KOKO\Mimi
426 lines
18 KiB
C++
426 lines
18 KiB
C++
#include "fesa/model/shell_geometry.h"
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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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#include "fesa/math/vector3.h"
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#include "math/dense_blas_internal.h"
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#include "math/vector3_operations.h"
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namespace fesa {
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namespace {
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using math_internal::DerivativeSum;
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using math_internal::WeightedSum;
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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> xi_derivatives;
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std::array<double, 4> eta_derivatives;
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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 area_weight;
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};
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ShapeData ShapeDataAt(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) * (1.0 + kEtaSigns[node] * eta);
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data.xi_derivatives[node] =
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0.25 * kXiSigns[node] * (1.0 + kEtaSigns[node] * eta);
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data.eta_derivatives[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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Result<ShellGeometry> GeometryFailure(std::string code,
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const SourceLocation& location,
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std::string keyword, 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::kModel,
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{{Severity::kError, std::move(code), location, std::move(keyword),
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std::move(identity), 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(const Vector3& first, const Vector3& second,
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const Vector3& third, const Vector3& normal) {
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return (second - first).Cross(third - first).Dot(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) || (first > 0.0 && second < 0.0);
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}
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/// @brief Detects a proper projected edge crossing without a tolerance clamp.
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bool SegmentsProperlyIntersect(const Vector3& first_start,
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const Vector3& first_end,
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const Vector3& second_start,
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const Vector3& second_end,
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const Vector3& normal) {
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const double first_side_start =
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Orientation(first_start, first_end, second_start, normal);
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const double first_side_end =
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Orientation(first_start, first_end, second_end, normal);
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const double second_side_start =
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Orientation(second_start, second_end, first_start, normal);
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const double second_side_end =
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Orientation(second_start, second_end, first_end, normal);
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return HasOppositeSigns(first_side_start, first_side_end) &&
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HasOppositeSigns(second_side_start, second_side_end);
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}
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/// @brief Orders incident shell contributions by stable source identity.
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bool SourceIdentityLess(const Mitc4ShellDefinition& left,
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std::size_t left_index,
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const Mitc4ShellDefinition& right,
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std::size_t right_index) {
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return std::tie(left.source_id.instance_name, left.source_id.source_label,
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left.source_id.source_label_text, left_index) <
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std::tie(right.source_id.instance_name, right.source_id.source_label,
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right.source_id.source_label_text, right_index);
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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::kCenter, 0U, {0.0, 0.0, 0.0}},
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{ShellGeometryPointKind::kStiffness, 0U, {-g, -g, -g}},
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{ShellGeometryPointKind::kStiffness, 1U, {-g, -g, g}},
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{ShellGeometryPointKind::kStiffness, 2U, {g, -g, -g}},
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{ShellGeometryPointKind::kStiffness, 3U, {g, -g, g}},
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{ShellGeometryPointKind::kStiffness, 4U, {g, g, -g}},
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{ShellGeometryPointKind::kStiffness, 5U, {g, g, g}},
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{ShellGeometryPointKind::kStiffness, 6U, {-g, g, -g}},
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{ShellGeometryPointKind::kStiffness, 7U, {-g, g, g}},
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{ShellGeometryPointKind::kTying, 0U, {0.0, -1.0, 0.0}},
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{ShellGeometryPointKind::kTying, 1U, {0.0, 1.0, 0.0}},
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{ShellGeometryPointKind::kTying, 2U, {-1.0, 0.0, 0.0}},
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{ShellGeometryPointKind::kTying, 3U, {1.0, 0.0, 0.0}},
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{ShellGeometryPointKind::kRecovery, 0U, {-g, -g, 0.0}},
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{ShellGeometryPointKind::kRecovery, 1U, {g, -g, 0.0}},
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{ShellGeometryPointKind::kRecovery, 2U, {g, g, 0.0}},
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{ShellGeometryPointKind::kRecovery, 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.element_data.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> surface_gauss_points{
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Vector3{-g, -g, 0.0}, Vector3{g, -g, 0.0}, Vector3{g, g, 0.0},
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Vector3{-g, g, 0.0}};
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for (std::size_t element_index = 0U; element_index < elements.size();
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++element_index) {
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const auto& element = elements[element_index];
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ElementWork current{};
