feat(linear-static-mitc4-shell): step 3 - mitc4-kinematics-constitutive
This commit is contained in:
KOKO\Mimi
@@ -13,6 +13,7 @@ add_executable(
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unit/core/source_identity_test.cpp
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unit/core/status_test.cpp
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unit/elements/euler_beam_3d_test.cpp
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unit/elements/mitc4_shell_test.cpp
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unit/fem/dof_manager_test.cpp
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unit/math/matrix_test.cpp
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unit/math/sparse_matrix_test.cpp
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@@ -0,0 +1,383 @@
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#include "fesa/elements/mitc4_shell.hpp"
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#include <gtest/gtest.h>
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#include <array>
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#include <cmath>
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#include <cstddef>
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#include <cstdint>
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#include <limits>
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#include <string>
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namespace {
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using Vector3 = std::array<double, 3>;
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fesa::Node node(std::int64_t label, Vector3 coordinates) {
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return {
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{"Shell-Instance", label, std::to_string(label)},
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coordinates,
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{"mitc4-shell.inp", static_cast<std::size_t>(label + 1)}};
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}
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std::array<const fesa::Node*, 4> nodePointers(
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const std::array<fesa::Node, 4>& nodes) {
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return {&nodes[0], &nodes[1], &nodes[2], &nodes[3]};
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}
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fesa::ShellSection section(double thickness = 2.0) {
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return {"Section", thickness, 0U, {"mitc4-shell.inp", 20U}};
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}
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fesa::LinearElasticMaterial material(
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double youngsModulus = 120.0,
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double poissonRatio = 0.25) {
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return {
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"Material",
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youngsModulus,
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poissonRatio,
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{"mitc4-shell.inp", 21U}};
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}
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std::array<Vector3, 4> directors(Vector3 director = {0.0, 0.0, 1.0}) {
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return {director, director, director, director};
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}
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double dot(const Vector3& left, const Vector3& right) {
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return left[0] * right[0] + left[1] * right[1] + left[2] * right[2];
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}
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Vector3 cross(const Vector3& left, const Vector3& right) {
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return {
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left[1] * right[2] - left[2] * right[1],
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left[2] * right[0] - left[0] * right[2],
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left[0] * right[1] - left[1] * right[0]};
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}
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double norm(const Vector3& value) {
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return std::sqrt(dot(value, value));
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}
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void expectVectorNear(
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const Vector3& actual,
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const Vector3& expected,
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double tolerance = 1.0e-12) {
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for (std::size_t component = 0U; component < actual.size(); ++component) {
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EXPECT_NEAR(actual[component], expected[component], tolerance);
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}
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}
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void expectOrthonormalRightHanded(const fesa::Mitc4LocalFrame& frame) {
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EXPECT_NEAR(norm(frame.e1), 1.0, 1.0e-12);
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EXPECT_NEAR(norm(frame.e2), 1.0, 1.0e-12);
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EXPECT_NEAR(norm(frame.e3), 1.0, 1.0e-12);
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EXPECT_NEAR(dot(frame.e1, frame.e2), 0.0, 1.0e-12);
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EXPECT_NEAR(dot(frame.e1, frame.e3), 0.0, 1.0e-12);
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EXPECT_NEAR(dot(frame.e2, frame.e3), 0.0, 1.0e-12);
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expectVectorNear(cross(frame.e1, frame.e2), frame.e3);
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}
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void expectMatrixNear(
