From 9477ca64efa1bdfd3527c50f57890237106e19b8 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Wed, 15 Nov 2006 10:10:27 +0000
Subject: [PATCH] code review. Added support for nontrivial reference strain.
Fixed one bug in the matrix assembly
[[Imported from SVN: r1040]]
---
src/rodassembler.cc | 438 ++++++++++++++++++++------------------------
src/rodassembler.hh | 72 ++++++--
2 files changed, 248 insertions(+), 262 deletions(-)
diff --git a/src/rodassembler.cc b/src/rodassembler.cc
index dd29d9d7..c627d6b8 100644
--- a/src/rodassembler.cc
+++ b/src/rodassembler.cc
@@ -45,7 +45,7 @@ getNeighborsPerVertex(MatrixIndexSet& nb) const
template <class GridType>
void Dune::RodAssembler<GridType>::
assembleMatrix(const std::vector<Configuration>& sol,
- BCRSMatrix<MatrixBlock>& matrix)
+ BCRSMatrix<MatrixBlock>& matrix) const
{
const typename GridType::Traits::LevelIndexSet& indexSet = grid_->levelIndexSet(grid_->maxLevel());
@@ -65,7 +65,7 @@ assembleMatrix(const std::vector<Configuration>& sol,
= Dune::LagrangeShapeFunctions<double, double, gridDim>::general(it->geometry().type(), elementOrder);
const int numOfBaseFct = baseSet.size();
- mat.resize(numOfBaseFct, numOfBaseFct);
+ mat.setSize(numOfBaseFct, numOfBaseFct);
// Extract local solution
std::vector<Configuration> localSolution(numOfBaseFct);
@@ -74,7 +74,7 @@ assembleMatrix(const std::vector<Configuration>& sol,
localSolution[i] = sol[indexSet.template subIndex<gridDim>(*it,i)];
// setup matrix
- getLocalMatrix( *it, localSolution, numOfBaseFct, mat);
+ getLocalMatrix( it, localSolution, sol, numOfBaseFct, mat);
// Add element matrix to global stiffness matrix
for(int i=0; i<numOfBaseFct; i++) {
@@ -153,8 +153,9 @@ getFirstDerivativesOfDirectors(const Quaternion<double>& q,
template <class GridType>
template <class MatrixType>
void Dune::RodAssembler<GridType>::
-getLocalMatrix( EntityType &entity,
+getLocalMatrix( EntityPointer &entity,
const std::vector<Configuration>& localSolution,
+ const std::vector<Configuration>& globalSolution,
const int matSize, MatrixType& localMat) const
{
const typename GridType::Traits::LevelIndexSet& indexSet = grid_->levelIndexSet(grid_->maxLevel());
@@ -167,11 +168,11 @@ getLocalMatrix( EntityType &entity,
localMat[i][j] = 0;
const LagrangeShapeFunctionSet<double, double, gridDim> & baseSet
- = Dune::LagrangeShapeFunctions<double, double, gridDim>::general(entity.geometry().type(), elementOrder);
+ = Dune::LagrangeShapeFunctions<double, double, gridDim>::general(entity->geometry().type(), elementOrder);
// Get quadrature rule
int polOrd = 2;
- const QuadratureRule<double, gridDim>& quad = QuadratureRules<double, gridDim>::rule(entity.geometry().type(), polOrd);
+ const QuadratureRule<double, gridDim>& quad = QuadratureRules<double, gridDim>::rule(entity->geometry().type(), polOrd);
/* Loop over all integration points */
for (int ip=0; ip<quad.size(); ip++) {
@@ -180,8 +181,8 @@ getLocalMatrix( EntityType &entity,
const FieldVector<double,gridDim>& quadPos = quad[ip].position();
// calc Jacobian inverse before integration element is evaluated
- const FieldMatrix<double,gridDim,gridDim>& inv = entity.geometry().jacobianInverseTransposed(quadPos);
- const double integrationElement = entity.geometry().integrationElement(quadPos);
+ const FieldMatrix<double,gridDim,gridDim>& inv = entity->geometry().jacobianInverseTransposed(quadPos);
+ const double integrationElement = entity->geometry().integrationElement(quadPos);
/* Compute the weight of the current integration point */
double weight = quad[ip].weight() * integrationElement;
@@ -190,16 +191,16 @@ getLocalMatrix( EntityType &entity,
/* compute gradients of the shape functions */
/**********************************************/
