21namespace LinearBMatrix
25template <
int NPOINTS,
typename DNDX_Type,
typename BMatrixType>
28 for (
int i = 0; i < NPOINTS; ++i)
30 B(1, NPOINTS + i) = dNdx(1, i);
31 B(3, i) = dNdx(1, i) / std::sqrt(2);
32 B(3, NPOINTS + i) = dNdx(0, i) / std::sqrt(2);
39template <
int DisplacementDim,
47 const bool is_axially_symmetric)
49 static_assert(0 < DisplacementDim && DisplacementDim <= 3,
50 "LinearBMatrix::computeBMatrix: DisplacementDim must be in "
53 BMatrixType B = BMatrixType::Zero(
55 NPOINTS * DisplacementDim);
57 switch (DisplacementDim)
60 for (
int i = 0; i < NPOINTS; ++i)
62 B(2, 2 * NPOINTS + i) = dNdx(2, i);
63 B(4, NPOINTS + i) = dNdx(2, i) / std::sqrt(2);
64 B(4, 2 * NPOINTS + i) = dNdx(1, i) / std::sqrt(2);
65 B(5, i) = dNdx(2, i) / std::sqrt(2);
66 B(5, 2 * NPOINTS + i) = dNdx(0, i) / std::sqrt(2);
72 if (is_axially_symmetric)
74 for (
int i = 0; i < NPOINTS; ++i)
76 B(2, i) = N[i] / radius;
87template <
int DisplacementDim,
int NPOINTS,
typename ShapeFunction,
88 typename BBarMatrixType,
typename ShapeMatricesType,
typename IpData>
90 std::vector<IpData, Eigen::aligned_allocator<IpData>>
const& ip_data,
93 const bool is_axially_symmetric)
95 unsigned const n_integration_points =
98 BBarMatrixType B_bar = BBarMatrixType::Zero(3, ShapeFunction::NPOINTS);
102 for (
unsigned ip = 0; ip < n_integration_points; ip++)
104 auto const& w = ip_data[ip].integration_weight;
108 for (
int i = 0; i < NPOINTS; i++)
110 B_bar.col(i).noalias() +=
112 ShapeMatricesType, IpData>(
113 i, element, integration_method, ip_data, is_axially_symmetric);
116 return B_bar / volume;
121template <
int DisplacementDim,
int NPOINTS,
typename BBarMatrixType,
122 typename BMatrixType>
123void applyBbar(BBarMatrixType
const& B_bar, BMatrixType& B,
124 const bool is_axially_symmetric)
126 if constexpr (DisplacementDim == 3)
128 for (
int i = 0; i < NPOINTS; ++i)
130 auto const B_bar_i = B_bar.col(i);
136 for (
int k = 0; k < 3; k++)
139 auto B_i_k = B.col(k * NPOINTS + i);
141 B_i_k.template segment<3>(0) -=
142 Eigen::Vector3d::Constant((B_i_k[k] - B_bar_i[k]) / 3.0);
150 for (
int i = 0; i < NPOINTS; ++i)
152 auto B_i_0 = B.col(i);
153 auto B_i_1 = B.col(NPOINTS + i);
155 auto const B_bar_i = B_bar.col(i);
157 if (is_axially_symmetric)
159 double const b0_dil_pertubation =
160 (B_i_0[0] - B_bar_i[0] + B_i_0[2] - B_bar_i[2]);
161 B_i_0.template segment<3>(0) -=
162 Eigen::Vector3d::Constant((b0_dil_pertubation) / 3.);
163 B_i_1.template segment<3>(0) -=
164 Eigen::Vector3d::Constant((B_i_1[1] - B_bar_i[1]) / 3.);
169 B_i_0.template segment<2>(0) -=
170 Eigen::Vector2d::Constant((B_i_0[0] - B_bar_i[0]) / 2.);
171 B_i_1.template segment<2>(0) -=
172 Eigen::Vector2d::Constant((B_i_1[1] - B_bar_i[1]) / 2.);
123void applyBbar(BBarMatrixType
const& B_bar, BMatrixType& B, {
…}
178template <
int DisplacementDim,
int NPOINTS,
typename BBarMatrixType,
179 typename BMatrixType,
typename N_Type,
typename DNDX_Type>
181 DNDX_Type
const& dNdx,
183 std::optional<BBarMatrixType>
const& B_dil_bar,
185 const bool is_axially_symmetric)
187 auto B =
computeBMatrix<DisplacementDim, NPOINTS, BMatrixType, N_Type,
188 DNDX_Type>(dNdx, N, radius, is_axially_symmetric);
196 *B_dil_bar, B, is_axially_symmetric);
21namespace LinearBMatrix {
…}
unsigned getNumberOfPoints() const
constexpr int kelvin_vector_dimensions(int const displacement_dim)
Kelvin vector dimensions for given displacement dimension.
Eigen::Vector3d averageGradShapeFunction(int const local_node_id, MeshLib::Element const &element, NumLib::GenericIntegrationMethod const &integration_method, std::vector< IpData, Eigen::aligned_allocator< IpData > > const &ip_data, const bool is_axially_symmetric)
void fillBMatrix2DCartesianPart(DNDX_Type const &dNdx, BMatrixType &B)
void applyBbar(BBarMatrixType const &B_bar, BMatrixType &B, const bool is_axially_symmetric)
BBarMatrixType computeDilatationalBbar(std::vector< IpData, Eigen::aligned_allocator< IpData > > const &ip_data, MeshLib::Element const &element, NumLib::GenericIntegrationMethod const &integration_method, const bool is_axially_symmetric)
BMatrixType computeBMatrixPossiblyWithBbar(DNDX_Type const &dNdx, N_Type const &N, std::optional< BBarMatrixType > const &B_dil_bar, const double radius, const bool is_axially_symmetric)
Fills a B matrix, or a B bar matrix if required.
BMatrixType computeBMatrix(DNDX_Type const &dNdx, N_Type const &N, const double radius, const bool is_axially_symmetric)
Fills a B-matrix based on given shape function dN/dx values.