feat(linear-static-mitc4-shell): step 2 - shell-director-geometry
This commit is contained in:
KOKO\Mimi
@@ -21,6 +21,7 @@ add_library(
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math/sparse_matrix.cpp
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math/vector.cpp
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model/domain.cpp
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model/shell_geometry.cpp
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results/result_recovery.cpp
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solvers/linear/mkl_pardiso_solver.cpp
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)
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@@ -1,5 +1,7 @@
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#include "fesa/io/abaqus/domain_mapper.hpp"
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#include "fesa/model/shell_geometry.hpp"
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#include <algorithm>
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#include <array>
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#include <cerrno>
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@@ -1768,6 +1770,21 @@ private:
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if (failure_) {
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return;
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}
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if (!definition_.shellElements.empty()) {
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auto geometry = preprocessShellGeometry(
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definition_.nodes,
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definition_.shellElements,
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definition_.shellSections);
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if (!geometry.hasValue()) {
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const auto& status = geometry.status();
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failure_ = MappingFailure{
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status.failureCategory().value_or(FailureCategory::model),
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status.diagnostics().front()};
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return;
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}
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definition_.shellNodeInitialFrames =
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std::move(geometry.value().nodalFrames);
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}
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expandAssemblySets();
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if (failure_) {
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return;
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@@ -0,0 +1,491 @@
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#include "fesa/model/shell_geometry.hpp"
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#include <algorithm>
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#include <cmath>
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#include <tuple>
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#include <utility>
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namespace fesa {
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namespace {
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using Vector3 = std::array<double, 3>;
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constexpr std::array<double, 4> kXiSigns{-1.0, 1.0, 1.0, -1.0};
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constexpr std::array<double, 4> kEtaSigns{-1.0, -1.0, 1.0, 1.0};
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struct ShapeData {
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std::array<double, 4> values;
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std::array<double, 4> xiDerivatives;
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std::array<double, 4> etaDerivatives;
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};
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struct ElementWork {
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std::array<Vector3, 4> coordinates;
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Vector3 normal;
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double areaWeight;
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};
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Vector3 add(const Vector3& left, const Vector3& right) {
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return {
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left[0] + right[0], left[1] + right[1], left[2] + right[2]};
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}
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Vector3 subtract(const Vector3& left, const Vector3& right) {
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return {
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left[0] - right[0], left[1] - right[1], left[2] - right[2]};
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}
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Vector3 scale(double factor, const Vector3& value) {
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return {factor * value[0], factor * value[1], factor * value[2]};
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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::hypot(value[0], value[1], value[2]);
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}
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bool isFinite(const Vector3& value) {
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return std::all_of(value.begin(), value.end(), [](double component) {
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return std::isfinite(component);
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});
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}
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ShapeData shapeData(double xi, double eta) {
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ShapeData data{};
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for (std::size_t node = 0U; node < 4U; ++node) {
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data.values[node] =
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0.25 * (1.0 + kXiSigns[node] * xi) *
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(1.0 + kEtaSigns[node] * eta);
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data.xiDerivatives[node] =
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0.25 * kXiSigns[node] * (1.0 + kEtaSigns[node] * eta);
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data.etaDerivatives[node] =
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0.25 * kEtaSigns[node] * (1.0 + kXiSigns[node] * xi);
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}
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return data;
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}
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Vector3 weightedSum(
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const std::array<double, 4>& weights,
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const std::array<Vector3, 4>& values) {
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Vector3 result{};
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for (std::size_t node = 0U; node < values.size(); ++node) {
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result = add(result, scale(weights[node], values[node]));
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}
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return result;
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}
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Vector3 derivativeSum(
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const std::array<double, 4>& derivatives,
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const std::array<Vector3, 4>& coordinates) {
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// Shape derivatives sum to zero, so translating by node 1 improves the
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// numerical cancellation without changing the covariant tangent.
