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| Fem3DElementCorotationalTetrahedron () |
| Constructor. More...
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| Fem3DElementCorotationalTetrahedron (std::array< size_t, 4 > nodeIds) |
| Constructor. More...
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| Fem3DElementCorotationalTetrahedron (std::shared_ptr< FemElementStructs::FemElementParameter > elementData) |
| Constructor for FemElement object factory. More...
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| SURGSIM_CLASSNAME (SurgSim::Physics::Fem3DElementCorotationalTetrahedron) |
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void | initialize (const SurgSim::Math::OdeState &state) override |
| Initialize the FemElement once everything has been set. More...
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| Fem3DElementTetrahedron () |
| Constructor. More...
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| Fem3DElementTetrahedron (std::array< size_t, 4 > nodeIds) |
| Constructor. More...
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| Fem3DElementTetrahedron (std::shared_ptr< FemElementStructs::FemElementParameter > elementData) |
| Constructor for FemElement object factory. More...
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void | initialize (const SurgSim::Math::OdeState &state) override |
| Initialize the FemElement once everything has been set. More...
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double | getVolume (const SurgSim::Math::OdeState &state) const override |
| Gets the element volume based on the input state (in m-3) More...
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SurgSim::Math::Vector | computeCartesianCoordinate (const SurgSim::Math::OdeState &state, const SurgSim::Math::Vector &naturalCoordinate) const override |
| Computes a given natural coordinate in cartesian coordinates. More...
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SurgSim::Math::Vector | computeNaturalCoordinate (const SurgSim::Math::OdeState &state, const SurgSim::Math::Vector &cartesianCoordinate) const override |
| Computes a natural coordinate given a global coordinate. More...
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| FemElement () |
| Constructor. More...
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virtual | ~FemElement () |
| Virtual destructor. More...
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size_t | getNumDofPerNode () const |
| Gets the number of degree of freedom per node. More...
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size_t | getNumNodes () const |
| Gets the number of nodes connected by this element. More...
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size_t | getNodeId (size_t elementNodeId) const |
| Gets the elementNodeId-th node id. More...
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const std::vector< size_t > & | getNodeIds () const |
| Gets the node ids for this element. More...
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void | setYoungModulus (double E) |
| Sets the Young modulus (in N.m-2) More...
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double | getYoungModulus () const |
| Gets the Young modulus (in N.m-2) More...
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void | setPoissonRatio (double nu) |
| Sets the Poisson ratio (unitless) More...
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double | getPoissonRatio () const |
| Gets the Poisson ratio (unitless) More...
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void | setMassDensity (double rho) |
| Sets the mass density (in Kg.m-3) More...
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double | getMassDensity () const |
| Gets the mass density (in Kg.m-3) More...
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double | getMass (const SurgSim::Math::OdeState &state) const |
| Gets the element mass based on the input state (in Kg) More...
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virtual void | addForce (SurgSim::Math::Vector *F, double scale=1.0) const |
| Adds the element force (computed for a given state) to a complete system force vector F (assembly) More...
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virtual void | addMass (SurgSim::Math::SparseMatrix *M, double scale=1.0) const |
| Adds the element mass matrix M (computed for a given state) to a complete system mass matrix M (assembly) More...
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virtual void | addDamping (SurgSim::Math::SparseMatrix *D, double scale=1.0) const |
| Adds the element damping matrix D (= -df/dv) (comuted for a given state) to a complete system damping matrix D (assembly) More...
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virtual void | addStiffness (SurgSim::Math::SparseMatrix *K, double scale=1.0) const |
| Adds the element stiffness matrix K (= -df/dx) (computed for a given state) to a complete system stiffness matrix K (assembly) More...
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virtual void | addFMDK (SurgSim::Math::Vector *F, SurgSim::Math::SparseMatrix *M, SurgSim::Math::SparseMatrix *D, SurgSim::Math::SparseMatrix *K) const |
| Adds the element force vector, mass, stiffness and damping matrices (computed for a given state) into a complete system data structure F, M, D, K (assembly) More...
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virtual void | addMatVec (double alphaM, double alphaD, double alphaK, const SurgSim::Math::Vector &x, SurgSim::Math::Vector *F) const |
| Adds the element matrix-vector contribution F += (alphaM.M + alphaD.D + alphaK.K).x (computed for a given state) into a complete system data structure F (assembly) More...
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bool | isValidCoordinate (const SurgSim::Math::Vector &naturalCoordinate) const |
| Determines whether a given natural coordinate is valid. More...
