feat: add mitc4 covariant strain tying
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NINI
@@ -1301,6 +1301,64 @@ struct MITC4IntegrationBasis {
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}
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};
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using MITC4ElementDofVector = std::array<Real, 24>;
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using MITC4StrainVector = std::array<Real, 6>;
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using MITC4StrainRow = std::array<Real, 24>;
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enum class MITC4StrainComponent {
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Eps11 = 0,
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Eps22 = 1,
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Eps33 = 2,
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Gamma23 = 3,
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Gamma13 = 4,
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Gamma12 = 5
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};
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inline std::size_t strainComponentIndex(MITC4StrainComponent component) {
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return static_cast<std::size_t>(component);
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}
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inline std::array<std::string, 6> mitc4StrainComponentLabels() {
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return {"eps11", "eps22", "eps33", "gamma23", "gamma13", "gamma12"};
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}
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struct MITC4LocalRotations {
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Real alpha = 0.0;
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Real beta = 0.0;
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Real gamma = 0.0;
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};
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struct MITC4DisplacementDerivatives {
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ShapeData shape;
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Vec3 displacement;
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Vec3 du_dxi;
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Vec3 du_deta;
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Vec3 du_dzeta;
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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 MITC4StrainEvaluation {
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MITC4StrainVector values{};
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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 MITC4StrainRows {
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std::array<MITC4StrainRow, 6> rows{};
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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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@@ -1317,6 +1375,10 @@ 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, Real xi, Real eta) {
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MITC4MidsurfaceDerivatives result;
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result.shape = shapeFunctions(xi, eta);
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@@ -1436,6 +1498,132 @@ inline MITC4IntegrationBasis computeMITC4IntegrationBasis(const MITC4Geometry& g
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return result;
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}
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inline Vec3 mitc4NodalTranslation(const MITC4ElementDofVector& values, std::size_t node) {
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const std::size_t base = 6 * node;
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return {values[base + 0], values[base + 1], values[base + 2]};
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}
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inline Vec3 mitc4NodalRotation(const MITC4ElementDofVector& values, std::size_t node) {
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const std::size_t base = 6 * node;
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return {values[base + 3], values[base + 4], values[base + 5]};
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}
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inline MITC4LocalRotations mitc4LocalRotations(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
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return {dot(global_rotation, frame.v1), dot(global_rotation, frame.v2), dot(global_rotation, frame.vn)};
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}
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inline Vec3 mitc4DirectorIncrement(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
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const MITC4LocalRotations rotations = mitc4LocalRotations(frame, global_rotation);
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return (-rotations.alpha) * frame.v2 + rotations.beta * frame.v1;
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}
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inline MITC4DisplacementDerivatives mitc4DisplacementDerivatives(const MITC4Geometry& geometry, const MITC4ElementDofVector& values,
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Real xi, Real eta, Real zeta) {
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MITC4DisplacementDerivatives 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 node = 0; node < 4; ++node) {
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const Vec3 translation = mitc4NodalTranslation(values, node);
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const Vec3 rotation = mitc4NodalRotation(values, node);
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const Vec3 q = mitc4DirectorIncrement(geometry.nodal_frames[node], rotation);
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const Real n = result.shape.n[node];
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const Real dn_dxi = result.shape.dr[node];
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const Real dn_deta = result.shape.ds[node];
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result.displacement = result.displacement + n * translation + (0.5 * zeta * geometry.thickness * n) * q;
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result.du_dxi = result.du_dxi + dn_dxi * translation + (0.5 * zeta * geometry.thickness * dn_dxi) * q;
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result.du_deta = result.du_deta + dn_deta * translation + (0.5 * zeta * geometry.thickness * dn_deta) * q;
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result.du_dzeta = result.du_dzeta + (0.5 * geometry.thickness * n) * q;
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}
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return result;
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}
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inline void assignMITC4CovariantStrain(MITC4StrainVector& values, const MITC4IntegrationBasis& basis,
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const MITC4DisplacementDerivatives& derivatives) {
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values[strainComponentIndex(MITC4StrainComponent::Eps11)] = dot(derivatives.du_dxi, basis.g1);
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values[strainComponentIndex(MITC4StrainComponent::Eps22)] = dot(derivatives.du_deta, basis.g2);