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std::array<Vector3, 4> relative{};
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for (std::size_t node = 0U; node < coordinates.size(); ++node) {
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relative[node] = subtract(coordinates[node], coordinates[0]);
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}
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return weightedSum(derivatives, relative);
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}
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Result<ShellGeometry> geometryFailure(
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std::string code,
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const SourceLocation& location,
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std::string keyword,
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std::string identity,
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std::string message) {
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return Result<ShellGeometry>::failure(Status::failure(
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FailureCategory::model,
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{{Severity::error,
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std::move(code),
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location,
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std::move(keyword),
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std::move(identity),
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std::move(message)}}));
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}
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bool sameCoordinates(const Vector3& left, const Vector3& right) {
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return left == right;
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}
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double orientation(
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const Vector3& first,
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const Vector3& second,
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const Vector3& third,
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const Vector3& normal) {
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return dot(cross(subtract(second, first), subtract(third, first)), normal);
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}
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bool hasOppositeSigns(double first, double second) {
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return (first < 0.0 && second > 0.0) ||
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(first > 0.0 && second < 0.0);
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}
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bool segmentsProperlyIntersect(
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const Vector3& firstStart,
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const Vector3& firstEnd,
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const Vector3& secondStart,
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const Vector3& secondEnd,
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const Vector3& normal) {
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const double firstSideStart =
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orientation(firstStart, firstEnd, secondStart, normal);
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const double firstSideEnd =
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orientation(firstStart, firstEnd, secondEnd, normal);
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const double secondSideStart =
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orientation(secondStart, secondEnd, firstStart, normal);
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const double secondSideEnd =
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orientation(secondStart, secondEnd, firstEnd, normal);
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return hasOppositeSigns(firstSideStart, firstSideEnd) &&
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hasOppositeSigns(secondSideStart, secondSideEnd);
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}
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bool sourceIdentityLess(
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const Mitc4ShellDefinition& left,
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std::size_t leftIndex,
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const Mitc4ShellDefinition& right,
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std::size_t rightIndex) {
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return std::tie(
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left.sourceId.instanceName,
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left.sourceId.sourceLabel,
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left.sourceId.sourceLabelText,
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leftIndex) <
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std::tie(
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right.sourceId.instanceName,
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right.sourceId.sourceLabel,
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right.sourceId.sourceLabelText,
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rightIndex);
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}
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} // namespace
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const std::array<ShellGeometryValidationPoint, 17>&
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shellGeometryValidationPoints() noexcept {
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static const std::array<ShellGeometryValidationPoint, 17> points = [] {
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const double g = 1.0 / std::sqrt(3.0);
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return std::array<ShellGeometryValidationPoint, 17>{
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ShellGeometryValidationPoint{
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ShellGeometryPointKind::center, 0U, {0.0, 0.0, 0.0}},
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{ShellGeometryPointKind::stiffness, 0U, {-g, -g, -g}},
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{ShellGeometryPointKind::stiffness, 1U, {-g, -g, g}},
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{ShellGeometryPointKind::stiffness, 2U, {g, -g, -g}},
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{ShellGeometryPointKind::stiffness, 3U, {g, -g, g}},
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{ShellGeometryPointKind::stiffness, 4U, {g, g, -g}},
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{ShellGeometryPointKind::stiffness, 5U, {g, g, g}},
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{ShellGeometryPointKind::stiffness, 6U, {-g, g, -g}},
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{ShellGeometryPointKind::stiffness, 7U, {-g, g, g}},
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{ShellGeometryPointKind::tying, 0U, {0.0, -1.0, 0.0}},
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{ShellGeometryPointKind::tying, 1U, {0.0, 1.0, 0.0}},
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{ShellGeometryPointKind::tying, 2U, {-1.0, 0.0, 0.0}},
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{ShellGeometryPointKind::tying, 3U, {1.0, 0.0, 0.0}},
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{ShellGeometryPointKind::recovery, 0U, {-g, -g, 0.0}},
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{ShellGeometryPointKind::recovery, 1U, {g, -g, 0.0}},
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{ShellGeometryPointKind::recovery, 2U, {g, g, 0.0}},
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{ShellGeometryPointKind::recovery, 3U, {-g, g, 0.0}}};
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}();