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for (std::size_t local_node = 0U; local_node < 4U; ++local_node) {
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if (element.node_indices[local_node] >= nodes.size()) {
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return GeometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.source_id.source_label_text,
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"Shell geometry references an unavailable internal node.");
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}
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current.coordinates[local_node] =
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Vector3{nodes[element.node_indices[local_node]].coordinates};
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if (!current.coordinates[local_node].IsFinite()) {
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return GeometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.source_id.source_label_text,
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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.node_indices[first] == element.node_indices[second] ||
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SameCoordinates(current.coordinates[first],
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current.coordinates[second])) {
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return GeometryFailure("invalid-shell-geometry", element.location,
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"ELEMENT", element.source_id.source_label_text,
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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 = ShapeDataAt(0.0, 0.0);
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const Vector3 center_xi =
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DerivativeSum(center.xi_derivatives, current.coordinates);
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const Vector3 center_eta =
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DerivativeSum(center.eta_derivatives, current.coordinates);
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const Vector3 center_cross = center_xi.Cross(center_eta);
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const double center_measure = center_cross.Norm();
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if (!center_xi.IsFinite() || !center_eta.IsFinite() ||
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!center_cross.IsFinite() || !std::isfinite(center_measure) ||
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!(center_measure > 0.0)) {
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return GeometryFailure(
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"invalid-shell-geometry", element.location, "ELEMENT",
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element.source_id.source_label_text,
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"Shell center has no finite nonzero normal candidate.");
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}
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current.normal = (1.0 / center_measure) * center_cross;
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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("invalid-shell-geometry", element.location,
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"ELEMENT", element.source_id.source_label_text,
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"Shell boundary is self-intersecting in the "
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"center-normal projection.");
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}
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double area_weight = 0.0;
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for (const auto& point : surface_gauss_points) {
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const ShapeData shape = ShapeDataAt(point[0], point[1]);
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const Vector3 tangent_xi =
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DerivativeSum(shape.xi_derivatives, current.coordinates);
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const Vector3 tangent_eta =
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DerivativeSum(shape.eta_derivatives, current.coordinates);
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const Vector3 area_vector = tangent_xi.Cross(tangent_eta);
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const double measure = area_vector.Norm();
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if (!tangent_xi.IsFinite() || !tangent_eta.IsFinite() ||
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!area_vector.IsFinite() || !std::isfinite(measure) ||
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!(measure > 0.0) || !(area_vector.Dot(current.normal) > 0.0)) {
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return GeometryFailure("invalid-shell-geometry", element.location,
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"ELEMENT", element.source_id.source_label_text,
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"Shell surface is zero-area or locally reversed "
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"at a required point.");
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}
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area_weight += measure;
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}
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if (!std::isfinite(area_weight) || !(area_weight > 0.0)) {
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return GeometryFailure("invalid-shell-geometry", element.location,
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"ELEMENT", element.source_id.source_label_text,
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"Shell surface-area weight is nonfinite or zero.");
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}
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current.area_weight = area_weight;
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work.push_back(current);
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geometry.element_data.push_back({static_cast<EntityIndex>(element_index),
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current.normal.Components(), area_weight});
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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 element_index = 0U; element_index < elements.size();
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++element_index) {
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for (const EntityIndex node_index : elements[element_index].node_indices) {
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incident[node_index].push_back(element_index);
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}
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}
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geometry.nodal_frames.reserve(nodes.size());
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std::vector<const ShellNodeInitialFrame*> frame_by_node(nodes.size(),
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nullptr);
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for (std::size_t node_index = 0U; node_index < incident.size();
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++node_index) {
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auto& node_incident = incident[node_index];
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if (node_incident.empty()) {
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continue;
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}
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std::sort(node_incident.begin(), node_incident.end(),
