description
Simple beam element with two nodes and ANCF gradient-deficient formulation.
For this 'basic' implementation, constant section and constant material are assumed along the beam coordinate. Torsional stiffness is impossible because of the formulation.
Based on the formulation in
"Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation", J. Gerstmayr, A. Shabana, Nonlinear Dynamics (2006) 45: 109-130, DOI: 10.1007/s11071-006-1856-1
#include <ChElementCableANCF.h>
Public Types | |
using | ShapeVector = ChMatrixNM< double, 1, 4 > |
Public Member Functions | |
virtual int | GetNnodes () override |
Get the number of nodes used by this element. | |
virtual int | GetNdofs () override |
Get the number of coordinates in the field used by the referenced nodes. | |
virtual int | GetNdofs_active () override |
Get the number of active coordinates in the field used by the referenced nodes. | |
virtual int | GetNodeNdofs (int n) override |
Get the number of coordinates from the n-th node used by this element. | |
virtual int | GetNodeNdofs_active (int n) override |
Get the number of coordinates from the n-th node used by this element. | |
virtual std::shared_ptr< ChNodeFEAbase > | GetNodeN (int n) override |
Access the nth node. | |
virtual void | SetNodes (std::shared_ptr< ChNodeFEAxyzD > nodeA, std::shared_ptr< ChNodeFEAxyzD > nodeB) |
void | SetSection (std::shared_ptr< ChBeamSectionCable > section) |
Set the section & material of beam element. More... | |
std::shared_ptr< ChBeamSectionCable > | GetSection () |
Get the section & material of the element. | |
std::shared_ptr< ChNodeFEAxyzD > | GetNodeA () |
Get the first node (beginning). | |
std::shared_ptr< ChNodeFEAxyzD > | GetNodeB () |
Get the second node (ending). | |
double | GetCurrLength () |
Get element length. | |
virtual void | ShapeFunctions (ShapeVector &N, double xi) |
Fills the N shape function matrix with the values of shape functions at abscissa 'xi'. More... | |
virtual void | ShapeFunctionsDerivatives (ShapeVector &Nd, double xi) |
Fills the N shape function derivative matrix with the values of shape function derivatives at abscissa 'xi'. More... | |
virtual void | ShapeFunctionsDerivatives2 (ShapeVector &Ndd, double xi) |
Fills the N shape function derivative matrix with the values of shape function 2nd derivatives at abscissa 'xi'. More... | |
virtual void | Update () override |
Update, called at least at each time step. More... | |
virtual void | GetStateBlock (ChVectorDynamic<> &mD) override |
Fills the D vector with the current field values at the nodes of the element, with proper ordering. More... | |
virtual void | ComputeInternalJacobians (double Kfactor, double Rfactor) |
Computes the stiffness matrix of the element: K = integral( .... More... | |
virtual void | ComputeMassMatrix () |
Computes the mass matrix of the element. More... | |
virtual void | ComputeMmatrixGlobal (ChMatrixRef M) override |
Sets M as the global mass matrix. | |
virtual void | ComputeKRMmatricesGlobal (ChMatrixRef H, double Kfactor, double Rfactor=0, double Mfactor=0) override |
Sets H as the global stiffness matrix K, scaled by Kfactor. More... | |
virtual void | ComputeInternalForces (ChVectorDynamic<> &Fi) override |
Computes the internal forces and set values in the Fi vector. More... | |
virtual void | ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector<> &G_acc) override |
Compute the generalized force vector due to gravity using the efficient ANCF specific method. | |
virtual void | EvaluateSectionDisplacement (const double eta, ChVector<> &u_displ, ChVector<> &u_rotaz) override |
Gets the xyz displacement of a point on the beam line and the rotation RxRyRz of section plane, at abscissa 'eta'. More... | |
virtual void | EvaluateSectionFrame (const double eta, ChVector<> &point, ChQuaternion<> &rot) override |
Gets the absolute xyz position of a point on the beam line and the absolute rotation of section plane, at abscissa 'eta'. More... | |
virtual void | EvaluateSectionForceTorque (const double eta, ChVector<> &Fforce, ChVector<> &Mtorque) override |
Gets the force (traction x, shear y, shear z) and the torque (torsion on x, bending on y, on bending on z) at a section along the beam line, at abscissa 'eta'. More... | |