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const fesa::Matrix& actual,
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const fesa::Matrix& expected,
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double tolerance = 1.0e-12) {
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ASSERT_EQ(actual.rows(), expected.rows());
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ASSERT_EQ(actual.columns(), expected.columns());
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for (std::size_t row = 0U; row < actual.rows(); ++row) {
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for (std::size_t column = 0U; column < actual.columns(); ++column) {
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EXPECT_NEAR(actual(row, column), expected(row, column), tolerance)
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<< "at (" << row << ", " << column << ")";
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}
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}
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}
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void expectSymmetric(const fesa::Matrix& matrix) {
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ASSERT_EQ(matrix.rows(), matrix.columns());
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for (std::size_t row = 0U; row < matrix.rows(); ++row) {
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for (std::size_t column = 0U; column < matrix.columns(); ++column) {
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EXPECT_NEAR(matrix(row, column), matrix(column, row), 1.0e-12);
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}
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}
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}
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bool hasPositiveCholeskyPivots(const fesa::Matrix& matrix) {
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if (matrix.rows() != matrix.columns()) {
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return false;
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}
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fesa::Matrix lower{matrix.rows(), matrix.columns()};
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for (std::size_t row = 0U; row < matrix.rows(); ++row) {
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for (std::size_t column = 0U; column <= row; ++column) {
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double value = matrix(row, column);
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for (std::size_t inner = 0U; inner < column; ++inner) {
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value -= lower(row, inner) * lower(column, inner);
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}
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if (row == column) {
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if (!std::isfinite(value) || !(value > 0.0)) {
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return false;
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}
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lower(row, column) = std::sqrt(value);
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} else {
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lower(row, column) = value / lower(column, column);
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}
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}
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}
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return true;
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}
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std::array<fesa::Node, 4> planarNodes() {
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return {
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node(1, {-1.0, -1.0, 0.0}),
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node(2, {1.0, -1.0, 0.0}),
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node(3, {1.0, 1.0, 0.0}),
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node(4, {-1.0, 1.0, 0.0})};
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}
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} // namespace
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// MITC4-KIN-001
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TEST(Mitc4ShellKinematics, ShapeFunctionsSatisfyNodalAndDerivativeIdentities) {
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constexpr std::array<Vector3, 4> naturalNodes{
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Vector3{-1.0, -1.0, 0.0},
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Vector3{1.0, -1.0, 0.0},
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Vector3{1.0, 1.0, 0.0},
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Vector3{-1.0, 1.0, 0.0}};
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for (std::size_t point = 0U; point < naturalNodes.size(); ++point) {
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const auto shape = fesa::Mitc4Shell::shapeFunctions(
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naturalNodes[point][0], naturalNodes[point][1]);
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for (std::size_t nodeIndex = 0U; nodeIndex < naturalNodes.size(); ++nodeIndex) {
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EXPECT_DOUBLE_EQ(shape.values[nodeIndex], point == nodeIndex ? 1.0 : 0.0);
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}
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}
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const auto shape = fesa::Mitc4Shell::shapeFunctions(0.25, -0.5);
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double valueSum = 0.0;
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double xiDerivativeSum = 0.0;
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double etaDerivativeSum = 0.0;
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for (std::size_t nodeIndex = 0U; nodeIndex < 4U; ++nodeIndex) {
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valueSum += shape.values[nodeIndex];
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xiDerivativeSum += shape.xiDerivatives[nodeIndex];
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etaDerivativeSum += shape.etaDerivatives[nodeIndex];