FieldVector<double,gridDim> shapeGrad[ndof];
+ FieldVector<double,gridDim> tmp;
for (int dof=0; dof<ndof; dof++) {
for (int i=0; i<gridDim; i++)
- shapeGrad[dof][i] = baseSet[dof].evaluateDerivative(0,i,quadPos);
+ tmp[i] = baseSet[dof].evaluateDerivative(0,i,quadPos);
// multiply with jacobian inverse
- FieldVector<double,gridDim> tmp(0);
- inv.umv(shapeGrad[dof], tmp);
- shapeGrad[dof] = tmp;
+ shapeGrad[dof] = 0;
+ inv.umv(tmp,shapeGrad[dof]);
}
@@ -318,9 +319,15 @@ getLocalMatrix( EntityType &entity,
hatq_s[3] = localSolution[0].q[3]*shapeGrad[0] + localSolution[1].q[3]*shapeGrad[1];
// The Darboux vector
- FieldVector<double,3> u = darboux(hatq, hatq_s);
+ //FieldVector<double,3> u = darboux(hatq, hatq_s);
FieldVector<double,3> darbouxCan = darbouxCanonical(hatq, hatq_s);
+ // The current strain
+ FieldVector<double,blocksize> strain = getStrain(globalSolution, entity, quadPos);
+
+ // The reference strain
+ FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration_, entity, quadPos);
+
// Contains \partial u (canonical) / \partial v^i_j at v = 0
FieldVector<double,3> duCan_dvij[2][3];
FieldVector<double,3> duLocal_dvij[2][3];
@@ -368,56 +375,46 @@ getLocalMatrix( EntityType &entity,
for (int l=0; l<3; l++) {
- // ////////////////////////////////////////////
- // The translational part
- // ////////////////////////////////////////////
-
- // \partial W^2 \partial r^i_j \partial r^k_l
- localMat[i][k][j][l] += weight
- * ( A1 * shapeGrad[i] * hatq.director(0)[j] * shapeGrad[k] * hatq.director(0)[l]
- + A2 * shapeGrad[i] * hatq.director(1)[j] * shapeGrad[k] * hatq.director(1)[l]
- + A3 * shapeGrad[i] * hatq.director(2)[j] * shapeGrad[k] * hatq.director(2)[l]);
-
- // \partial W^2 \partial v^i_j \partial r^k_l
- localMat[i][k][j][l+3] += weight
- * (A1 * shapeGrad[k]*hatq.director(0)[l]*(r_s*dd_dvij[0][i][j])
- + A1 * (r_s*hatq.director(0)) * shapeGrad[k] * dd_dvij[0][i][j][l]
- + A2 * shapeGrad[k]*hatq.director(1)[l]*(r_s*dd_dvij[1][i][j])
- + A2 * (r_s*hatq.director(1)) * shapeGrad[k] * dd_dvij[1][i][j][l]
- + A3 * shapeGrad[k]*hatq.director(2)[l]*(r_s*dd_dvij[2][i][j])
- + A3 * (r_s*hatq.director(2)-1) * shapeGrad[k] * dd_dvij[2][i][j][l]);
-
- // This is programmed stupidly. To ensure the equality it is enough to make
- // the following assignment once and not for each quadrature point
- localMat[k][i][l+3][j] = localMat[i][k][j][l+3];
-
- // \partial W^2 \partial v^i_j \partial v^k_l
- localMat[i][k][j+3][l+3] += weight
- * (A1 * (r_s * dd_dvij[0][k][l]) * (r_s * dd_dvij[0][i][j])
- + A1 * (r_s * hatq.director(0)) * (r_s * dd_dvij_dvkl[0][i][j][k][l])
- + A2 * (r_s * dd_dvij[1][k][l]) * (r_s * dd_dvij[1][i][j])
- + A2 * (r_s * hatq.director(1)) * (r_s * dd_dvij_dvkl[1][i][j][k][l])
- + A3 * (r_s * dd_dvij[2][k][l]) * (r_s * dd_dvij[2][i][j])
- + A3 * (r_s * hatq.director(2)) * (r_s * dd_dvij_dvkl[2][i][j][k][l]));
-
- // ////////////////////////////////////////////
- // The rotational part
- // ////////////////////////////////////////////
- // Stupid: I want those as an array
- double K[3] = {K1, K2, K3};
-
- // \partial W^2 \partial v^i_j \partial v^k_l
- // All other derivatives are zero
for (int m=0; m<3; m++) {
+ // ////////////////////////////////////////////
+ // The translational part
+ // ////////////////////////////////////////////
+
+ // \partial W^2 \partial r^i_j \partial r^k_l
+ localMat[i][k][j][l] += weight
+ * A_[m] * shapeGrad[i] * hatq.director(m)[j] * shapeGrad[k] * hatq.director(m)[l];
+
+ // \partial W^2 \partial v^i_j \partial r^k_l
+ localMat[i][k][j][l+3] += weight
+ * ( A_[m] * shapeGrad[k]*hatq.director(m)[l]*(r_s*dd_dvij[m][i][j])
+ + A_[m] * (strain[m] - referenceStrain[m]) * shapeGrad[k] * dd_dvij[m][i][j][l]);
+