virtual void | EvaluateSectionStrain (const double eta, ChVector<> &StrainV) override |
Gets the axial and bending strain of the ANCF element torque (torsion on x, bending on y, on bending on z) at a section along the beam line, at abscissa 'eta'. More... | |
void | SetAlphaDamp (double a) |
Set structural damping. | |
virtual int | LoadableGet_ndof_x () override |
Gets the number of DOFs affected by this element (position part). | |
virtual int | LoadableGet_ndof_w () override |
Gets the number of DOFs affected by this element (speed part). | |
virtual void | LoadableGetStateBlock_x (int block_offset, ChState &mD) override |
Gets all the DOFs packed in a single vector (position part). | |
virtual void | LoadableGetStateBlock_w (int block_offset, ChStateDelta &mD) override |
Gets all the DOFs packed in a single vector (speed part) | |
virtual void | LoadableStateIncrement (const unsigned int off_x, ChState &x_new, const ChState &x, const unsigned int off_v, const ChStateDelta &Dv) override |
Increment all DOFs using a delta. | |
virtual int | Get_field_ncoords () override |
Number of coordinates in the interpolated field. | |
virtual int | GetSubBlocks () override |
Get the number of DOFs sub-blocks. | |
virtual unsigned int | GetSubBlockOffset (int nblock) override |
Get the offset of the specified sub-block of DOFs in global vector. | |
virtual unsigned int | GetSubBlockSize (int nblock) override |
Get the size of the specified sub-block of DOFs in global vector. | |
virtual bool | IsSubBlockActive (int nblock) const override |
Check if the specified sub-block of DOFs is active. | |
virtual void | LoadableGetVariables (std::vector< ChVariables * > &mvars) override |
Get the pointers to the contained ChVariables, appending to the mvars vector. | |
virtual void | ComputeNF (const double U, ChVectorDynamic<> &Qi, double &detJ, const ChVectorDynamic<> &F, ChVectorDynamic<> *state_x, ChVectorDynamic<> *state_w) override |
Evaluate N'*F , where N is some type of shape function evaluated at U,V coordinates of the surface, each ranging in -1..+1. More... | |
virtual void | ComputeNF (const double U, const double V, const double W, ChVectorDynamic<> &Qi, double &detJ, const ChVectorDynamic<> &F, ChVectorDynamic<> *state_x, ChVectorDynamic<> *state_w) override |
Evaluate N'*F , where N is some type of shape function evaluated at U,V,W coordinates of the volume, each ranging in -1..+1. More... | |
virtual double | GetDensity () override |
Return the material density for this element. | |
Public Member Functions inherited from chrono::fea::ChElementBeam | |
double | GetMass () |
The full mass of the beam, (with const. section, density, etc.) | |
double | GetRestLength () |
The rest length of the bar. | |
void | SetRestLength (double ml) |
Set the rest length of the bar (usually this should be automatically done when SetupInitial is called on beams element, given the current state, but one might need to override this, ex for precompressed beams etc). | |
Public Member Functions inherited from chrono::fea::ChElementGeneric | |
ChKblockGeneric & | Kstiffness () |
Access the proxy to stiffness, for sparse solver. | |
virtual void | EleIntLoadResidual_F (ChVectorDynamic<> &R, const double c) override |
Add the internal forces (pasted at global nodes offsets) into a global vector R, multiplied by a scaling factor c, as R += forces * c This default implementation is SLIGHTLY INEFFICIENT. | |
virtual void | EleIntLoadResidual_Mv (ChVectorDynamic<> &R, const ChVectorDynamic<> &w, const double c) override |
Add the product of element mass M by a vector w (pasted at global nodes offsets) into a global vector R, multiplied by a scaling factor c, as R += M * w * c This default implementation is VERY INEFFICIENT. | |
virtual void | EleIntLoadResidual_F_gravity (ChVectorDynamic<> &R, const ChVector<> &G_acc, const double c) override |
Add the contribution of gravity loads, multiplied by a scaling factor c, as: R += M * g * c This default implementation is VERY INEFFICIENT. More... | |
virtual void | InjectKRMmatrices (ChSystemDescriptor &descriptor) override |
