refactor: extract mitc4 geometry strain helpers
This commit is contained in:
NINI
@@ -1,5 +1,7 @@
|
||||
#pragma once
|
||||
|
||||
#include "fesa/Element/MITC4Geometry.hpp"
|
||||
#include "fesa/Element/MITC4Kinematics.hpp"
|
||||
#include "fesa/ModuleInfo.hpp"
|
||||
|
||||
namespace fesa::module {
|
||||
|
||||
@@ -0,0 +1,265 @@
|
||||
#pragma once
|
||||
|
||||
#include "fesa/Math/Math.hpp"
|
||||
#include "fesa/Util/Util.hpp"
|
||||
|
||||
#include <array>
|
||||
#include <optional>
|
||||
#include <string>
|
||||
#include <utility>
|
||||
#include <vector>
|
||||
|
||||
namespace fesa {
|
||||
|
||||
struct ShapeData {
|
||||
std::array<Real, 4> n{};
|
||||
std::array<Real, 4> dr{};
|
||||
std::array<Real, 4> ds{};
|
||||
};
|
||||
|
||||
inline ShapeData shapeFunctions(Real r, Real s) {
|
||||
return { {
|
||||
0.25 * (1.0 - r) * (1.0 - s),
|
||||
0.25 * (1.0 + r) * (1.0 - s),
|
||||
0.25 * (1.0 + r) * (1.0 + s),
|
||||
0.25 * (1.0 - r) * (1.0 + s),
|
||||
},
|
||||
{
|
||||
-0.25 * (1.0 - s),
|
||||
0.25 * (1.0 - s),
|
||||
0.25 * (1.0 + s),
|
||||
-0.25 * (1.0 + s),
|
||||
},
|
||||
{
|
||||
-0.25 * (1.0 - r),
|
||||
-0.25 * (1.0 + r),
|
||||
0.25 * (1.0 + r),
|
||||
0.25 * (1.0 - r),
|
||||
} };
|
||||
}
|
||||
|
||||
struct LocalBasis {
|
||||
Vec3 e1;
|
||||
Vec3 e2;
|
||||
Vec3 e3;
|
||||
};
|
||||
|
||||
struct MITC4NaturalPoint {
|
||||
Real xi = 0.0;
|
||||
Real eta = 0.0;
|
||||
};
|
||||
|
||||
struct MITC4TyingPoint {
|
||||
std::string label;
|
||||
MITC4NaturalPoint natural;
|
||||
std::array<LocalIndex, 2> edge_node_indices{};
|
||||
};
|
||||
|
||||
inline std::array<MITC4NaturalPoint, 4> mitc4NodeNaturalCoordinates() {
|
||||
return {{{-1.0, -1.0}, {1.0, -1.0}, {1.0, 1.0}, {-1.0, 1.0}}};
|
||||
}
|
||||
|
||||
inline std::array<MITC4TyingPoint, 4> mitc4TyingPoints() {
|
||||
return {{{"A", {0.0, -1.0}, {0, 1}},
|
||||
{"B", {-1.0, 0.0}, {0, 3}},
|
||||
{"C", {0.0, 1.0}, {3, 2}},
|
||||
{"D", {1.0, 0.0}, {1, 2}}}};
|
||||
}
|
||||
|
||||
struct MITC4DirectorFrame {
|
||||
Vec3 v1;
|
||||
Vec3 v2;
|
||||
Vec3 vn;
|
||||
};
|
||||
|
||||
struct MITC4MidsurfaceDerivatives {
|
||||
ShapeData shape;
|
||||
Vec3 g1;
|
||||
Vec3 g2;
|
||||
};
|
||||
|
||||
struct MITC4Geometry {
|
||||
std::array<Vec3, 4> coordinates{};
|
||||
Real thickness = 0.0;
|
||||
ShapeData center_shape;
|
||||
Vec3 g1_center;
|
||||
Vec3 g2_center;
|
||||
Vec3 center_normal;
|
||||
std::array<MITC4DirectorFrame, 4> nodal_frames{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4IntegrationBasis {
|
||||
ShapeData shape;
|
||||
Vec3 g1;
|
||||
Vec3 g2;
|
||||
Vec3 g3;
|
||||
Real jacobian = 0.0;
|
||||
LocalBasis local;
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
inline Vec3 globalEX() {
|
||||
return {1.0, 0.0, 0.0};
|
||||
}
|
||||
|
||||
inline Vec3 globalEY() {
|
||||
return {0.0, 1.0, 0.0};
|
||||
}
|
||||
|
||||
inline Vec3 globalEZ() {
|
||||
return {0.0, 0.0, 1.0};
|
||||
}
|
||||
|
||||
inline Diagnostic mitc4Diagnostic(std::string code, std::string message) {
|
||||
return makeDiagnostic(Severity::Error, std::move(code), std::move(message), "mitc4", "<element>", 0);
|
||||
}
|
||||
|
||||
inline void appendDiagnostics(std::vector<Diagnostic>& target, const std::vector<Diagnostic>& source) {
|
||||
target.insert(target.end(), source.begin(), source.end());
|
||||
}
|
||||
|
||||
inline MITC4MidsurfaceDerivatives mitc4MidsurfaceDerivatives(const std::array<Vec3, 4>& coordinates,
|
||||
Real xi,
|
||||
Real eta) {
|
||||
MITC4MidsurfaceDerivatives result;
|
||||
result.shape = shapeFunctions(xi, eta);
|
||||
for (std::size_t i = 0; i < 4; ++i) {
|
||||
result.g1 = result.g1 + result.shape.dr[i] * coordinates[i];
|
||||
result.g2 = result.g2 + result.shape.ds[i] * coordinates[i];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline std::optional<Vec3> firstNormalizedCross(const std::array<Vec3, 3>& axes, const Vec3& vector, Real tolerance) {
|
||||
for (const Vec3& axis : axes) {