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}
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EXPECT_DOUBLE_EQ(valueSum, 1.0);
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EXPECT_DOUBLE_EQ(xiDerivativeSum, 0.0);
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EXPECT_DOUBLE_EQ(etaDerivativeSum, 0.0);
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EXPECT_EQ(
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shape.values,
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(std::array<double, 4>{0.28125, 0.46875, 0.15625, 0.09375}));
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}
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// MITC4-KIN-002
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TEST(Mitc4ShellKinematics, BuildsRightHandedFramesAndSeparatePhysicalDrillingMaps) {
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const std::array<fesa::Node, 4> nodes{
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node(1, {0.0, -1.0, -1.0}),
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node(2, {0.0, 1.0, -1.0}),
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node(3, {0.0, 1.0, 1.0}),
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node(4, {0.0, -1.0, 1.0})};
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const auto candidate = fesa::Mitc4Shell::create(
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nodePointers(nodes), directors({1.0, 0.0, 0.0}), section(), material());
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ASSERT_TRUE(candidate.hasValue());
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const auto& shell = candidate.value();
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const auto frame = shell.localFrame(0.0, 0.0);
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expectVectorNear(frame.e1, {0.0, 1.0, 0.0});
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expectVectorNear(frame.e2, {0.0, 0.0, 1.0});
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expectVectorNear(frame.e3, {1.0, 0.0, 0.0});
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expectOrthonormalRightHanded(frame);
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const auto physical = shell.physicalTransformation20();
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const auto drilling = shell.drillingTransformation4();
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ASSERT_EQ(physical.rows(), 20U);
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ASSERT_EQ(physical.columns(), 24U);
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ASSERT_EQ(drilling.rows(), 4U);
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ASSERT_EQ(drilling.columns(), 24U);
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for (std::size_t nodeIndex = 0U; nodeIndex < 4U; ++nodeIndex) {
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const std::size_t physicalOffset = 5U * nodeIndex;
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const std::size_t globalOffset = 6U * nodeIndex;
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for (std::size_t component = 0U; component < 3U; ++component) {
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EXPECT_DOUBLE_EQ(
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physical(physicalOffset + component, globalOffset + component),
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1.0);
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}
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EXPECT_DOUBLE_EQ(physical(physicalOffset + 3U, globalOffset + 4U), 1.0);
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EXPECT_DOUBLE_EQ(physical(physicalOffset + 4U, globalOffset + 5U), 1.0);
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EXPECT_DOUBLE_EQ(drilling(nodeIndex, globalOffset + 3U), 1.0);
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for (std::size_t globalDof = 0U; globalDof < 24U; ++globalDof) {
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if (globalDof != globalOffset + 4U) {
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EXPECT_DOUBLE_EQ(physical(physicalOffset + 3U, globalDof), 0.0);
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}
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if (globalDof != globalOffset + 5U) {
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EXPECT_DOUBLE_EQ(physical(physicalOffset + 4U, globalDof), 0.0);
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}
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if (globalDof != globalOffset + 3U) {
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EXPECT_DOUBLE_EQ(drilling(nodeIndex, globalDof), 0.0);
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}
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}
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}
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auto invalidDirectors = directors({1.0, 0.0, 0.0});
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invalidDirectors[2] = {0.0, 0.0, 0.0};
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EXPECT_FALSE(fesa::Mitc4Shell::create(
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nodePointers(nodes), invalidDirectors, section(), material())
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.hasValue());
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}
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// MITC4-KIN-003
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TEST(Mitc4ShellKinematics, FormsDirectColumnsAndAllCovariantTyingSamples) {
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const auto nodes = planarNodes();
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const auto candidate = fesa::Mitc4Shell::create(
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nodePointers(nodes), directors(), section(), material());
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ASSERT_TRUE(candidate.hasValue());
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const auto& shell = candidate.value();
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const auto direct = shell.directStrainDisplacement20(0.0, 0.0, 0.5);
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ASSERT_EQ(direct.rows(), 5U);
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ASSERT_EQ(direct.columns(), 20U);
