refactor: extract mitc4 geometry strain helpers
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NINI
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#pragma once
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#include "fesa/Math/Math.hpp"
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#include "fesa/Util/Util.hpp"
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#include <array>
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#include <optional>
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#include <string>
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#include <utility>
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#include <vector>
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namespace fesa {
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struct ShapeData {
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std::array<Real, 4> n{};
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std::array<Real, 4> dr{};
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std::array<Real, 4> ds{};
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};
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inline ShapeData shapeFunctions(Real r, Real s) {
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return { {
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0.25 * (1.0 - r) * (1.0 - s),
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0.25 * (1.0 + r) * (1.0 - s),
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0.25 * (1.0 + r) * (1.0 + s),
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0.25 * (1.0 - r) * (1.0 + s),
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},
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{
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-0.25 * (1.0 - s),
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0.25 * (1.0 - s),
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0.25 * (1.0 + s),
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-0.25 * (1.0 + s),
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},
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{
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-0.25 * (1.0 - r),
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-0.25 * (1.0 + r),
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0.25 * (1.0 + r),
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0.25 * (1.0 - r),
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} };
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}
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struct LocalBasis {
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Vec3 e1;
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Vec3 e2;
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Vec3 e3;
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};
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struct MITC4NaturalPoint {
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Real xi = 0.0;
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Real eta = 0.0;
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};
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struct MITC4TyingPoint {
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std::string label;
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MITC4NaturalPoint natural;
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std::array<LocalIndex, 2> edge_node_indices{};
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};
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inline std::array<MITC4NaturalPoint, 4> mitc4NodeNaturalCoordinates() {
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return {{{-1.0, -1.0}, {1.0, -1.0}, {1.0, 1.0}, {-1.0, 1.0}}};
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}
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inline std::array<MITC4TyingPoint, 4> mitc4TyingPoints() {
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return {{{"A", {0.0, -1.0}, {0, 1}},
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{"B", {-1.0, 0.0}, {0, 3}},
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{"C", {0.0, 1.0}, {3, 2}},
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{"D", {1.0, 0.0}, {1, 2}}}};
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}
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struct MITC4DirectorFrame {
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Vec3 v1;
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Vec3 v2;
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Vec3 vn;
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};
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struct MITC4MidsurfaceDerivatives {
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ShapeData shape;
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Vec3 g1;
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Vec3 g2;
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};
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struct MITC4Geometry {
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std::array<Vec3, 4> coordinates{};
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Real thickness = 0.0;
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ShapeData center_shape;
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Vec3 g1_center;
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Vec3 g2_center;
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Vec3 center_normal;
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std::array<MITC4DirectorFrame, 4> nodal_frames{};
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std::vector<Diagnostic> diagnostics;
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bool ok() const {
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return !hasError(diagnostics);
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}
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};
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struct MITC4IntegrationBasis {
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ShapeData shape;
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Vec3 g1;
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Vec3 g2;
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Vec3 g3;
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Real jacobian = 0.0;
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LocalBasis local;
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std::vector<Diagnostic> diagnostics;
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bool ok() const {
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return !hasError(diagnostics);
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}
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};
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inline Vec3 globalEX() {
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return {1.0, 0.0, 0.0};
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}
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inline Vec3 globalEY() {
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return {0.0, 1.0, 0.0};
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}
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inline Vec3 globalEZ() {
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return {0.0, 0.0, 1.0};
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}
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inline Diagnostic mitc4Diagnostic(std::string code, std::string message) {
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return makeDiagnostic(Severity::Error, std::move(code), std::move(message), "mitc4", "<element>", 0);
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}
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inline void appendDiagnostics(std::vector<Diagnostic>& target, const std::vector<Diagnostic>& source) {
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target.insert(target.end(), source.begin(), source.end());
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}
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inline MITC4MidsurfaceDerivatives mitc4MidsurfaceDerivatives(const std::array<Vec3, 4>& coordinates,
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Real xi,
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Real eta) {
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MITC4MidsurfaceDerivatives result;
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result.shape = shapeFunctions(xi, eta);
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for (std::size_t i = 0; i < 4; ++i) {
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result.g1 = result.g1 + result.shape.dr[i] * coordinates[i];
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result.g2 = result.g2 + result.shape.ds[i] * coordinates[i];
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}
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return result;
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}
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inline std::optional<Vec3> firstNormalizedCross(const std::array<Vec3, 3>& axes, const Vec3& vector, Real tolerance) {
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for (const Vec3& axis : axes) {
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auto candidate = normalizedIfValid(cross(axis, vector), tolerance);