|
||||
auto candidate = normalizedIfValid(cross(axis, vector), tolerance);
|
||||
if (candidate) {
|
||||
return candidate;
|
||||
}
|
||||
}
|
||||
return std::nullopt;
|
||||
}
|
||||
|
||||
inline std::optional<MITC4DirectorFrame> buildMITC4DirectorFrame(const Vec3& normal, Real tolerance) {
|
||||
auto v1 = normalizedIfValid(cross(globalEY(), normal), tolerance);
|
||||
if (!v1) {
|
||||
v1 = firstNormalizedCross({globalEZ(), globalEX(), globalEY()}, normal, tolerance);
|
||||
}
|
||||
if (!v1) {
|
||||
return std::nullopt;
|
||||
}
|
||||
auto v2 = normalizedIfValid(cross(normal, *v1), tolerance);
|
||||
if (!v2) {
|
||||
return std::nullopt;
|
||||
}
|
||||
return MITC4DirectorFrame{*v1, *v2, normal};
|
||||
}
|
||||
|
||||
inline MITC4Geometry buildMITC4Geometry(const std::array<Vec3, 4>& coordinates,
|
||||
Real thickness,
|
||||
Real tolerance = 1.0e-12) {
|
||||
MITC4Geometry geometry;
|
||||
geometry.coordinates = coordinates;
|
||||
geometry.thickness = thickness;
|
||||
if (!isFinite(thickness) || thickness <= tolerance) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-THICKNESS", "MITC4 shell thickness must be positive and finite"));
|
||||
}
|
||||
for (const Vec3& coordinate : coordinates) {
|
||||
if (!isFinite(coordinate)) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-COORDINATE", "MITC4 element coordinates must be finite"));
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
const auto center = mitc4MidsurfaceDerivatives(coordinates, 0.0, 0.0);
|
||||
geometry.center_shape = center.shape;
|
||||
geometry.g1_center = center.g1;
|
||||
geometry.g2_center = center.g2;
|
||||
const auto normal = normalizedIfValid(cross(center.g1, center.g2), tolerance);
|
||||
if (!normal) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-NORMAL", "MITC4 element center normal is near zero"));
|
||||
return geometry;
|
||||
}
|
||||
geometry.center_normal = *normal;
|
||||
|
||||
const auto frame = buildMITC4DirectorFrame(*normal, tolerance);
|
||||
if (!frame) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 nodal director basis could not be constructed"));
|
||||
return geometry;
|
||||
}
|
||||
geometry.nodal_frames.fill(*frame);
|
||||
return geometry;
|
||||
}
|
||||
|
||||
inline MITC4IntegrationBasis computeMITC4IntegrationBasis(const MITC4Geometry& geometry,
|
||||
Real xi,
|
||||
Real eta,
|
||||
Real zeta,
|
||||
Real tolerance = 1.0e-12) {
|
||||
MITC4IntegrationBasis result;
|
||||
result.diagnostics = geometry.diagnostics;
|
||||
result.shape = shapeFunctions(xi, eta);
|
||||
for (std::size_t i = 0; i < 4; ++i) {
|
||||
const Vec3& coordinate = geometry.coordinates[i];
|
||||
const Vec3& normal = geometry.nodal_frames[i].vn;
|
||||
result.g1 = result.g1 + result.shape.dr[i] * coordinate +
|
||||
(0.5 * zeta * geometry.thickness * result.shape.dr[i]) * normal;
|
||||
result.g2 = result.g2 + result.shape.ds[i] * coordinate +
|
||||
(0.5 * zeta * geometry.thickness * result.shape.ds[i]) * normal;
|
||||
result.g3 = result.g3 + (0.5 * geometry.thickness * result.shape.n[i]) * normal;
|
||||
}
|
||||
|
||||
result.jacobian = dot(cross(result.g1, result.g2), result.g3);
|
||||
if (!isFinite(result.jacobian) || std::fabs(result.jacobian) <= tolerance) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-JACOBIAN", "MITC4 element Jacobian is near zero"));
|
||||
}
|
||||
|
||||
const auto e3 = normalizedIfValid(result.g3, tolerance);
|
||||
if (!e3) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis normal is near zero"));
|
||||
return result;
|
||||
}
|
||||
auto e1 = normalizedIfValid(cross(result.g2, *e3), tolerance);
|
||||
if (!e1) {
|
||||
e1 = firstNormalizedCross({globalEY(), globalEZ(), globalEX()}, *e3, tolerance);
|
||||
}
|
||||
if (!e1) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis tangent could not be constructed"));
|
||||
return result;
|
||||
}
|
||||
const auto e2 = normalizedIfValid(cross(*e3, *e1), tolerance);
|
||||