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[&elements](std::size_t left, std::size_t right) {
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return SourceIdentityLess(elements[left], left, elements[right],
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right);
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});
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for (std::size_t first = 0U; first < node_incident.size(); ++first) {
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for (std::size_t second = first + 1U; second < node_incident.size();
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++second) {
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const double pair_dot = work[node_incident[first]].normal.Dot(
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work[node_incident[second]].normal);
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if (!std::isfinite(pair_dot) || !(pair_dot > 0.0)) {
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return GeometryFailure("opposed-incident-normal",
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nodes[node_index].location, "NODE",
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nodes[node_index].source_id.source_label_text,
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"Incident shell normal candidates do not "
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"share a positive orientation hemisphere.");
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}
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}
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}
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double maximum_weight = 0.0;
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for (const std::size_t element_index : node_incident) {
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maximum_weight =
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std::max(maximum_weight, work[element_index].area_weight);
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}
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Vector3 director_sum{};
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for (const std::size_t element_index : node_incident) {
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director_sum =
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director_sum + (work[element_index].area_weight / maximum_weight) *
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work[element_index].normal;
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}
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const double director_norm = director_sum.Norm();
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if (!director_sum.IsFinite() || !std::isfinite(director_norm) ||
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!(director_norm > 0.0)) {
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return GeometryFailure(
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"invalid-shell-director", nodes[node_index].location, "NODE",
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nodes[node_index].source_id.source_label_text,
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"Area-weighted shell director is nonfinite or zero.");
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}
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const Vector3 director = (1.0 / director_norm) * director_sum;
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const std::array<Vector3, 3> global_axes{
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Vector3{1.0, 0.0, 0.0}, Vector3{0.0, 1.0, 0.0}, Vector3{0.0, 0.0, 1.0}};
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std::size_t selected_axis = 0U;
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double selected_alignment = std::abs(global_axes[0].Dot(director));
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for (std::size_t axis = 1U; axis < global_axes.size(); ++axis) {
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const double alignment = std::abs(global_axes[axis].Dot(director));
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if (alignment < selected_alignment) {
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selected_alignment = alignment;
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selected_axis = axis;
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}
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}
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const Vector3 tangent_candidate =
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global_axes[selected_axis] -
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global_axes[selected_axis].Dot(director) * director;
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const double tangent_norm = tangent_candidate.Norm();
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if (!tangent_candidate.IsFinite() || !std::isfinite(tangent_norm) ||
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!(tangent_norm > 0.0)) {
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return GeometryFailure(
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"invalid-shell-director", nodes[node_index].location, "NODE",
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nodes[node_index].source_id.source_label_text,
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"Least-aligned-axis tangent frame construction failed.");
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}
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const Vector3 tangent_a = (1.0 / tangent_norm) * tangent_candidate;
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const Vector3 tangent_b = director.Cross(tangent_a);
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if (!tangent_b.IsFinite() || !(tangent_b.Norm() > 0.0)) {
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return GeometryFailure(
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"invalid-shell-director", nodes[node_index].location, "NODE",
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nodes[node_index].source_id.source_label_text,
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"Right-handed shell tangent frame construction failed.");
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}
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geometry.nodal_frames.push_back(
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{static_cast<EntityIndex>(node_index), director.Components(),
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tangent_a.Components(), tangent_b.Components()});
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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.nodal_frames) {
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frame_by_node[frame.node_index] = &frame;
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}
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for (std::size_t element_index = 0U; element_index < elements.size();
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++element_index) {
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const auto& element = elements[element_index];
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if (element.section_index >= sections.size()) {
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return GeometryFailure("invalid-shell-jacobian", element.location,
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"ELEMENT", element.source_id.source_label_text,
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"Shell geometry cannot resolve its thickness for "
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"Jacobian validation.");