+ // This is programmed stupidly. To ensure the symmetry it is enough to make
+ // the following assignment once and not for each quadrature point
+ localMat[k][i][l+3][j] = localMat[i][k][j][l+3];
+
+ // \partial W^2 \partial v^i_j \partial v^k_l
+ localMat[i][k][j+3][l+3] += weight
+ * ( A_[m] * (r_s * dd_dvij[m][k][l]) * (r_s * dd_dvij[m][i][j])
+ + A_[m] * (strain[m] - referenceStrain[m]) * (r_s * dd_dvij_dvkl[m][i][j][k][l]) );
+
+ // ////////////////////////////////////////////
+ // The rotational part
+ // ////////////////////////////////////////////
+
+ // \partial W^2 \partial v^i_j \partial v^k_l
+ // All other derivatives are zero
+
double sum = duLocal_dvij[k][l][m] * (duCan_dvij[i][j] * hatq.director(m) + darbouxCan*dd_dvij[m][i][j]);
- sum += u[m] * (duCan_dvij_dvkl[i][j][k][l] * hatq.director(m)
+ sum += strain[m+3] * (duCan_dvij_dvkl[i][j][k][l] * hatq.director(m)
+ duCan_dvij[i][j] * dd_dvij[m][k][l]
+ duCan_dvij[k][l] * dd_dvij[m][i][j]
+ darbouxCan * dd_dvij_dvkl[m][i][j][k][l]);
- localMat[i][k][j+3][l+3] += weight *K[m] * sum;
+#warning Reference strain missing here!
+ localMat[i][k][j+3][l+3] += weight *K_[m] * sum;
}
@@ -517,8 +514,11 @@ assembleGradient(const std::vector<Configuration>& sol,
hatq_s[2] = localSolution[0].q[2]*shapeGrad[0] + localSolution[1].q[2]*shapeGrad[1];
hatq_s[3] = localSolution[0].q[3]*shapeGrad[0] + localSolution[1].q[3]*shapeGrad[1];
- // The Darboux vector
- FieldVector<double,3> u = darboux(hatq, hatq_s);
+ // The current strain
+ FieldVector<double,blocksize> strain = getStrain(sol, it, quadPos);
+
+ // The reference strain
+ FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration_, it, quadPos);
// Contains \partial q / \partial v^i_j at v = 0
FixedArray<FixedArray<Quaternion<double>,3>,2> dq_dvij;
@@ -557,9 +557,9 @@ assembleGradient(const std::vector<Configuration>& sol,
for (int j=0; j<3; j++) {
grad[globalDof][j] += weight
- * ((A1 * (r_s*hatq.director(0)) * shapeGrad[i] * hatq.director(0)[j])
- + (A2 * (r_s*hatq.director(1)) * shapeGrad[i] * hatq.director(1)[j])
- + (A3 * (r_s*hatq.director(2) - 1) * shapeGrad[i] * hatq.director(2)[j]));
+ * (( A_[0] * (strain[0] - referenceStrain[0]) * shapeGrad[i] * hatq.director(0)[j])
+ + (A_[1] * (strain[1] - referenceStrain[1]) * shapeGrad[i] * hatq.director(1)[j])
+ + (A_[2] * (strain[2] - referenceStrain[2]) * shapeGrad[i] * hatq.director(2)[j]));
}
@@ -567,25 +567,16 @@ assembleGradient(const std::vector<Configuration>& sol,
for (int j=0; j<3; j++) {
grad[globalDof][3+j] += weight
- * ((A1 * (r_s*hatq.director(0)) * (r_s*dd_dvij[0][i][j]))
- + (A2 * (r_s*hatq.director(1)) * (r_s*dd_dvij[1][i][j]))
- + (A3 * (r_s*hatq.director(2) - 1) * (r_s*dd_dvij[2][i][j])));
-
-// if (globalDof==1) {
-// printf("directorder:\n");
-// std::cout << dd_dvij[0][i][j] << std::endl << dd_dvij[1][i][j] << std::endl << dd_dvij[2][i][j] << std::endl;
-// printf("i %d j %d ", i, j);
-// std::cout << grad[globalDof] << std::endl;
-// }
+ * ( (A_[0] * (strain[0] - referenceStrain[0]) * (r_s*dd_dvij[0][i][j]))
+ + (A_[1] * (strain[1] - referenceStrain[1]) * (r_s*dd_dvij[1][i][j]))
+ + (A_[2] * (strain[2] - referenceStrain[2]) * (r_s*dd_dvij[2][i][j])));
+
}
// /////////////////////////////////////////////
// The rotational part
// /////////////////////////////////////////////
- // Stupid: I want those as an array
- double K[3] = {K1, K2, K3};
-
// \partial \bar{W}_v / \partial v^i_j
for (int j=0; j<3; j++) {
@@ -602,7 +593,8 @@ assembleGradient(const std::vector<Configuration>& sol,
double addend1 = du_dvij * hatq.director(m);
double addend2 = darbouxCan * dd_dvij[m][i][j];
- grad[globalDof][3+j] += weight*K[m]*u[m] * (addend1 + addend2);
+#warning Reference strain missing here!