if (!e2) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis is not right-handed"));
|
||||
return result;
|
||||
}
|
||||
result.local = {*e1, *e2, *e3};
|
||||
return result;
|
||||
}
|
||||
|
||||
inline LocalBasis computeLocalBasis(const std::array<Vec3, 4>& coordinates) {
|
||||
const MITC4Geometry geometry = buildMITC4Geometry(coordinates, 1.0);
|
||||
if (!geometry.ok()) {
|
||||
throw std::runtime_error("invalid MITC4 geometry");
|
||||
}
|
||||
const MITC4DirectorFrame& frame = geometry.nodal_frames[0];
|
||||
return {frame.v1, frame.v2, frame.vn};
|
||||
}
|
||||
|
||||
} // namespace fesa
|
||||
@@ -0,0 +1,205 @@
|
||||
#pragma once
|
||||
|
||||
#include "fesa/Element/MITC4Geometry.hpp"
|
||||
|
||||
#include <array>
|
||||
#include <cstddef>
|
||||
#include <string>
|
||||
#include <vector>
|
||||
|
||||
namespace fesa {
|
||||
|
||||
using MITC4ElementDofVector = std::array<Real, 24>;
|
||||
using MITC4StrainVector = std::array<Real, 6>;
|
||||
using MITC4StrainRow = std::array<Real, 24>;
|
||||
using MITC4MaterialMatrix = std::array<std::array<Real, 6>, 6>;
|
||||
|
||||
enum class MITC4StrainComponent {
|
||||
Eps11 = 0,
|
||||
Eps22 = 1,
|
||||
Eps33 = 2,
|
||||
Gamma23 = 3,
|
||||
Gamma13 = 4,
|
||||
Gamma12 = 5
|
||||
};
|
||||
|
||||
inline std::size_t strainComponentIndex(MITC4StrainComponent component) {
|
||||
return static_cast<std::size_t>(component);
|
||||
}
|
||||
|
||||
inline std::array<std::string, 6> mitc4StrainComponentLabels() {
|
||||
return {"eps11", "eps22", "eps33", "gamma23", "gamma13", "gamma12"};
|
||||
}
|
||||
|
||||
struct MITC4LocalRotations {
|
||||
Real alpha = 0.0;
|
||||
Real beta = 0.0;
|
||||
Real gamma = 0.0;
|
||||
};
|
||||
|
||||
struct MITC4DisplacementDerivatives {
|
||||
ShapeData shape;
|
||||
Vec3 displacement;
|
||||
Vec3 du_dxi;
|
||||
Vec3 du_deta;
|
||||
Vec3 du_dzeta;
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4StrainEvaluation {
|
||||
MITC4StrainVector values{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4StrainRows {
|
||||
std::array<MITC4StrainRow, 6> rows{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
inline Vec3 mitc4NodalTranslation(const MITC4ElementDofVector& values, std::size_t node) {
|
||||
const std::size_t base = 6 * node;
|
||||
return {values[base + 0], values[base + 1], values[base + 2]};
|
||||
}
|
||||
|
||||
inline Vec3 mitc4NodalRotation(const MITC4ElementDofVector& values, std::size_t node) {
|
||||
const std::size_t base = 6 * node;
|
||||
return {values[base + 3], values[base + 4], values[base + 5]};
|
||||
}
|
||||
|
||||
inline MITC4LocalRotations mitc4LocalRotations(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
|
||||
return {dot(global_rotation, frame.v1), dot(global_rotation, frame.v2), dot(global_rotation, frame.vn)};
|
||||
}
|
||||
|
||||
inline Vec3 mitc4DirectorIncrement(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
|
||||
const MITC4LocalRotations rotations = mitc4LocalRotations(frame, global_rotation);
|
||||
return (-rotations.alpha) * frame.v2 + rotations.beta * frame.v1;
|
||||
}
|
||||
|
||||
inline MITC4DisplacementDerivatives mitc4DisplacementDerivatives(const MITC4Geometry& geometry,
|
||||
const MITC4ElementDofVector& values,
|
||||
Real xi,
|
||||
Real eta,
|
||||
Real zeta) {
|
||||
MITC4DisplacementDerivatives result;
|
||||
result.diagnostics = geometry.diagnostics;
|
||||
result.shape = shapeFunctions(xi, eta);
|
||||
for (std::size_t node = 0; node < 4; ++node) {
|
||||
const Vec3 translation = mitc4NodalTranslation(values, node);
|
||||
const Vec3 rotation = mitc4NodalRotation(values, node);
|
||||
const Vec3 q = mitc4DirectorIncrement(geometry.nodal_frames[node], rotation);
|
||||
const Real n = result.shape.n[node];
|
||||
const Real dn_dxi = result.shape.dr[node];
|
||||
const Real dn_deta = result.shape.ds[node];
|
||||
result.displacement = result.displacement + n * translation + (0.5 * zeta * geometry.thickness * n) * q;