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if (candidate) {
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return candidate;
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}
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}
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return std::nullopt;
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}
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inline std::optional<MITC4DirectorFrame> buildMITC4DirectorFrame(const Vec3& normal, Real tolerance) {
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auto v1 = normalizedIfValid(cross(globalEY(), normal), tolerance);
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if (!v1) {
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v1 = firstNormalizedCross({globalEZ(), globalEX(), globalEY()}, normal, tolerance);
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}
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if (!v1) {
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return std::nullopt;
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}
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auto v2 = normalizedIfValid(cross(normal, *v1), tolerance);
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if (!v2) {
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return std::nullopt;
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}
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return MITC4DirectorFrame{*v1, *v2, normal};
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}
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inline MITC4Geometry buildMITC4Geometry(const std::array<Vec3, 4>& coordinates,
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Real thickness,
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Real tolerance = 1.0e-12) {
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MITC4Geometry geometry;
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geometry.coordinates = coordinates;
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geometry.thickness = thickness;
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if (!isFinite(thickness) || thickness <= tolerance) {
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geometry.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-THICKNESS", "MITC4 shell thickness must be positive and finite"));
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}
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for (const Vec3& coordinate : coordinates) {
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if (!isFinite(coordinate)) {
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geometry.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-COORDINATE", "MITC4 element coordinates must be finite"));
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break;
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}
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}
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const auto center = mitc4MidsurfaceDerivatives(coordinates, 0.0, 0.0);
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geometry.center_shape = center.shape;
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geometry.g1_center = center.g1;
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geometry.g2_center = center.g2;
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const auto normal = normalizedIfValid(cross(center.g1, center.g2), tolerance);
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if (!normal) {
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geometry.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-SINGULAR-NORMAL", "MITC4 element center normal is near zero"));
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return geometry;
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}
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geometry.center_normal = *normal;
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const auto frame = buildMITC4DirectorFrame(*normal, tolerance);
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if (!frame) {
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geometry.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 nodal director basis could not be constructed"));
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return geometry;
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}
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geometry.nodal_frames.fill(*frame);
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return geometry;
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}
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inline MITC4IntegrationBasis computeMITC4IntegrationBasis(const MITC4Geometry& geometry,
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Real xi,
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Real eta,
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Real zeta,
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Real tolerance = 1.0e-12) {
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MITC4IntegrationBasis result;
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result.diagnostics = geometry.diagnostics;
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result.shape = shapeFunctions(xi, eta);
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for (std::size_t i = 0; i < 4; ++i) {
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const Vec3& coordinate = geometry.coordinates[i];
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const Vec3& normal = geometry.nodal_frames[i].vn;
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result.g1 = result.g1 + result.shape.dr[i] * coordinate +
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(0.5 * zeta * geometry.thickness * result.shape.dr[i]) * normal;
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result.g2 = result.g2 + result.shape.ds[i] * coordinate +
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(0.5 * zeta * geometry.thickness * result.shape.ds[i]) * normal;
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result.g3 = result.g3 + (0.5 * geometry.thickness * result.shape.n[i]) * normal;
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}
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result.jacobian = dot(cross(result.g1, result.g2), result.g3);
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if (!isFinite(result.jacobian) || std::fabs(result.jacobian) <= tolerance) {
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result.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-SINGULAR-JACOBIAN", "MITC4 element Jacobian is near zero"));
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}
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const auto e3 = normalizedIfValid(result.g3, tolerance);
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if (!e3) {
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result.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis normal is near zero"));
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return result;
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}
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auto e1 = normalizedIfValid(cross(result.g2, *e3), tolerance);
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if (!e1) {
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e1 = firstNormalizedCross({globalEY(), globalEZ(), globalEX()}, *e3, tolerance);
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}
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if (!e1) {
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result.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis tangent could not be constructed"));
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return result;
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}
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const auto e2 = normalizedIfValid(cross(*e3, *e1), tolerance);
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if (!e2) {
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result.diagnostics.push_back(
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mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis is not right-handed"));
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return result;
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}
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result.local = {*e1, *e2, *e3};
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return result;
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}
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inline LocalBasis computeLocalBasis(const std::array<Vec3, 4>& coordinates) {
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const MITC4Geometry geometry = buildMITC4Geometry(coordinates, 1.0);
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if (!geometry.ok()) {
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throw std::runtime_error("invalid MITC4 geometry");
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}
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const MITC4DirectorFrame& frame = geometry.nodal_frames[0];
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return {frame.v1, frame.v2, frame.vn};
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}
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} // namespace fesa
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