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return points;
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}
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Result<ShellGeometry> preprocessShellGeometry(
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const std::vector<Node>& nodes,
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const std::vector<Mitc4ShellDefinition>& elements,
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const std::vector<ShellSection>& sections) {
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ShellGeometry geometry;
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geometry.elementData.reserve(elements.size());
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std::vector<ElementWork> work;
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work.reserve(elements.size());
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const double g = 1.0 / std::sqrt(3.0);
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const std::array<Vector3, 4> surfaceGaussPoints{
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Vector3{-g, -g, 0.0},
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Vector3{g, -g, 0.0},
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Vector3{g, g, 0.0},
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Vector3{-g, g, 0.0}};
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for (std::size_t elementIndex = 0U;
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elementIndex < elements.size();
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++elementIndex) {
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const auto& element = elements[elementIndex];
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ElementWork current{};
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for (std::size_t localNode = 0U; localNode < 4U; ++localNode) {
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if (element.nodeIndices[localNode] >= nodes.size()) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell geometry references an unavailable internal node.");
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}
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current.coordinates[localNode] =
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nodes[element.nodeIndices[localNode]].coordinates;
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if (!isFinite(current.coordinates[localNode])) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell geometry contains a nonfinite source coordinate.");
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}
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}
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for (std::size_t first = 0U; first < 4U; ++first) {
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for (std::size_t second = first + 1U; second < 4U; ++second) {
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if (element.nodeIndices[first] == element.nodeIndices[second] ||
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sameCoordinates(
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current.coordinates[first], current.coordinates[second])) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell geometry contains duplicate nodes.");
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}
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}
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}
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const ShapeData center = shapeData(0.0, 0.0);
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const Vector3 centerXi =
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derivativeSum(center.xiDerivatives, current.coordinates);
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const Vector3 centerEta =
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derivativeSum(center.etaDerivatives, current.coordinates);
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const Vector3 centerCross = cross(centerXi, centerEta);
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const double centerMeasure = norm(centerCross);
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if (!isFinite(centerXi) || !isFinite(centerEta) ||
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!isFinite(centerCross) || !std::isfinite(centerMeasure) ||
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!(centerMeasure > 0.0)) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell center has no finite nonzero normal candidate.");
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}
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current.normal = scale(1.0 / centerMeasure, centerCross);
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if (segmentsProperlyIntersect(
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current.coordinates[0], current.coordinates[1],
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current.coordinates[2], current.coordinates[3], current.normal) ||
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segmentsProperlyIntersect(
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current.coordinates[1], current.coordinates[2],
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current.coordinates[3], current.coordinates[0], current.normal)) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell boundary is self-intersecting in the center-normal projection.");
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}
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double areaWeight = 0.0;
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for (const auto& point : surfaceGaussPoints) {
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const ShapeData shape = shapeData(point[0], point[1]);
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const Vector3 tangentXi =
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derivativeSum(shape.xiDerivatives, current.coordinates);
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const Vector3 tangentEta =
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derivativeSum(shape.etaDerivatives, current.coordinates);
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const Vector3 areaVector = cross(tangentXi, tangentEta);
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const double measure = norm(areaVector);
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if (!isFinite(tangentXi) || !isFinite(tangentEta) ||
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!isFinite(areaVector) || !std::isfinite(measure) ||
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!(measure > 0.0) || !(dot(areaVector, current.normal) > 0.0)) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell surface is zero-area or locally reversed at a required point.");
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}
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areaWeight += measure;
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}
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if (!std::isfinite(areaWeight) || !(areaWeight > 0.0)) {
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return geometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.sourceId.sourceLabelText,
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"Shell surface-area weight is nonfinite or zero.");
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}
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current.areaWeight = areaWeight;
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work.push_back(current);
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geometry.elementData.push_back({
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static_cast<EntityIndex>(elementIndex), current.normal, areaWeight});
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}
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std::vector<std::vector<std::size_t>> incident(nodes.size());
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for (std::size_t elementIndex = 0U;
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elementIndex < elements.size();
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++elementIndex) {