|
||||
result.du_dxi = result.du_dxi + dn_dxi * translation + (0.5 * zeta * geometry.thickness * dn_dxi) * q;
|
||||
result.du_deta = result.du_deta + dn_deta * translation + (0.5 * zeta * geometry.thickness * dn_deta) * q;
|
||||
result.du_dzeta = result.du_dzeta + (0.5 * geometry.thickness * n) * q;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline void assignMITC4CovariantStrain(MITC4StrainVector& values,
|
||||
const MITC4IntegrationBasis& basis,
|
||||
const MITC4DisplacementDerivatives& derivatives) {
|
||||
values[strainComponentIndex(MITC4StrainComponent::Eps11)] = dot(derivatives.du_dxi, basis.g1);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Eps22)] = dot(derivatives.du_deta, basis.g2);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Eps33)] = 0.0;
|
||||
values[strainComponentIndex(MITC4StrainComponent::Gamma23)] = dot(derivatives.du_deta, basis.g3) + dot(derivatives.du_dzeta, basis.g2);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Gamma13)] = dot(derivatives.du_dxi, basis.g3) + dot(derivatives.du_dzeta, basis.g1);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Gamma12)] = dot(derivatives.du_dxi, basis.g2) + dot(derivatives.du_deta, basis.g1);
|
||||
}
|
||||
|
||||
inline MITC4StrainEvaluation mitc4DirectCovariantStrain(const MITC4Geometry& geometry,
|
||||
const MITC4ElementDofVector& values,
|
||||
Real xi,
|
||||
Real eta,
|
||||
Real zeta) {
|
||||
MITC4StrainEvaluation result;
|
||||
const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, basis.diagnostics);
|
||||
const auto derivatives = mitc4DisplacementDerivatives(geometry, values, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, derivatives.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
assignMITC4CovariantStrain(result.values, basis, derivatives);
|
||||
return result;
|
||||
}
|
||||
|
||||
inline MITC4StrainRows mitc4DirectCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
|
||||
MITC4StrainRows result;
|
||||
const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, basis.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
for (std::size_t dof = 0; dof < 24; ++dof) {
|
||||
MITC4ElementDofVector unit{};
|
||||
unit.fill(0.0);
|
||||
unit[dof] = 1.0;
|
||||
const auto derivatives = mitc4DisplacementDerivatives(geometry, unit, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, derivatives.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
MITC4StrainVector values{};
|
||||
assignMITC4CovariantStrain(values, basis, derivatives);
|
||||
for (std::size_t component = 0; component < 6; ++component) {
|
||||
result.rows[component][dof] = values[component];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline MITC4StrainEvaluation evaluateMITC4StrainRows(const MITC4StrainRows& rows,
|
||||
const MITC4ElementDofVector& values) {
|
||||
MITC4StrainEvaluation result;
|
||||
result.diagnostics = rows.diagnostics;
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
for (std::size_t component = 0; component < 6; ++component) {
|
||||
for (std::size_t dof = 0; dof < 24; ++dof) {
|
||||
result.values[component] += rows.rows[component][dof] * values[dof];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline MITC4StrainRows mitc4TiedCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
|
||||
MITC4StrainRows result = mitc4DirectCovariantStrainRows(geometry, xi, eta, zeta);
|
||||
const auto direct_a = mitc4DirectCovariantStrainRows(geometry, 0.0, -1.0, zeta);
|
||||
const auto direct_b = mitc4DirectCovariantStrainRows(geometry, -1.0, 0.0, zeta);
|
||||
const auto direct_c = mitc4DirectCovariantStrainRows(geometry, 0.0, 1.0, zeta);
|
||||
const auto direct_d = mitc4DirectCovariantStrainRows(geometry, 1.0, 0.0, zeta);
|
||||
appendDiagnostics(result.diagnostics, direct_a.diagnostics);
|
||||
appendDiagnostics(result.diagnostics, direct_b.diagnostics);
|
||||
appendDiagnostics(result.diagnostics, direct_c.diagnostics);
|
||||