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values[strainComponentIndex(MITC4StrainComponent::Eps33)] = 0.0;
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values[strainComponentIndex(MITC4StrainComponent::Gamma23)] = dot(derivatives.du_deta, basis.g3) + dot(derivatives.du_dzeta, basis.g2);
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values[strainComponentIndex(MITC4StrainComponent::Gamma13)] = dot(derivatives.du_dxi, basis.g3) + dot(derivatives.du_dzeta, basis.g1);
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values[strainComponentIndex(MITC4StrainComponent::Gamma12)] = dot(derivatives.du_dxi, basis.g2) + dot(derivatives.du_deta, basis.g1);
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}
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inline MITC4StrainEvaluation mitc4DirectCovariantStrain(const MITC4Geometry& geometry, const MITC4ElementDofVector& values,
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Real xi, Real eta, Real zeta) {
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MITC4StrainEvaluation result;
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const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
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appendDiagnostics(result.diagnostics, basis.diagnostics);
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const auto derivatives = mitc4DisplacementDerivatives(geometry, values, xi, eta, zeta);
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appendDiagnostics(result.diagnostics, derivatives.diagnostics);
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if (hasError(result.diagnostics)) {
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return result;
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}
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assignMITC4CovariantStrain(result.values, basis, derivatives);
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return result;
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}
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inline MITC4StrainRows mitc4DirectCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
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MITC4StrainRows result;
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const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
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appendDiagnostics(result.diagnostics, basis.diagnostics);
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if (hasError(result.diagnostics)) {
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return result;
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}
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for (std::size_t dof = 0; dof < 24; ++dof) {
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MITC4ElementDofVector unit{};
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unit.fill(0.0);
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unit[dof] = 1.0;
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const auto derivatives = mitc4DisplacementDerivatives(geometry, unit, xi, eta, zeta);
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appendDiagnostics(result.diagnostics, derivatives.diagnostics);
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if (hasError(result.diagnostics)) {
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return result;
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}
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MITC4StrainVector values{};
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assignMITC4CovariantStrain(values, basis, derivatives);
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for (std::size_t component = 0; component < 6; ++component) {
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result.rows[component][dof] = values[component];
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}
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}
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return result;
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}
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inline MITC4StrainEvaluation evaluateMITC4StrainRows(const MITC4StrainRows& rows, const MITC4ElementDofVector& values) {
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MITC4StrainEvaluation result;
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result.diagnostics = rows.diagnostics;
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if (hasError(result.diagnostics)) {
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return result;
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}
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for (std::size_t component = 0; component < 6; ++component) {
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for (std::size_t dof = 0; dof < 24; ++dof) {
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result.values[component] += rows.rows[component][dof] * values[dof];
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}
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}
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return result;
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}
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inline MITC4StrainRows mitc4TiedCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
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MITC4StrainRows result = mitc4DirectCovariantStrainRows(geometry, xi, eta, zeta);
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const auto direct_a = mitc4DirectCovariantStrainRows(geometry, 0.0, -1.0, zeta);
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const auto direct_b = mitc4DirectCovariantStrainRows(geometry, -1.0, 0.0, zeta);
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const auto direct_c = mitc4DirectCovariantStrainRows(geometry, 0.0, 1.0, zeta);
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const auto direct_d = mitc4DirectCovariantStrainRows(geometry, 1.0, 0.0, zeta);
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appendDiagnostics(result.diagnostics, direct_a.diagnostics);
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appendDiagnostics(result.diagnostics, direct_b.diagnostics);
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appendDiagnostics(result.diagnostics, direct_c.diagnostics);
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appendDiagnostics(result.diagnostics, direct_d.diagnostics);
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if (hasError(result.diagnostics)) {
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return result;
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}
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const std::size_t gamma23 = strainComponentIndex(MITC4StrainComponent::Gamma23);
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const std::size_t gamma13 = strainComponentIndex(MITC4StrainComponent::Gamma13);
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for (std::size_t dof = 0; dof < 24; ++dof) {
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result.rows[gamma13][dof] = 0.5 * (1.0 - eta) * direct_a.rows[gamma13][dof] +
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0.5 * (1.0 + eta) * direct_c.rows[gamma13][dof];
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result.rows[gamma23][dof] = 0.5 * (1.0 - xi) * direct_b.rows[gamma23][dof] +
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0.5 * (1.0 + xi) * direct_d.rows[gamma23][dof];
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}
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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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