Tell to a system descriptor that there are item(s) of type ChKblock in this object (for further passing it to a solver) | |
virtual void | KRMmatricesLoad (double Kfactor, double Rfactor, double Mfactor) override |
Add the current stiffness K and damping R and mass M matrices in encapsulated ChKblock item(s), if any. More... | |
virtual void | VariablesFbLoadInternalForces (double factor=1.) override |
Add the internal forces, expressed as nodal forces, into the encapsulated ChVariables. | |
virtual void | VariablesFbIncrementMq () override |
Add M*q (internal masses multiplied current 'qb'). | |
Public Member Functions inherited from chrono::fea::ChElementBase | |
virtual void | ComputeNodalMass () |
Compute element's nodal masses. | |
virtual void | EleDoIntegration () |
This is optionally implemented if there is some internal state that requires integration. | |
Public Member Functions inherited from chrono::ChLoadableUVW | |
virtual bool | IsTetrahedronIntegrationNeeded () |
If true, use quadrature over u,v,w in [0..1] range as tetrahedron volumetric coords (with z=1-u-v-w) otherwise use default quadrature over u,v,w in [-1..+1] as box isoparametric coords. | |
virtual bool | IsTrianglePrismIntegrationNeeded () |
If true, use quadrature over u,v in [0..1] range as triangle natural coords (with z=1-u-v), and use linear quadrature over w in [-1..+1], otherwise use default quadrature over u,v,w in [-1..+1] as box isoparametric coords. | |
Public Attributes | |
bool | m_use_damping |
Boolean indicating whether internal damping is added. | |
double | m_alpha |
Scaling factor for internal damping. | |
Additional Inherited Members | |
Protected Attributes inherited from chrono::fea::ChElementANCF | |
int | m_element_dof |
actual number of degrees of freedom for the element | |
bool | m_full_dof |
true if all node variables are active (not fixed) | |
ChArray< int > | m_mapping_dof |
indices of active DOFs (set only is some are fixed) | |
Protected Attributes inherited from chrono::fea::ChElementBeam | |
double | mass |
double | length |
Protected Attributes inherited from chrono::fea::ChElementGeneric | |
ChKblockGeneric | Kmatr |
Member Function Documentation
◆ ComputeInternalForces()
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overridevirtual |
Computes the internal forces and set values in the Fi vector.
(e.g. the actual position of nodes is not in relaxed reference position).
Implements chrono::fea::ChElementBase.
◆ ComputeInternalJacobians()
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virtual |
Computes the stiffness matrix of the element: K = integral( ....
), Note: in this 'basic' implementation, constant section and constant material are assumed.
◆ ComputeKRMmatricesGlobal()
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overridevirtual |
Sets H as the global stiffness matrix K, scaled by Kfactor.
Optionally, also superimposes global damping matrix R, scaled by Rfactor, and global mass matrix M multiplied by Mfactor.
Implements chrono::fea::ChElementBase.
◆ ComputeMassMatrix()
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virtual |
Computes the mass matrix of the element.
Note: in this 'basic' implementation, constant section and constant material are assumed.
◆ ComputeNF() [1/2]
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overridevirtual |
Evaluate N'*F , where N is some type of shape function evaluated at U,V coordinates of the surface, each ranging in -1..+1.
F is a load, N'*F is the resulting generalized load. Returns also det[J] with J=[dx/du,..], that might be useful in gauss quadrature.
- Parameters
-
U parametric coordinate in line Qi Return result of Q = N'*F here detJ Return det[J] here F Input F vector, size is =n. field coords. state_x if != 0, update state (pos. part) to this, then evaluate Q state_w if != 0, update state (speed part) to this, then evaluate Q
Implements chrono::ChLoadableU.
◆ ComputeNF() [2/2]
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overridevirtual |
Evaluate N'*F , where N is some type of shape function evaluated at U,V,W coordinates of the volume, each ranging in -1..+1.
F is a load, N'*F is the resulting generalized load. Returns also det[J] with J=[dx/du,..], that might be useful in gauss quadrature.