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for (const EntityIndex nodeIndex : elements[elementIndex].nodeIndices) {
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incident[nodeIndex].push_back(elementIndex);
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}
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}
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geometry.nodalFrames.reserve(nodes.size());
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std::vector<const ShellNodeInitialFrame*> frameByNode(nodes.size(), nullptr);
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for (std::size_t nodeIndex = 0U; nodeIndex < incident.size(); ++nodeIndex) {
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auto& nodeIncident = incident[nodeIndex];
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if (nodeIncident.empty()) {
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continue;
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}
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std::sort(
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nodeIncident.begin(), nodeIncident.end(),
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[&elements](std::size_t left, std::size_t right) {
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return sourceIdentityLess(
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elements[left], left, elements[right], right);
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});
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for (std::size_t first = 0U; first < nodeIncident.size(); ++first) {
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for (std::size_t second = first + 1U;
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second < nodeIncident.size();
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++second) {
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const double pairDot = dot(
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work[nodeIncident[first]].normal,
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work[nodeIncident[second]].normal);
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if (!std::isfinite(pairDot) || !(pairDot > 0.0)) {
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return geometryFailure(
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"opposed-incident-normal", nodes[nodeIndex].location,
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"NODE", nodes[nodeIndex].sourceId.sourceLabelText,
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"Incident shell normal candidates do not share a positive orientation hemisphere.");
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}
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}
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}
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double maximumWeight = 0.0;
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for (const std::size_t elementIndex : nodeIncident) {
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maximumWeight = std::max(maximumWeight, work[elementIndex].areaWeight);
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}
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Vector3 directorSum{};
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for (const std::size_t elementIndex : nodeIncident) {
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directorSum = add(
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directorSum,
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scale(
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work[elementIndex].areaWeight / maximumWeight,
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work[elementIndex].normal));
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}
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const double directorNorm = norm(directorSum);
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if (!isFinite(directorSum) || !std::isfinite(directorNorm) ||
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!(directorNorm > 0.0)) {
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return geometryFailure(
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"invalid-shell-director", nodes[nodeIndex].location, "NODE",
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nodes[nodeIndex].sourceId.sourceLabelText,
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"Area-weighted shell director is nonfinite or zero.");
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}
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const Vector3 director = scale(1.0 / directorNorm, directorSum);
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const std::array<Vector3, 3> globalAxes{
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Vector3{1.0, 0.0, 0.0},
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Vector3{0.0, 1.0, 0.0},
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Vector3{0.0, 0.0, 1.0}};
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std::size_t selectedAxis = 0U;
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double selectedAlignment = std::abs(dot(globalAxes[0], director));
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for (std::size_t axis = 1U; axis < globalAxes.size(); ++axis) {
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const double alignment = std::abs(dot(globalAxes[axis], director));
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if (alignment < selectedAlignment) {
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selectedAlignment = alignment;
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selectedAxis = axis;
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}
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}
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const Vector3 tangentCandidate = subtract(
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globalAxes[selectedAxis],
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scale(dot(globalAxes[selectedAxis], director), director));
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const double tangentNorm = norm(tangentCandidate);
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if (!isFinite(tangentCandidate) || !std::isfinite(tangentNorm) ||
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!(tangentNorm > 0.0)) {
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return geometryFailure(
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"invalid-shell-director", nodes[nodeIndex].location, "NODE",
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nodes[nodeIndex].sourceId.sourceLabelText,
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"Least-aligned-axis tangent frame construction failed.");
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}
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const Vector3 tangentA = scale(1.0 / tangentNorm, tangentCandidate);
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const Vector3 tangentB = cross(director, tangentA);
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if (!isFinite(tangentB) || !(norm(tangentB) > 0.0)) {
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return geometryFailure(
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"invalid-shell-director", nodes[nodeIndex].location, "NODE",
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nodes[nodeIndex].sourceId.sourceLabelText,
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"Right-handed shell tangent frame construction failed.");
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}
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geometry.nodalFrames.push_back({
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static_cast<EntityIndex>(nodeIndex), director, tangentA, tangentB});
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}
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// Build lookup only after frame storage is complete so later code never
|
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// observes a pointer invalidated by vector growth.