appendDiagnostics(result.diagnostics, direct_d.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
const std::size_t gamma23 = strainComponentIndex(MITC4StrainComponent::Gamma23);
|
||||
const std::size_t gamma13 = strainComponentIndex(MITC4StrainComponent::Gamma13);
|
||||
for (std::size_t dof = 0; dof < 24; ++dof) {
|
||||
result.rows[gamma13][dof] = 0.5 * (1.0 - eta) * direct_a.rows[gamma13][dof] +
|
||||
0.5 * (1.0 + eta) * direct_c.rows[gamma13][dof];
|
||||
result.rows[gamma23][dof] = 0.5 * (1.0 - xi) * direct_b.rows[gamma23][dof] +
|
||||
0.5 * (1.0 + xi) * direct_d.rows[gamma23][dof];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
} // namespace fesa
|
||||
+1
-429
@@ -2,6 +2,7 @@
|
||||
|
||||
#include "fesa/Boundary/Boundary.hpp"
|
||||
#include "fesa/Core/Core.hpp"
|
||||
#include "fesa/Element/Element.hpp"
|
||||
#include "fesa/IO/IO.hpp"
|
||||
#include "fesa/Load/Load.hpp"
|
||||
#include "fesa/Math/Math.hpp"
|
||||
@@ -68,161 +69,6 @@ inline std::vector<Real> recoverFullReaction(const DenseMatrix& k_full, const st
|
||||
return reaction;
|
||||
}
|
||||
|
||||
struct ShapeData {
|
||||
std::array<Real, 4> n{};
|
||||
std::array<Real, 4> dr{};
|
||||
std::array<Real, 4> ds{};
|
||||
};
|
||||
|
||||
inline ShapeData shapeFunctions(Real r, Real s) {
|
||||
return {{
|
||||
0.25 * (1.0 - r) * (1.0 - s),
|
||||
0.25 * (1.0 + r) * (1.0 - s),
|
||||
0.25 * (1.0 + r) * (1.0 + s),
|
||||
0.25 * (1.0 - r) * (1.0 + s),
|
||||
},
|
||||
{
|
||||
-0.25 * (1.0 - s),
|
||||
0.25 * (1.0 - s),
|
||||
0.25 * (1.0 + s),
|
||||
-0.25 * (1.0 + s),
|
||||
},
|
||||
{
|
||||
-0.25 * (1.0 - r),
|
||||
-0.25 * (1.0 + r),
|
||||
0.25 * (1.0 + r),
|
||||
0.25 * (1.0 - r),
|
||||
}};
|
||||
}
|
||||
|
||||
struct LocalBasis {
|
||||
Vec3 e1;
|
||||
Vec3 e2;
|
||||
Vec3 e3;
|
||||
};
|
||||
|
||||
struct MITC4NaturalPoint {
|
||||
Real xi = 0.0;
|
||||
Real eta = 0.0;
|
||||
};
|
||||
|
||||
struct MITC4TyingPoint {
|
||||
std::string label;
|
||||
MITC4NaturalPoint natural;
|
||||
std::array<LocalIndex, 2> edge_node_indices{};
|
||||
};
|
||||
|
||||
inline std::array<MITC4NaturalPoint, 4> mitc4NodeNaturalCoordinates() {
|
||||
return {{{-1.0, -1.0}, {1.0, -1.0}, {1.0, 1.0}, {-1.0, 1.0}}};
|
||||
}
|
||||
|
||||
inline std::array<MITC4TyingPoint, 4> mitc4TyingPoints() {
|
||||
return {{{"A", {0.0, -1.0}, {0, 1}},
|
||||
{"B", {-1.0, 0.0}, {0, 3}},
|
||||
{"C", {0.0, 1.0}, {3, 2}},
|
||||
{"D", {1.0, 0.0}, {1, 2}}}};
|
||||
}
|
||||
|
||||
struct MITC4DirectorFrame {
|
||||
Vec3 v1;
|
||||
Vec3 v2;
|
||||
Vec3 vn;
|
||||
};
|
||||
|
||||
struct MITC4MidsurfaceDerivatives {
|
||||
ShapeData shape;
|
||||
Vec3 g1;
|
||||
Vec3 g2;
|
||||
};
|
||||
|
||||
struct MITC4Geometry {
|
||||
std::array<Vec3, 4> coordinates{};
|
||||
Real thickness = 0.0;
|
||||
ShapeData center_shape;
|
||||
Vec3 g1_center;
|
||||
Vec3 g2_center;
|
||||
Vec3 center_normal;
|
||||
std::array<MITC4DirectorFrame, 4> nodal_frames{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4IntegrationBasis {
|
||||
ShapeData shape;
|
||||
Vec3 g1;
|
||||
Vec3 g2;
|
||||
Vec3 g3;
|
||||
Real jacobian = 0.0;
|
||||
LocalBasis local;
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
using MITC4ElementDofVector = std::array<Real, 24>;
|
||||
using MITC4StrainVector = std::array<Real, 6>;
|
||||
using MITC4StrainRow = std::array<Real, 24>;
|
||||
using MITC4MaterialMatrix = std::array<std::array<Real, 6>, 6>;
|
||||
|
||||
enum class MITC4StrainComponent {
|
||||
Eps11 = 0,
|
||||
Eps22 = 1,
|
||||
Eps33 = 2,
|
||||
Gamma23 = 3,
|
||||
Gamma13 = 4,
|
||||
Gamma12 = 5
|
||||
};
|
||||
|
||||
inline std::size_t strainComponentIndex(MITC4StrainComponent component) {
|
||||
return static_cast<std::size_t>(component);
|
||||
}
|
||||
|
||||
inline std::array<std::string, 6> mitc4StrainComponentLabels() {
|
||||
return {"eps11", "eps22", "eps33", "gamma23", "gamma13", "gamma12"};
|
||||
}
|
||||
|
||||
struct MITC4LocalRotations {
|
||||
Real alpha = 0.0;
|
||||