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}
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const double thickness = sections[element.section_index].thickness;
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std::array<Vector3, 4> directors{};
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for (std::size_t local_node = 0U; local_node < 4U; ++local_node) {
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const auto* frame = frame_by_node[element.node_indices[local_node]];
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if (frame == nullptr) {
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return GeometryFailure("invalid-shell-director", element.location,
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"ELEMENT", element.source_id.source_label_text,
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"Shell element is missing a nodal director.");
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}
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directors[local_node] = Vector3{frame->director};
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}
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for (const auto& point : ShellGeometryValidationPoints()) {
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const double xi = point.natural_coordinates[0];
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const double eta = point.natural_coordinates[1];
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const double zeta = point.natural_coordinates[2];
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const ShapeData shape = ShapeDataAt(xi, eta);
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const Vector3 midsurface_xi =
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DerivativeSum(shape.xi_derivatives, work[element_index].coordinates);
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const Vector3 midsurface_eta =
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DerivativeSum(shape.eta_derivatives, work[element_index].coordinates);
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const Vector3 area_vector = midsurface_xi.Cross(midsurface_eta);
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const double surface_measure = area_vector.Norm();
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if (!midsurface_xi.IsFinite() || !midsurface_eta.IsFinite() ||
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!area_vector.IsFinite() || !std::isfinite(surface_measure) ||
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!(surface_measure > 0.0) ||
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!(area_vector.Dot(work[element_index].normal) > 0.0)) {
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return GeometryFailure("invalid-shell-geometry", element.location,
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"ELEMENT", element.source_id.source_label_text,
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"Shell surface basis is nonfinite, zero, or "
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"reversed at a required point.");
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}
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const Vector3 director_xi = WeightedSum(shape.xi_derivatives, directors);
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const Vector3 director_eta =
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WeightedSum(shape.eta_derivatives, directors);
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const Vector3 director_value = WeightedSum(shape.values, directors);
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const Vector3 covariant_xi =
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midsurface_xi + 0.5 * thickness * zeta * director_xi;
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const Vector3 covariant_eta =
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midsurface_eta + 0.5 * thickness * zeta * director_eta;
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const Vector3 covariant_zeta = 0.5 * thickness * director_value;
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const double jacobian =
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covariant_xi.Dot(covariant_eta.Cross(covariant_zeta));
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if (!covariant_xi.IsFinite() || !covariant_eta.IsFinite() ||
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!covariant_zeta.IsFinite() || !std::isfinite(jacobian) ||
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!(jacobian > 0.0)) {
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return GeometryFailure(
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"invalid-shell-jacobian", element.location, "ELEMENT",
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element.source_id.source_label_text,
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"Shell Jacobian is nonfinite or nonpositive at a required point.");
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}
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bool finite_actions = std::isfinite(1.0 / jacobian) &&
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covariant_eta.Cross(covariant_zeta).IsFinite() &&
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covariant_zeta.Cross(covariant_xi).IsFinite() &&
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covariant_xi.Cross(covariant_eta).IsFinite();
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if (finite_actions) {
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Matrix coefficients{3U, 3U};
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for (std::size_t i = 0; i < 3U; ++i) {
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coefficients(i, 0) = covariant_xi[i];
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coefficients(i, 1) = covariant_eta[i];
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coefficients(i, 2) = covariant_zeta[i];
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}
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const auto factor = dense_blas_internal::DenseFactor::Lu(coefficients);
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finite_actions = factor.HasValue();
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Matrix rhs{3U, 1U};
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for (std::size_t axis = 0; finite_actions && axis < 3U; ++axis) {
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if (axis != 0U) rhs(axis - 1U, 0U) = 0.0;
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rhs(axis, 0U) = 1.0;
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finite_actions = factor.Value().Solve(rhs, true).HasValue();
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}
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}
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if (!finite_actions) {
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return GeometryFailure(
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"invalid-shell-jacobian", element.location, "ELEMENT",
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element.source_id.source_label_text,
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"Shell reciprocal basis is nonfinite at a required point.");
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}
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}
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}
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return Result<ShellGeometry>::Success(std::move(geometry));
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}
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} // namespace fesa
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