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for (const auto& frame : geometry.nodalFrames) {
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frameByNode[frame.nodeIndex] = &frame;
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}
|
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|
||||
for (std::size_t elementIndex = 0U;
|
||||
elementIndex < elements.size();
|
||||
++elementIndex) {
|
||||
const auto& element = elements[elementIndex];
|
||||
if (element.sectionIndex >= sections.size()) {
|
||||
return geometryFailure(
|
||||
"invalid-shell-jacobian", element.location, "ELEMENT",
|
||||
element.sourceId.sourceLabelText,
|
||||
"Shell geometry cannot resolve its thickness for Jacobian validation.");
|
||||
}
|
||||
const double thickness = sections[element.sectionIndex].thickness;
|
||||
std::array<Vector3, 4> directors{};
|
||||
for (std::size_t localNode = 0U; localNode < 4U; ++localNode) {
|
||||
const auto* frame = frameByNode[element.nodeIndices[localNode]];
|
||||
if (frame == nullptr) {
|
||||
return geometryFailure(
|
||||
"invalid-shell-director", element.location, "ELEMENT",
|
||||
element.sourceId.sourceLabelText,
|
||||
"Shell element is missing a nodal director.");
|
||||
}
|
||||
directors[localNode] = frame->director;
|
||||
}
|
||||
|
||||
for (const auto& point : shellGeometryValidationPoints()) {
|
||||
const double xi = point.naturalCoordinates[0];
|
||||
const double eta = point.naturalCoordinates[1];
|
||||
const double zeta = point.naturalCoordinates[2];
|
||||
const ShapeData shape = shapeData(xi, eta);
|
||||
const Vector3 midsurfaceXi =
|
||||
derivativeSum(shape.xiDerivatives, work[elementIndex].coordinates);
|
||||
const Vector3 midsurfaceEta =
|
||||
derivativeSum(shape.etaDerivatives, work[elementIndex].coordinates);
|
||||
const Vector3 areaVector = cross(midsurfaceXi, midsurfaceEta);
|
||||
const double surfaceMeasure = norm(areaVector);
|
||||
if (!isFinite(midsurfaceXi) || !isFinite(midsurfaceEta) ||
|
||||
!isFinite(areaVector) || !std::isfinite(surfaceMeasure) ||
|
||||
!(surfaceMeasure > 0.0) ||
|
||||
!(dot(areaVector, work[elementIndex].normal) > 0.0)) {
|
||||
return geometryFailure(
|
||||
"invalid-shell-geometry", element.location, "ELEMENT",
|
||||
element.sourceId.sourceLabelText,
|
||||
"Shell surface basis is nonfinite, zero, or reversed at a required point.");
|
||||
}
|
||||
|
||||
const Vector3 directorXi =
|
||||
weightedSum(shape.xiDerivatives, directors);
|
||||
const Vector3 directorEta =
|
||||
weightedSum(shape.etaDerivatives, directors);
|
||||
const Vector3 directorValue = weightedSum(shape.values, directors);
|
||||
const Vector3 covariantXi = add(
|
||||
midsurfaceXi, scale(0.5 * thickness * zeta, directorXi));
|
||||
const Vector3 covariantEta = add(
|
||||
midsurfaceEta, scale(0.5 * thickness * zeta, directorEta));
|
||||
const Vector3 covariantZeta = scale(0.5 * thickness, directorValue);
|
||||
const double jacobian =
|
||||
dot(covariantXi, cross(covariantEta, covariantZeta));
|
||||
if (!isFinite(covariantXi) || !isFinite(covariantEta) ||
|
||||
!isFinite(covariantZeta) || !std::isfinite(jacobian) ||
|
||||
!(jacobian > 0.0)) {
|
||||
return geometryFailure(
|
||||
"invalid-shell-jacobian", element.location, "ELEMENT",
|
||||
element.sourceId.sourceLabelText,
|
||||
"Shell Jacobian is nonfinite or nonpositive at a required point.");
|
||||
}
|
||||
const Vector3 reciprocalXi =
|
||||
scale(1.0 / jacobian, cross(covariantEta, covariantZeta));
|
||||
const Vector3 reciprocalEta =
|
||||
scale(1.0 / jacobian, cross(covariantZeta, covariantXi));
|
||||
const Vector3 reciprocalZeta =
|
||||
scale(1.0 / jacobian, cross(covariantXi, covariantEta));
|
||||
if (!isFinite(reciprocalXi) || !isFinite(reciprocalEta) ||
|
||||
!isFinite(reciprocalZeta)) {
|
||||
return geometryFailure(
|
||||
"invalid-shell-jacobian", element.location, "ELEMENT",
|
||||
element.sourceId.sourceLabelText,
|
||||
"Shell reciprocal basis is nonfinite at a required point.");
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return Result<ShellGeometry>::success(std::move(geometry));
|
||||
}
|
||||
|
||||
} // namespace fesa
|
||||
Reference in New Issue
Block a user