Real beta = 0.0;
|
||||
Real gamma = 0.0;
|
||||
};
|
||||
|
||||
struct MITC4DisplacementDerivatives {
|
||||
ShapeData shape;
|
||||
Vec3 displacement;
|
||||
Vec3 du_dxi;
|
||||
Vec3 du_deta;
|
||||
Vec3 du_dzeta;
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4StrainEvaluation {
|
||||
MITC4StrainVector values{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4StrainRows {
|
||||
std::array<MITC4StrainRow, 6> rows{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
|
||||
bool ok() const {
|
||||
return !hasError(diagnostics);
|
||||
}
|
||||
};
|
||||
|
||||
struct MITC4MaterialMatrixEvaluation {
|
||||
MITC4MaterialMatrix matrix{};
|
||||
std::vector<Diagnostic> diagnostics;
|
||||
@@ -271,271 +117,6 @@ struct MITC4MaterialIntegrationData {
|
||||
}
|
||||
};
|
||||
|
||||
inline Vec3 globalEX() {
|
||||
return {1.0, 0.0, 0.0};
|
||||
}
|
||||
|
||||
inline Vec3 globalEY() {
|
||||
return {0.0, 1.0, 0.0};
|
||||
}
|
||||
|
||||
inline Vec3 globalEZ() {
|
||||
return {0.0, 0.0, 1.0};
|
||||
}
|
||||
|
||||
inline Diagnostic mitc4Diagnostic(std::string code, std::string message) {
|
||||
return makeDiagnostic(Severity::Error, std::move(code), std::move(message), "mitc4", "<element>", 0);
|
||||
}
|
||||
|
||||
inline void appendDiagnostics(std::vector<Diagnostic>& target, const std::vector<Diagnostic>& source) {
|
||||
target.insert(target.end(), source.begin(), source.end());
|
||||
}
|
||||
|
||||
inline MITC4MidsurfaceDerivatives mitc4MidsurfaceDerivatives(const std::array<Vec3, 4>& coordinates, Real xi, Real eta) {
|
||||
MITC4MidsurfaceDerivatives result;
|
||||
result.shape = shapeFunctions(xi, eta);
|
||||
for (std::size_t i = 0; i < 4; ++i) {
|
||||
result.g1 = result.g1 + result.shape.dr[i] * coordinates[i];
|
||||
result.g2 = result.g2 + result.shape.ds[i] * coordinates[i];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline std::optional<Vec3> firstNormalizedCross(const std::array<Vec3, 3>& axes, const Vec3& vector, Real tolerance) {
|
||||
for (const Vec3& axis : axes) {
|
||||
auto candidate = normalizedIfValid(cross(axis, vector), tolerance);
|
||||
if (candidate) {
|
||||
return candidate;
|
||||
}
|
||||
}
|
||||
return std::nullopt;
|
||||
}
|
||||
|
||||
inline std::optional<MITC4DirectorFrame> buildMITC4DirectorFrame(const Vec3& normal, Real tolerance) {
|
||||
auto v1 = normalizedIfValid(cross(globalEY(), normal), tolerance);
|
||||
if (!v1) {
|
||||
v1 = firstNormalizedCross({globalEZ(), globalEX(), globalEY()}, normal, tolerance);
|
||||
}
|
||||
if (!v1) {
|
||||
return std::nullopt;
|
||||
}
|
||||
auto v2 = normalizedIfValid(cross(normal, *v1), tolerance);
|
||||
if (!v2) {
|
||||
return std::nullopt;
|
||||
}
|
||||
return MITC4DirectorFrame{*v1, *v2, normal};
|
||||
}
|
||||
|
||||
inline MITC4Geometry buildMITC4Geometry(const std::array<Vec3, 4>& coordinates, Real thickness, Real tolerance = 1.0e-12) {
|
||||
MITC4Geometry geometry;
|
||||
geometry.coordinates = coordinates;
|
||||
geometry.thickness = thickness;
|
||||
if (!isFinite(thickness) || thickness <= tolerance) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-THICKNESS", "MITC4 shell thickness must be positive and finite"));
|
||||
}
|
||||
for (const Vec3& coordinate : coordinates) {
|
||||
if (!isFinite(coordinate)) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-COORDINATE", "MITC4 element coordinates must be finite"));
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
const auto center = mitc4MidsurfaceDerivatives(coordinates, 0.0, 0.0);
|
||||
geometry.center_shape = center.shape;
|
||||
geometry.g1_center = center.g1;
|
||||
geometry.g2_center = center.g2;
|
||||
const auto normal = normalizedIfValid(cross(center.g1, center.g2), tolerance);
|
||||
if (!normal) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-NORMAL", "MITC4 element center normal is near zero"));
|
||||
return geometry;
|
||||
}
|
||||
geometry.center_normal = *normal;
|
||||
|
||||