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template<typename DerivedSub , typename T , int Opt, typename Index > |
void | assembleMatrixBlocks (const DerivedSub &subMatrix, const std::vector< size_t > blockIds, size_t blockSize, Eigen::SparseMatrix< T, Opt, Index > *matrix, bool initialize=true) const |
| Helper method to add a sub-matrix made of squared-blocks into a matrix, for the sake of clarity. More...
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void | updateFMDK (const Math::OdeState &state, int options) |
| Update the FemElement based on the given state. More...
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void | computeRotationMassAndStiffness (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix33d *R, Math::Matrix *Me, Math::Matrix *Ke) const |
| Compute the rotation, mass and stiffness matrices of the element from the given state. More...
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void | doUpdateFMDK (const Math::OdeState &state, int options) override |
| Update the FemElement based on the given state. More...
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void | initializeMembers () |
| Initializes variables needed before Initialize() is called. More...
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void | doUpdateFMDK (const Math::OdeState &state, int options) override |
| Update the FemElement based on the given state. More...
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void | computeShapeFunctions (const SurgSim::Math::OdeState &state, double *volume, std::array< double, 4 > *ai, std::array< double, 4 > *bi, std::array< double, 4 > *ci, std::array< double, 4 > *di) const |
| Computes the tetrahedron shape functions. More...
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void | computeStiffness (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *k) |
| Computes the tetrahedron stiffness matrix. More...
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void | computeMass (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *m) |
| Computes the tetrahedron mass matrix. More...
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void | setNumDofPerNode (size_t numDofPerNode) |
| Sets the number of degrees of freedom per node. More...
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void | initializeFMDK () |
| Initialize f, M, D, K variables. More...
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virtual void | doInitializeFMDK () |
| Function to be overridden by the derived classes to initialize the f, M, D, K variables. More...
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SurgSim::Math::Matrix44d | m_Vinverse |
| The constant inverse matrix of the undeformed tetrahedron homogeneous 4 points coordinates. More...
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Eigen::Matrix< double, 12, 12 > | m_MLinear |
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Eigen::Matrix< double, 12, 12 > | m_KLinear |
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SurgSim::Math::Matrix33d | m_R |
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double | m_restVolume |
| Shape functions: Tetrahedron rest volume. More...
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std::array< double, 4 > | m_ai |
| Shape functions coefficients Ni(x,y,z) = 1/6V ( ai + x.bi + y.ci + z.di ) More...
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std::array< double, 4 > | m_bi |
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std::array< double, 4 > | m_ci |
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std::array< double, 4 > | m_di |
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Eigen::Matrix< double, 12, 1 > | m_x0 |
| The tetrahedon rest state. More...
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Eigen::Matrix< double, 6, 6 > | m_Em |
| Elasticity material matrix (contains the elastic properties of the material) More...
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Eigen::Matrix< double, 6, 12 > | m_strain |
| Strain matrix. More...
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Eigen::Matrix< double, 6, 12 > | m_stress |
| Stress matrix. More...
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size_t | m_numDofPerNode |
| Number of degree of freedom per node for this element. More...
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std::vector< size_t > | m_nodeIds |
| Node ids connected by this element. More...
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double | m_rho |
| Mass density (in Kg.m-3) More...
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double | m_E |
| Young modulus (in N.m-2) More...
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double | m_nu |
| Poisson ratio (unitless) More...
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SurgSim::Math::Vector | m_f |
| The force vector. More...
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SurgSim::Math::Matrix | m_M |
| The mass matrix. More...
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SurgSim::Math::Matrix | m_D |
| The damping matrix. More...
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bool | m_useDamping |
| Flag to specify of the damping is used. More...
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SurgSim::Math::Matrix | m_K |
| The stiffness matrix. More...
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Fem Element 3D co-rotational based on a tetrahedron volume discretization.
- Note
- This class derives from the linear version of the FEM 3D element tetrahedron, adding a rigid frame
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attached to the tetrahedron element to follow its rigid motion. Therefore it computes deformation in the
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local coordinate system of the tetrahedron. This class is based on 2 papers:
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"Interactive Virtual Materials", Muller, Gross. Graphics Interface 2004
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"Exact Corotational Linear FEM Stiffness Matrix", Jernej Barbic. Technical Report USC 2012.
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Only the force and stiffness calculation are different, involving some changes as well in addMatVec
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(it uses the updated stiffness matrix).
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The update method takes care of extracting the rigid motion of the element.
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This element is updating its stiffness matrix at each new time step, which means that it cannot
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be used with any OdeSolverLinearXXX, it needs an ode solver that recomputes the data at each iteration.