+ grad[globalDof][3+j] += weight*K_[m]*strain[m+3] * (addend1 + addend2);
}
@@ -650,64 +642,25 @@ computeEnergy(const std::vector<Configuration>& sol) const
// formula, even though it should be second order. This prevents shear-locking
// ///////////////////////////////////////////////////////////////////////////////
const int shearingPolOrd = 2;
- const QuadratureRule<double, gridDim>& shearingQuad = QuadratureRules<double, gridDim>::rule(it->geometry().type(), shearingPolOrd);
+ const QuadratureRule<double, gridDim>& shearingQuad
+ = QuadratureRules<double, gridDim>::rule(it->geometry().type(), shearingPolOrd);
for (int pt=0; pt<shearingQuad.size(); pt++) {
// Local position of the quadrature point
const FieldVector<double,gridDim>& quadPos = shearingQuad[pt].position();
- const FieldMatrix<double,1,1>& inv = it->geometry().jacobianInverseTransposed(quadPos);
const double integrationElement = it->geometry().integrationElement(quadPos);
double weight = shearingQuad[pt].weight() * integrationElement;
- // ///////////////////////////////////////
- // Compute deformation gradient
- // ///////////////////////////////////////
- std::vector<FieldVector<double,gridDim> > shapeGrad(numOfBaseFct);
-
- for (int dof=0; dof<numOfBaseFct; dof++) {
-
- for (int i=0; i<gridDim; i++)
- shapeGrad[dof][i] = baseSet[dof].evaluateDerivative(0,i,quadPos);
-
- // multiply with jacobian inverse
- FieldVector<double,gridDim> tmp(0);
- inv.umv(shapeGrad[dof], tmp);
- shapeGrad[dof] = tmp;
-
- }
-
- // Get the value of the shape functions
- double shapeFunction[2];
- for(int i=0; i<2; i++)
- shapeFunction[i] = baseSet[i].evaluateFunction(0,quadPos);
-
- // //////////////////////////////////
- // Interpolate
- // //////////////////////////////////
-
- FieldVector<double,3> r_s;
- r_s[0] = localSolution[0].r[0]*shapeGrad[0][0] + localSolution[1].r[0]*shapeGrad[1][0];
- r_s[1] = localSolution[0].r[1]*shapeGrad[0][0] + localSolution[1].r[1]*shapeGrad[1][0];
- r_s[2] = localSolution[0].r[2]*shapeGrad[0][0] + localSolution[1].r[2]*shapeGrad[1][0];
-
- // Interpolate the rotation at the quadrature point
- Quaternion<double> q = Quaternion<double>::interpolate(localSolution[0].q, localSolution[1].q,quadPos[0]);
-
- // /////////////////////////////////////////////
- // Sum it all up
- // Part I: the shearing and stretching energy
- // /////////////////////////////////////////////
+ FieldVector<double,blocksize> strain = getStrain(sol, it, quadPos);
- //std::cout << "tangent : " << r_s << std::endl;
- FieldVector<double,3> v;
- v[0] = r_s * q.director(0); // shear strain
- v[1] = r_s * q.director(1); // shear strain
- v[2] = r_s * q.director(2); // stretching strain
+ // The reference strain
+ FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration_, it, quadPos);
- energy += weight * 0.5 * (A1*v[0]*v[0] + A2*v[1]*v[1] + A3*(v[2]-1)*(v[2]-1));
+ for (int i=0; i<3; i++)
+ energy += weight * 0.5 * A_[i] * (strain[i] - referenceStrain[i]) * (strain[i] * referenceStrain[i]);
}
@@ -720,64 +673,16 @@ computeEnergy(const std::vector<Configuration>& sol) const
// Local position of the quadrature point
const FieldVector<double,gridDim>& quadPos = bendingQuad[pt].position();
- const FieldMatrix<double,1,1>& inv = it->geometry().jacobianInverseTransposed(quadPos);
-
double weight = bendingQuad[pt].weight() * it->geometry().integrationElement(quadPos);
- // ///////////////////////////////////////
- // Compute deformation gradient
