Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
#include "config.h"
#include <dune/foamgrid/foamgrid.hh>
#include <dune/geometry/type.hh>
#include <dune/geometry/quadraturerules.hh>
#include <dune/functions/functionspacebases/interpolate.hh>
#include <dune/functions/functionspacebases/lagrangebasis.hh>
#include <dune/functions/functionspacebases/powerbasis.hh>
#include <dune/gfe/cosseratvtkwriter.hh>
#include <dune/gfe/nonplanarcosseratshellenergy.hh>
#include <dune/gfe/rigidbodymotion.hh>
#include "multiindex.hh"
#include "valuefactory.hh"
using namespace Dune;
static const int dim = 2;
static const int dimworld = 3;
using GridType = FoamGrid<dim,dimworld>;
using TargetSpace = RigidBodyMotion<double,dimworld>;
//////////////////////////////////////////////////////////
// Make a test grid consisting of a single triangle
//////////////////////////////////////////////////////////
template <class GridType>
std::unique_ptr<GridType> makeSingleElementGrid()
{
constexpr auto triangle = Dune::GeometryTypes::triangle;
GridFactory<GridType> factory;
FieldVector<double,dimworld> vertex0{0,0,0};
FieldVector<double,dimworld> vertex1{0,1,0};
FieldVector<double,dimworld> vertex2{1,0,0};
factory.insertVertex(vertex0);
factory.insertVertex(vertex1);
factory.insertVertex(vertex2);
factory.insertElement(triangle, {0,1,2});
return std::unique_ptr<GridType>(factory.createGrid());
}
//////////////////////////////////////////////////////////////////////////////////////
// Test energy computation for the same grid with different refinement levels
//////////////////////////////////////////////////////////////////////////////////////
TargetSpace getConfiguration(const FieldVector<double, dimworld>& point) {
FieldVector<double, dimworld> displacementAtPoint(0);
FieldVector<double,4> rotationVectorAtPoint(0);
if (point[0] == 0 and point[1] == 0 and point[2] == 0) {
//0 0 0
displacementAtPoint = {0, 0, 0};
rotationVectorAtPoint = {0, 0, 0, 1};
} else if (point[0] == 1 and point[1] == 0 and point[2] == 0) {
//1 0 0
displacementAtPoint = {0, 0, 1};
rotationVectorAtPoint = {0, 0, 0, 1};
} else if (point[0] == 0 and point[1] == 1 and point[2] == 0) {
//0 1 0
displacementAtPoint = {0, 0, 1};
rotationVectorAtPoint = {0, 0, 0, 1};
} else if (point[0] == 0.5 and point[1] == 0 and point[2] == 0) {
//0.5 0 0
displacementAtPoint = {0, 0, 0.5};
rotationVectorAtPoint = {0, 0, 0, 1};
} else if (point[0] == 0 and point[1] == 0.5 and point[2] == 0) {
//0 0.5 0
displacementAtPoint = {0, 0, 0.5};
rotationVectorAtPoint = {0, 0, 0, 1};
} else if (point[0] == 0.5 and point[1] == 0.5 and point[2] == 0) {
//0.5 0.5 0
displacementAtPoint = {0, 0, 1};
rotationVectorAtPoint = {0, 0, 0, 1};
}
TargetSpace configuration;
for (int i = 0; i < dimworld; i++)
configuration.r[i] = point[i] + displacementAtPoint[i];
Rotation<double,dimworld> rotation(rotationVectorAtPoint);
FieldMatrix<double,dimworld,dimworld> rotationMatrix(0);
rotation.matrix(rotationMatrix);
configuration.q.set(rotationMatrix);
return configuration;
}
double calculateEnergy(const int numLevels)
{
ParameterTree materialParameters;
materialParameters["thickness"] = "0.1";
materialParameters["mu"] = "3.8462e+05";
materialParameters["lambda"] = "2.7149e+05";
materialParameters["mu_c"] = "0";
materialParameters["L_c"] = "1e-3";
materialParameters["q"] = "2.5";
materialParameters["kappa"] = "0.1";
materialParameters["b1"] = "1";
materialParameters["b2"] = "1";
materialParameters["b3"] = "1";
const std::unique_ptr<GridType> grid = makeSingleElementGrid<GridType>();
grid->globalRefine(numLevels-1);
GridType::LeafGridView gridView = grid->leafGridView();
using FEBasis = Dune::Functions::LagrangeBasis<typename GridType::LeafGridView,1>;
FEBasis feBasis(gridView);
using namespace Dune::Functions::BasisFactory;
using namespace Dune::TypeTree::Indices;
auto deformationPowerBasis = makeBasis(
gridView,
power<dimworld>(
lagrange<1>()
));
BlockVector<FieldVector<double,3> > helperVector;
Dune::Functions::interpolate(deformationPowerBasis, helperVector, [](FieldVector<double,dimworld> x){
auto out = x;
out[2] += x[0];
return out;
});
//Dune::Functions::interpolate(deformationPowerBasis, helperVector, [](FieldVector<double,dimworld> x){ return x; });
auto stressFreeConfiguration = Dune::Functions::makeDiscreteGlobalBasisFunction<FieldVector<double,dimworld>>(deformationPowerBasis, helperVector);
NonplanarCosseratShellEnergy<FEBasis, 3, double, decltype(stressFreeConfiguration)> localCosseratEnergyPlanar(materialParameters,
&stressFreeConfiguration,
nullptr,
nullptr,
nullptr);
BlockVector<FieldVector<double,3> > id;
Dune::Functions::interpolate(deformationPowerBasis, id, [](FieldVector<double,dimworld> x){ return x; });
BlockVector<TargetSpace> sol(feBasis.size());
TupleVector<std::vector<RealTuple<double,3> >,
std::vector<Rotation<double,3> > > solTuple;
solTuple[_0].resize(feBasis.size());
solTuple[_1].resize(feBasis.size());
for (int i = 0; i < feBasis.size(); i++) {
sol[i] = getConfiguration(id[i]);
solTuple[_0][i] = sol[i].r;
solTuple[_1][i] = sol[i].q;
}
CosseratVTKWriter<GridType>::write<FEBasis>(feBasis, solTuple, "configuration_l" + std::to_string(numLevels));
double energy = 0;
// A view on the FE basis on a single element
auto localView = feBasis.localView();
// Loop over all elements
for (const auto& element : elements(feBasis.gridView(), Dune::Partitions::interior))
{
localView.bind(element);
// Number of degrees of freedom on this element
size_t nDofs = localView.tree().size();
std::vector<TargetSpace> localSolution(nDofs);
for (size_t i=0; i<nDofs; i++)
localSolution[i] = sol[localView.index(i)[0]];
energy += localCosseratEnergyPlanar.energy(localView, localSolution);
}
return energy;
}
int main(int argc, char** argv)
{
MPIHelper::instance(argc, argv);
double energyFine = calculateEnergy(2);
double energyCoarse = calculateEnergy(1);
std::cout << "energyFine: " << energyFine << std::endl;
std::cout << "energyCoarse: " << energyCoarse << std::endl;
assert(std::abs(energyFine - energyCoarse) < 1e-3);
}