const auto frame = buildMITC4DirectorFrame(*normal, tolerance);
|
||||
if (!frame) {
|
||||
geometry.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 nodal director basis could not be constructed"));
|
||||
return geometry;
|
||||
}
|
||||
geometry.nodal_frames.fill(*frame);
|
||||
return geometry;
|
||||
}
|
||||
|
||||
inline MITC4IntegrationBasis computeMITC4IntegrationBasis(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta,
|
||||
Real tolerance = 1.0e-12) {
|
||||
MITC4IntegrationBasis result;
|
||||
result.diagnostics = geometry.diagnostics;
|
||||
result.shape = shapeFunctions(xi, eta);
|
||||
for (std::size_t i = 0; i < 4; ++i) {
|
||||
const Vec3& coordinate = geometry.coordinates[i];
|
||||
const Vec3& normal = geometry.nodal_frames[i].vn;
|
||||
result.g1 = result.g1 + result.shape.dr[i] * coordinate +
|
||||
(0.5 * zeta * geometry.thickness * result.shape.dr[i]) * normal;
|
||||
result.g2 = result.g2 + result.shape.ds[i] * coordinate +
|
||||
(0.5 * zeta * geometry.thickness * result.shape.ds[i]) * normal;
|
||||
result.g3 = result.g3 + (0.5 * geometry.thickness * result.shape.n[i]) * normal;
|
||||
}
|
||||
|
||||
result.jacobian = dot(cross(result.g1, result.g2), result.g3);
|
||||
if (!isFinite(result.jacobian) || std::fabs(result.jacobian) <= tolerance) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-JACOBIAN", "MITC4 element Jacobian is near zero"));
|
||||
}
|
||||
|
||||
const auto e3 = normalizedIfValid(result.g3, tolerance);
|
||||
if (!e3) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis normal is near zero"));
|
||||
return result;
|
||||
}
|
||||
auto e1 = normalizedIfValid(cross(result.g2, *e3), tolerance);
|
||||
if (!e1) {
|
||||
e1 = firstNormalizedCross({globalEY(), globalEZ(), globalEX()}, *e3, tolerance);
|
||||
}
|
||||
if (!e1) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis tangent could not be constructed"));
|
||||
return result;
|
||||
}
|
||||
const auto e2 = normalizedIfValid(cross(*e3, *e1), tolerance);
|
||||
if (!e2) {
|
||||
result.diagnostics.push_back(
|
||||
mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis is not right-handed"));
|
||||
return result;
|
||||
}
|
||||
result.local = {*e1, *e2, *e3};
|
||||
return result;
|
||||
}
|
||||
|
||||
inline Vec3 mitc4NodalTranslation(const MITC4ElementDofVector& values, std::size_t node) {
|
||||
const std::size_t base = 6 * node;
|
||||
return {values[base + 0], values[base + 1], values[base + 2]};
|
||||
}
|
||||
|
||||
inline Vec3 mitc4NodalRotation(const MITC4ElementDofVector& values, std::size_t node) {
|
||||
const std::size_t base = 6 * node;
|
||||
return {values[base + 3], values[base + 4], values[base + 5]};
|
||||
}
|
||||
|
||||
inline MITC4LocalRotations mitc4LocalRotations(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
|
||||
return {dot(global_rotation, frame.v1), dot(global_rotation, frame.v2), dot(global_rotation, frame.vn)};
|
||||
}
|
||||
|
||||
inline Vec3 mitc4DirectorIncrement(const MITC4DirectorFrame& frame, const Vec3& global_rotation) {
|
||||
const MITC4LocalRotations rotations = mitc4LocalRotations(frame, global_rotation);
|
||||
return (-rotations.alpha) * frame.v2 + rotations.beta * frame.v1;
|
||||
}
|
||||
|
||||
inline MITC4DisplacementDerivatives mitc4DisplacementDerivatives(const MITC4Geometry& geometry, const MITC4ElementDofVector& values,
|
||||
Real xi, Real eta, Real zeta) {
|
||||
MITC4DisplacementDerivatives result;
|
||||
result.diagnostics = geometry.diagnostics;
|
||||
result.shape = shapeFunctions(xi, eta);
|
||||
for (std::size_t node = 0; node < 4; ++node) {
|
||||
const Vec3 translation = mitc4NodalTranslation(values, node);
|
||||
const Vec3 rotation = mitc4NodalRotation(values, node);
|
||||
const Vec3 q = mitc4DirectorIncrement(geometry.nodal_frames[node], rotation);
|
||||
const Real n = result.shape.n[node];
|
||||
const Real dn_dxi = result.shape.dr[node];
|
||||
const Real dn_deta = result.shape.ds[node];