- // ///////////////////////////////////////
- std::vector<FieldVector<double,gridDim> > shapeGrad(numOfBaseFct);
-
- for (int dof=0; dof<numOfBaseFct; dof++) {
-
- for (int i=0; i<gridDim; i++)
- shapeGrad[dof][i] = baseSet[dof].evaluateDerivative(0,i,quadPos);
-
- // multiply with jacobian inverse
- FieldVector<double,gridDim> tmp(0);
- inv.umv(shapeGrad[dof], tmp);
- shapeGrad[dof] = tmp;
-
- }
+ FieldVector<double,blocksize> strain = getStrain(sol, it, quadPos);
- // Get the value of the shape functions
- double shapeFunction[2];
- for(int i=0; i<2; i++)
- shapeFunction[i] = baseSet[i].evaluateFunction(0,quadPos);
+ // The reference strain
+ FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration_, it, quadPos);
- // //////////////////////////////////
- // Interpolate
- // //////////////////////////////////
-
- // Get the rotation at the quadrature point by interpolating in $H$ and normalizing
- Quaternion<double> q;
- q[0] = localSolution[0].q[0]*shapeFunction[0] + localSolution[1].q[0]*shapeFunction[1];
- q[1] = localSolution[0].q[1]*shapeFunction[0] + localSolution[1].q[1]*shapeFunction[1];
- q[2] = localSolution[0].q[2]*shapeFunction[0] + localSolution[1].q[2]*shapeFunction[1];
- q[3] = localSolution[0].q[3]*shapeFunction[0] + localSolution[1].q[3]*shapeFunction[1];
-
- // The interpolated quaternion is not a unit quaternion anymore. We simply normalize
- q.normalize();
-
- assert((q-Quaternion<double>::interpolate(localSolution[0].q, localSolution[1].q,quadPos[0])).infinity_norm() < 1e-6);
-
- // Get the derivative of the rotation at the quadrature point by interpolating in $H$
- Quaternion<double> q_s;
- q_s[0] = localSolution[0].q[0]*shapeGrad[0][0] + localSolution[1].q[0]*shapeGrad[1][0];
- q_s[1] = localSolution[0].q[1]*shapeGrad[0][0] + localSolution[1].q[1]*shapeGrad[1][0];
- q_s[2] = localSolution[0].q[2]*shapeGrad[0][0] + localSolution[1].q[2]*shapeGrad[1][0];
- q_s[3] = localSolution[0].q[3]*shapeGrad[0][0] + localSolution[1].q[3]*shapeGrad[1][0];
-
- // /////////////////////////////////////////////
- // Sum it all up
- // /////////////////////////////////////////////
// Part II: the bending and twisting energy
-
- FieldVector<double,3> u = darboux(q, q_s); // The Darboux vector
- //std::cout << "Darboux vector : " << u << std::endl;
-
- energy += weight * 0.5 * (K1*u[0]*u[0] + K2*u[1]*u[1] + K3*u[2]*u[2]);
+ for (int i=0; i<3; i++)
+ energy += weight * 0.5 * K_[i] * (strain[i+3] - referenceStrain[i+3]) * (strain[i+3] * referenceStrain[i+3]);
}
@@ -828,79 +733,13 @@ getStrain(const std::vector<Configuration>& sol,
// Local position of the quadrature point
const FieldVector<double,gridDim>& quadPos = quad[pt].position();
-
- const FieldMatrix<double,1,1>& inv = it->geometry().jacobianInverseTransposed(quadPos);
- const double integrationElement = it->geometry().integrationElement(quadPos);
-
- double weight = quad[pt].weight() * integrationElement;
-
- // ///////////////////////////////////////
- // Compute deformation gradient
- // ///////////////////////////////////////
- std::vector<FieldVector<double,gridDim> > shapeGrad(numOfBaseFct);
-
- for (int dof=0; dof<numOfBaseFct; dof++) {
-
- for (int i=0; i<gridDim; i++)
- shapeGrad[dof][i] = baseSet[dof].evaluateDerivative(0,i,quadPos);
- //std::cout << "Gradient " << dof << ": " << shape_grads[dof] << std::endl;
-
- // multiply with jacobian inverse
- FieldVector<double,gridDim> tmp(0);