- Parameters
-
U parametric coordinate in volume V parametric coordinate in volume W parametric coordinate in volume Qi Return result of N'*F here, maybe with offset block_offset detJ Return det[J] here F Input F vector, size is = n.field coords. state_x if != 0, update state (pos. part) to this, then evaluate Q state_w if != 0, update state (speed part) to this, then evaluate Q
Implements chrono::ChLoadableUVW.
◆ EvaluateSectionDisplacement()
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overridevirtual |
Gets the xyz displacement of a point on the beam line and the rotation RxRyRz of section plane, at abscissa 'eta'.
Note, eta=-1 at node1, eta=+1 at node2. Note that 'displ' is the displ.state of 2 nodes, e.g. get it as GetStateBlock() Results are not corotated.
Implements chrono::fea::ChElementBeam.
◆ EvaluateSectionForceTorque()
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overridevirtual |
Gets the force (traction x, shear y, shear z) and the torque (torsion on x, bending on y, on bending on z) at a section along the beam line, at abscissa 'eta'.
Note, eta=-1 at node1, eta=+1 at node2. Note that 'displ' is the displ.state of 2 nodes, ex. get it as GetStateBlock(). Results are not corotated, and are expressed in the reference system of beam. This is not mandatory for the element to work, but it can be useful for plotting, showing results, etc.
Implements chrono::fea::ChElementBeam.
◆ EvaluateSectionFrame()
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overridevirtual |
Gets the absolute xyz position of a point on the beam line and the absolute rotation of section plane, at abscissa 'eta'.
Note, eta=-1 at node1, eta=+1 at node2. Note that 'displ' is the displ.state of 2 nodes, e.g. get it as GetStateBlock() Results are corotated (expressed in world reference)
Implements chrono::fea::ChElementBeam.
◆ EvaluateSectionStrain()
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overridevirtual |
Gets the axial and bending strain of the ANCF element torque (torsion on x, bending on y, on bending on z) at a section along the beam line, at abscissa 'eta'.
Note, eta=-1 at node1, eta=+1 at node2. Note that 'displ' is the displ.state of 2 nodes, ex. get it as GetStateBlock(). Results are not corotated, and are expressed in the reference system of beam. This is not mandatory for the element to work, but it can be useful for plotting, showing results, etc.
Implements chrono::fea::ChElementBeam.
◆ GetStateBlock()
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overridevirtual |
Fills the D vector with the current field values at the nodes of the element, with proper ordering.
If the D vector has not the size of this->GetNdofs(), it will be resized. {x_a y_a z_a Dx_a Dx_a Dx_a x_b y_b z_b Dx_b Dy_b Dz_b}
Implements chrono::fea::ChElementBase.
◆ SetSection()
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inline |
Set the section & material of beam element.
It is a shared property, so it can be shared between other beams.
◆ ShapeFunctions()
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virtual |
Fills the N shape function matrix with the values of shape functions at abscissa 'xi'.
Note, xi=0 at node1, xi=+1 at node2. N should be a 3x12 parse matrix, N = [s1*eye(3) s2*eye(3) s3*eye(3) s4*eye(3)], but is stored here in a compressed form: only the s1 s2 s3 s4 values in a 4x1 column vector.
◆ ShapeFunctionsDerivatives()
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virtual |
Fills the N shape function derivative matrix with the values of shape function derivatives at abscissa 'xi'.
Note, xi=0 at node1, xi=+1 at node2. In a compressed form, only four values are stored in a 4x1 column vector.
◆ ShapeFunctionsDerivatives2()
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virtual |
Fills the N shape function derivative matrix with the values of shape function 2nd derivatives at abscissa 'xi'.
Note, xi=0 at node1, xi=+1 at node2. In a compressed form, only four values are stored in a 4x1 column vector.
◆ Update()
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overridevirtual |
Update, called at least at each time step.
If the element has to keep updated some auxiliary data, such as the rotation matrices for corotational approach, this should be implemented in this function.
Reimplemented from chrono::fea::ChElementBase.
The documentation for this class was generated from the following files:
- /builds/uwsbel/chrono/src/chrono/fea/ChElementCableANCF.h
- /builds/uwsbel/chrono/src/chrono/fea/ChElementCableANCF.cpp