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EXPECT_DOUBLE_EQ(direct(0U, 0U), -0.25);
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EXPECT_DOUBLE_EQ(direct(0U, 4U), -0.125);
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EXPECT_DOUBLE_EQ(direct(1U, 1U), -0.25);
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EXPECT_DOUBLE_EQ(direct(1U, 3U), 0.125);
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EXPECT_DOUBLE_EQ(direct(2U, 0U), -0.25);
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EXPECT_DOUBLE_EQ(direct(2U, 1U), -0.25);
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EXPECT_DOUBLE_EQ(direct(2U, 3U), 0.125);
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EXPECT_DOUBLE_EQ(direct(2U, 4U), -0.125);
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EXPECT_DOUBLE_EQ(direct(3U, 2U), -0.25);
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EXPECT_DOUBLE_EQ(direct(3U, 4U), 0.25);
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EXPECT_DOUBLE_EQ(direct(4U, 2U), -0.25);
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EXPECT_DOUBLE_EQ(direct(4U, 3U), -0.25);
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const auto samples = shell.covariantTyingShearSamples20();
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ASSERT_EQ(samples.rows(), 4U);
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ASSERT_EQ(samples.columns(), 20U);
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EXPECT_DOUBLE_EQ(samples(0U, 2U), -0.25);
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EXPECT_DOUBLE_EQ(samples(0U, 4U), 0.25);
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EXPECT_DOUBLE_EQ(samples(0U, 7U), 0.25);
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EXPECT_DOUBLE_EQ(samples(0U, 9U), 0.25);
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EXPECT_DOUBLE_EQ(samples(1U, 12U), 0.25);
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EXPECT_DOUBLE_EQ(samples(1U, 14U), 0.25);
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EXPECT_DOUBLE_EQ(samples(1U, 17U), -0.25);
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EXPECT_DOUBLE_EQ(samples(1U, 19U), 0.25);
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EXPECT_DOUBLE_EQ(samples(2U, 2U), -0.25);
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EXPECT_DOUBLE_EQ(samples(2U, 3U), -0.25);
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EXPECT_DOUBLE_EQ(samples(2U, 17U), 0.25);
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EXPECT_DOUBLE_EQ(samples(2U, 18U), -0.25);
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EXPECT_DOUBLE_EQ(samples(3U, 7U), -0.25);
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EXPECT_DOUBLE_EQ(samples(3U, 8U), -0.25);
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EXPECT_DOUBLE_EQ(samples(3U, 12U), 0.25);
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EXPECT_DOUBLE_EQ(samples(3U, 13U), -0.25);
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const auto weights = fesa::Mitc4Shell::tyingWeights(0.25, -0.5);
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EXPECT_EQ(weights.xiZeta, (std::array<double, 2>{0.75, 0.25}));
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EXPECT_EQ(weights.etaZeta, (std::array<double, 2>{0.375, 0.625}));
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const auto tied = shell.strainDisplacement20(0.0, 0.0, 0.0);
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EXPECT_DOUBLE_EQ(
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tied(3U, 4U),
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2.0 * (0.5 * samples(0U, 4U) + 0.5 * samples(1U, 4U)));
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EXPECT_DOUBLE_EQ(
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tied(4U, 3U),
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2.0 * (0.5 * samples(2U, 3U) + 0.5 * samples(3U, 3U)));
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}
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// MITC4-KIN-004
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TEST(Mitc4ShellConstitutive, BuildsExactPositiveDefiniteSectionMatricesAndRescalesUnits) {
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const auto nodes = planarNodes();
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const auto candidate = fesa::Mitc4Shell::create(
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nodePointers(nodes), directors(), section(), material());
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ASSERT_TRUE(candidate.hasValue());
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const auto& shell = candidate.value();
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const auto cps = shell.planeStressConstitutive();
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const auto c5 = shell.materialConstitutive5();
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const auto a = shell.membraneSectionMatrix();
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const auto d = shell.bendingSectionMatrix();
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const auto as = shell.transverseShearSectionMatrix();
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EXPECT_EQ(cps.rows(), 3U);
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EXPECT_EQ(cps.columns(), 3U);
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EXPECT_EQ(c5.rows(), 5U);
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EXPECT_EQ(c5.columns(), 5U);
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EXPECT_EQ(a.rows(), 3U);
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EXPECT_EQ(d.rows(), 3U);
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EXPECT_EQ(as.rows(), 2U);
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EXPECT_DOUBLE_EQ(cps(0U, 0U), 128.0);
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EXPECT_DOUBLE_EQ(cps(0U, 1U), 32.0);
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EXPECT_DOUBLE_EQ(cps(2U, 2U), 48.0);
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EXPECT_DOUBLE_EQ(c5(3U, 3U), 40.0);
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EXPECT_DOUBLE_EQ(c5(4U, 4U), 40.0);
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EXPECT_DOUBLE_EQ(a(0U, 0U), 256.0);