- inv.umv(shapeGrad[dof], tmp);
- shapeGrad[dof] = tmp;
- //std::cout << "Gradient " << dof << ": " << shape_grads[dof] << std::endl;
-
- }
- // Get the value of the shape functions
- double shapeFunction[2];
- for(int i=0; i<2; i++)
- shapeFunction[i] = baseSet[i].evaluateFunction(0,quadPos);
+ double weight = quad[pt].weight() * it->geometry().integrationElement(quadPos);
- // //////////////////////////////////
- // Interpolate
- // //////////////////////////////////
-
- FieldVector<double,3> r_s;
- r_s[0] = localSolution[0].r[0]*shapeGrad[0][0] + localSolution[1].r[0]*shapeGrad[1][0];
- r_s[1] = localSolution[0].r[1]*shapeGrad[0][0] + localSolution[1].r[1]*shapeGrad[1][0];
- r_s[2] = localSolution[0].r[2]*shapeGrad[0][0] + localSolution[1].r[2]*shapeGrad[1][0];
-
- // Interpolate the rotation at the quadrature point
- Quaternion<double> q = Quaternion<double>::interpolate(localSolution[0].q, localSolution[1].q,quadPos[0]);
-
- // Get the derivative of the rotation at the quadrature point by interpolating in $H$
- Quaternion<double> q_s;
- q_s[0] = localSolution[0].q[0]*shapeGrad[0][0] + localSolution[1].q[0]*shapeGrad[1][0];
- q_s[1] = localSolution[0].q[1]*shapeGrad[0][0] + localSolution[1].q[1]*shapeGrad[1][0];
- q_s[2] = localSolution[0].q[2]*shapeGrad[0][0] + localSolution[1].q[2]*shapeGrad[1][0];
- q_s[3] = localSolution[0].q[3]*shapeGrad[0][0] + localSolution[1].q[3]*shapeGrad[1][0];
-
- // /////////////////////////////////////////////
- // Sum it all up
- // /////////////////////////////////////////////
-
- // Part I: the shearing and stretching strain
- //std::cout << "tangent : " << r_s << std::endl;
- FieldVector<double,3> v;
- v[0] = r_s * q.director(0); // shear strain
- v[1] = r_s * q.director(1); // shear strain
- v[2] = r_s * q.director(2); // stretching strain
-
- //std::cout << "strain : " << v << std::endl;
-
- // Part II: the Darboux vector
+ FieldVector<double,blocksize> localStrain = getStrain(sol, it, quad[pt].position());
- FieldVector<double,3> u = darboux(q, q_s);
-
// Sum it all up
- strain[elementIdx][0] += weight * v[0];
- strain[elementIdx][1] += weight * v[1];
- strain[elementIdx][2] += weight * v[2];
- strain[elementIdx][3] += weight * u[0];
- strain[elementIdx][4] += weight * u[1];
- strain[elementIdx][5] += weight * u[2];
+ strain.axpy(weight, localStrain);
}
@@ -915,3 +754,118 @@ getStrain(const std::vector<Configuration>& sol,
}
}
+
+template <class GridType>
+Dune::FieldVector<double, 6> Dune::RodAssembler<GridType>::getStrain(const std::vector<Configuration>& sol,
+ const EntityPointer& element,
+ double pos) const
+{
+ if (!element->isLeaf())
+ DUNE_THROW(Dune::NotImplemented, "Only for leaf elements");
+
+ const typename GridType::Traits::LeafIndexSet& indexSet = grid_->leafIndexSet();
+
+ if (sol.size()!=indexSet.size(gridDim))
+ DUNE_THROW(Exception, "Configuration vector doesn't match the grid!");
+
+ // Strain defined on each element
+ FieldVector<double, blocksize> strain(0);
+
+ // Extract local solution on this element
+ const LagrangeShapeFunctionSet<double, double, gridDim> & baseSet
+ = Dune::LagrangeShapeFunctions<double, double, gridDim>::general(element->geometry().type(), elementOrder);
+ int numOfBaseFct = baseSet.size();
+
+ Configuration localSolution[numOfBaseFct];
+
+ for (int i=0; i<numOfBaseFct; i++)
+ localSolution[i] = sol[indexSet.template subIndex<gridDim>(*element,i)];
+
+ const FieldMatrix<double,1,1>& inv = element->geometry().jacobianInverseTransposed(pos);
+
+ // ///////////////////////////////////////
+ // Compute deformation gradient
+ // ///////////////////////////////////////
+ FieldVector<double,gridDim> shapeGrad[numOfBaseFct];
+
+ for (int dof=0; dof<numOfBaseFct; dof++) {
+
+ for (int i=0; i<gridDim; i++)
+ shapeGrad[dof][i] = baseSet[dof].evaluateDerivative(0,i,pos);
+ //std::cout << "Gradient " << dof << ": " << shape_grads[dof] << std::endl;
+
+ // multiply with jacobian inverse
+ FieldVector<double,gridDim> tmp(0);
+ inv.umv(shapeGrad[dof], tmp);
+ shapeGrad[dof] = tmp;
+ //std::cout << "Gradient " << dof << ": " << shape_grads[dof] << std::endl;
+
+ }
+
+ // //////////////////////////////////
+ // Interpolate
+ // //////////////////////////////////
+
+ FieldVector<double,3> r_s;
+ r_s[0] = localSolution[0].r[0]*shapeGrad[0][0] + localSolution[1].r[0]*shapeGrad[1][0];
+ r_s[1] = localSolution[0].r[1]*shapeGrad[0][0] + localSolution[1].r[1]*shapeGrad[1][0];
+ r_s[2] = localSolution[0].r[2]*shapeGrad[0][0] + localSolution[1].r[2]*shapeGrad[1][0];
+
+ // Interpolate the rotation at the quadrature point
+ Quaternion<double> q = Quaternion<double>::interpolate(localSolution[0].q, localSolution[1].q, pos);
+
+ // Get the derivative of the rotation at the quadrature point by interpolating in $H$
+ Quaternion<double> q_s;
+ q_s[0] = localSolution[0].q[0]*shapeGrad[0][0] + localSolution[1].q[0]*shapeGrad[1][0];
+ q_s[1] = localSolution[0].q[1]*shapeGrad[0][0] + localSolution[1].q[1]*shapeGrad[1][0];
+ q_s[2] = localSolution[0].q[2]*shapeGrad[0][0] + localSolution[1].q[2]*shapeGrad[1][0];
+ q_s[3] = localSolution[0].q[3]*shapeGrad[0][0] + localSolution[1].q[3]*shapeGrad[1][0];
+
+ // /////////////////////////////////////////////
+ // Sum it all up
+ // /////////////////////////////////////////////
+
+ // Part I: the shearing and stretching strain
+ //std::cout << "tangent : " << r_s << std::endl;
+ strain[0] = r_s * q.director(0); // shear strain
+ strain[1] = r_s * q.director(1); // shear strain
+ strain[2] = r_s * q.director(2); // stretching strain
+
+ //std::cout << "strain : " << v << std::endl;
+
+ // Part II: the Darboux vector
+
+ FieldVector<double,3> u = darboux(q, q_s);
+
+ strain[3] = u[0];
+ strain[4] = u[1];
+ strain[5] = u[2];
+
+ return strain;
+}
+
+template <class GridType>
+Dune::FieldVector<double,3> Dune::RodAssembler<GridType>::
+getResultantForce(const std::vector<Configuration>& sol) const
+{
+ const typename GridType::Traits::LeafIndexSet& indexSet = grid_->leafIndexSet();
+
+ if (sol.size()!=indexSet.size(gridDim))
+ DUNE_THROW(Exception, "Solution vector doesn't match the grid!");
+
+ // HARDWIRED: the leftmost point on the grid
+ EntityPointer leftElement = grid_->template leafbegin<0>();
+ assert(leftElement->ileafbegin().boundary());
+
+ double pos = 0;
+
+ FieldVector<double, blocksize> strain = getStrain(sol, leftElement, pos);
+ FieldVector<double, blocksize> referenceStrain = getStrain(referenceConfiguration_, leftElement, pos);
+
+ FieldVector<double,3> localStress;
+ for (int i=0; i<3; i++)
+ localStress[i] = (strain[i] - referenceStrain[i]) * A_[i];
+
+ #warning Transformation fehlt
+ return localStress;
+}
diff --git a/src/rodassembler.hh b/src/rodassembler.hh
index 00bc6a27..bafe00bb 100644
--- a/src/rodassembler.hh
+++ b/src/rodassembler.hh
@@ -16,6 +16,7 @@ namespace Dune
class RodAssembler {
typedef typename GridType::template Codim<0>::Entity EntityType;