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EXPECT_NEAR(d(0U, 0U), 256.0 / 3.0, 1.0e-12);
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EXPECT_DOUBLE_EQ(as(0U, 0U), 80.0);
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expectSymmetric(cps);
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expectSymmetric(c5);
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EXPECT_TRUE(hasPositiveCholeskyPivots(cps));
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EXPECT_TRUE(hasPositiveCholeskyPivots(c5));
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EXPECT_TRUE(hasPositiveCholeskyPivots(a));
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EXPECT_TRUE(hasPositiveCholeskyPivots(d));
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EXPECT_TRUE(hasPositiveCholeskyPivots(as));
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constexpr double forceScale = 7.0;
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constexpr double lengthScale = 3.0;
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const auto scaledCandidate = fesa::Mitc4Shell::create(
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nodePointers(nodes),
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directors(),
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section(2.0 * lengthScale),
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material(120.0 * forceScale / (lengthScale * lengthScale), 0.25));
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ASSERT_TRUE(scaledCandidate.hasValue());
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const auto& scaled = scaledCandidate.value();
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fesa::Matrix expectedCps{3U, 3U};
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fesa::Matrix expectedC5{5U, 5U};
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fesa::Matrix expectedA{3U, 3U};
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fesa::Matrix expectedD{3U, 3U};
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fesa::Matrix expectedAs{2U, 2U};
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for (std::size_t row = 0U; row < 3U; ++row) {
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for (std::size_t column = 0U; column < 3U; ++column) {
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expectedCps(row, column) =
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cps(row, column) * forceScale / (lengthScale * lengthScale);
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expectedA(row, column) = a(row, column) * forceScale / lengthScale;
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expectedD(row, column) = d(row, column) * forceScale * lengthScale;
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}
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}
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for (std::size_t row = 0U; row < 2U; ++row) {
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for (std::size_t column = 0U; column < 2U; ++column) {
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expectedAs(row, column) = as(row, column) * forceScale / lengthScale;
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}
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}
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for (std::size_t row = 0U; row < 5U; ++row) {
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for (std::size_t column = 0U; column < 5U; ++column) {
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expectedC5(row, column) =
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c5(row, column) * forceScale / (lengthScale * lengthScale);
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}
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}
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expectMatrixNear(scaled.planeStressConstitutive(), expectedCps);
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expectMatrixNear(scaled.materialConstitutive5(), expectedC5);
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expectMatrixNear(scaled.membraneSectionMatrix(), expectedA);
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expectMatrixNear(scaled.bendingSectionMatrix(), expectedD);
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expectMatrixNear(scaled.transverseShearSectionMatrix(), expectedAs);
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EXPECT_FALSE(fesa::Mitc4Shell::create(
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nodePointers(nodes), directors(), section(0.0), material())
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.hasValue());
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EXPECT_FALSE(fesa::Mitc4Shell::create(
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nodePointers(nodes), directors(), section(), material(0.0, 0.25))
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.hasValue());
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EXPECT_FALSE(fesa::Mitc4Shell::create(
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nodePointers(nodes), directors(), section(), material(120.0, 0.5))
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.hasValue());
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}
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// MITC4-KIN-005
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TEST(Mitc4ShellKinematics, UsesOneFixedTwoByTwoByTwoQuadratureOrder) {
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const auto& points = fesa::Mitc4Shell::volumeQuadrature();
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ASSERT_EQ(points.size(), 8U);
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const double g = 1.0 / std::sqrt(3.0);
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const std::array<Vector3, 8> expected{
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Vector3{-g, -g, -g}, Vector3{-g, -g, g},
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Vector3{g, -g, -g}, Vector3{g, -g, g},
|
||||
Vector3{g, g, -g}, Vector3{g, g, g},
|
||||
Vector3{-g, g, -g}, Vector3{-g, g, g}};
|
||||
for (std::size_t point = 0U; point < points.size(); ++point) {
|
||||
EXPECT_EQ(points[point].naturalCoordinates, expected[point]);
|
||||
EXPECT_DOUBLE_EQ(points[point].weight, 1.0);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user