+ typedef typename GridType::template Codim<0>::EntityPointer EntityPointer;
typedef typename GridType::template Codim<0>::LevelIterator ElementIterator;
typedef typename GridType::template Codim<0>::LeafIterator ElementLeafIterator;
@@ -33,8 +34,11 @@ namespace Dune
const GridType* grid_;
/** \brief Material constants */
- double K1, K2, K3;
- double A1, A2, A3;
+ double K_[3];
+ double A_[3];
+
+ /** \brief The stress-free configuration */
+ std::vector<Configuration> referenceConfiguration_;
public:
@@ -42,20 +46,37 @@ namespace Dune
RodAssembler(const GridType &grid) :
grid_(&grid)
{
- K1 = K2 = K3 = 1;
- A1 = A2 = A3 = 1;
+ // Set dummy material parameters
+ K_[0] = K_[1] = K_[2] = 1;
+ A_[0] = A_[1] = A_[2] = 1;
+
+ referenceConfiguration_.resize(grid.size(gridDim));
+
+ typename GridType::template Codim<gridDim>::LeafIterator it = grid.template leafbegin<gridDim>();
+ typename GridType::template Codim<gridDim>::LeafIterator endIt = grid.template leafend<gridDim>();
+
+ for (; it != endIt; ++it) {
+
+ int idx = grid.leafIndexSet().index(*it);
+
+ referenceConfiguration_[idx].r[0] = 0;
+ referenceConfiguration_[idx].r[1] = 0;
+ referenceConfiguration_[idx].r[2] = it->geometry()[0][0];
+ referenceConfiguration_[idx].q = Quaternion<double>::identity();
+ }
+
}
~RodAssembler() {}
void setParameters(double k1, double k2, double k3,
double a1, double a2, double a3) {
- K1 = k1;
- K2 = k2;
- K3 = k3;
- A1 = a1;
- A2 = a2;
- A3 = a3;
+ K_[0] = k1;
+ K_[1] = k2;
+ K_[2] = k3;
+ A_[0] = a1;
+ A_[1] = a2;
+ A_[2] = a3;
}
/** \brief Set shape constants and material parameters
@@ -69,22 +90,22 @@ namespace Dune
// shear modulus
double G = E/(2+2*nu);
- K1 = E * J1;
- K2 = E * J2;
- K3 = G * (J1 + J2);
+ K_[0] = E * J1;
+ K_[1] = E * J2;
+ K_[2] = G * (J1 + J2);
- A1 = G * A;
- A2 = G * A;
- A3 = E * A;
+ A_[0] = G * A;
+ A_[1] = G * A;
+ A_[2] = E * A;
- printf("%g %g %g %g %g %g\n", K1, K2, K3, A1, A2, A3);
+ printf("%g %g %g %g %g %g\n", K_[0], K_[1], K_[2], A_[0], A_[1], A_[2]);
//exit(0);
}
/** \brief Assemble the tangent stiffness matrix and the right hand side
*/
void assembleMatrix(const std::vector<Configuration>& sol,
- BCRSMatrix<MatrixBlock>& matrix);
+ BCRSMatrix<MatrixBlock>& matrix) const;
void assembleGradient(const std::vector<Configuration>& sol,
BlockVector<FieldVector<double, blocksize> >& grad) const;
@@ -96,13 +117,24 @@ namespace Dune
void getStrain(const std::vector<Configuration>& sol,
BlockVector<FieldVector<double, blocksize> >& strain) const;
+
+ /** \brief Get the strain at a particular point of the grid */
+ FieldVector<double, 6> getStrain(const std::vector<Configuration>& sol,
+ const EntityPointer& element,
+ double pos) const;
+
+ /** \brief Return resultant force in canonical coordinates */
+ FieldVector<double,3> getResultantForce(const std::vector<Configuration>& sol) const;
+
protected:
- /** \brief Compute the element tangent stiffness matrix */
+ /** \brief Compute the element tangent stiffness matrix
+ \todo Handing over both the local and the global solution is pretty stupid. */
template <class MatrixType>
- void getLocalMatrix( EntityType &entity,
+ void getLocalMatrix( EntityPointer &entity,
const std::vector<Configuration>& localSolution,
+ const std::vector<Configuration>& globalSolution,
const int matSize, MatrixType& mat) const;
template <class T>
--
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