|
||||
result.displacement = result.displacement + n * translation + (0.5 * zeta * geometry.thickness * n) * q;
|
||||
result.du_dxi = result.du_dxi + dn_dxi * translation + (0.5 * zeta * geometry.thickness * dn_dxi) * q;
|
||||
result.du_deta = result.du_deta + dn_deta * translation + (0.5 * zeta * geometry.thickness * dn_deta) * q;
|
||||
result.du_dzeta = result.du_dzeta + (0.5 * geometry.thickness * n) * q;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline void assignMITC4CovariantStrain(MITC4StrainVector& values, const MITC4IntegrationBasis& basis,
|
||||
const MITC4DisplacementDerivatives& derivatives) {
|
||||
values[strainComponentIndex(MITC4StrainComponent::Eps11)] = dot(derivatives.du_dxi, basis.g1);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Eps22)] = dot(derivatives.du_deta, basis.g2);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Eps33)] = 0.0;
|
||||
values[strainComponentIndex(MITC4StrainComponent::Gamma23)] = dot(derivatives.du_deta, basis.g3) + dot(derivatives.du_dzeta, basis.g2);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Gamma13)] = dot(derivatives.du_dxi, basis.g3) + dot(derivatives.du_dzeta, basis.g1);
|
||||
values[strainComponentIndex(MITC4StrainComponent::Gamma12)] = dot(derivatives.du_dxi, basis.g2) + dot(derivatives.du_deta, basis.g1);
|
||||
}
|
||||
|
||||
inline MITC4StrainEvaluation mitc4DirectCovariantStrain(const MITC4Geometry& geometry, const MITC4ElementDofVector& values,
|
||||
Real xi, Real eta, Real zeta) {
|
||||
MITC4StrainEvaluation result;
|
||||
const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, basis.diagnostics);
|
||||
const auto derivatives = mitc4DisplacementDerivatives(geometry, values, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, derivatives.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
assignMITC4CovariantStrain(result.values, basis, derivatives);
|
||||
return result;
|
||||
}
|
||||
|
||||
inline MITC4StrainRows mitc4DirectCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
|
||||
MITC4StrainRows result;
|
||||
const auto basis = computeMITC4IntegrationBasis(geometry, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, basis.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
for (std::size_t dof = 0; dof < 24; ++dof) {
|
||||
MITC4ElementDofVector unit{};
|
||||
unit.fill(0.0);
|
||||
unit[dof] = 1.0;
|
||||
const auto derivatives = mitc4DisplacementDerivatives(geometry, unit, xi, eta, zeta);
|
||||
appendDiagnostics(result.diagnostics, derivatives.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
MITC4StrainVector values{};
|
||||
assignMITC4CovariantStrain(values, basis, derivatives);
|
||||
for (std::size_t component = 0; component < 6; ++component) {
|
||||
result.rows[component][dof] = values[component];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline MITC4StrainEvaluation evaluateMITC4StrainRows(const MITC4StrainRows& rows, const MITC4ElementDofVector& values) {
|
||||
MITC4StrainEvaluation result;
|
||||
result.diagnostics = rows.diagnostics;
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
for (std::size_t component = 0; component < 6; ++component) {
|
||||
for (std::size_t dof = 0; dof < 24; ++dof) {
|
||||
result.values[component] += rows.rows[component][dof] * values[dof];
|
||||
}
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline MITC4StrainRows mitc4TiedCovariantStrainRows(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta) {
|
||||
MITC4StrainRows result = mitc4DirectCovariantStrainRows(geometry, xi, eta, zeta);
|
||||
const auto direct_a = mitc4DirectCovariantStrainRows(geometry, 0.0, -1.0, zeta);
|
||||
const auto direct_b = mitc4DirectCovariantStrainRows(geometry, -1.0, 0.0, zeta);
|
||||
const auto direct_c = mitc4DirectCovariantStrainRows(geometry, 0.0, 1.0, zeta);
|
||||
const auto direct_d = mitc4DirectCovariantStrainRows(geometry, 1.0, 0.0, zeta);
|
||||
appendDiagnostics(result.diagnostics, direct_a.diagnostics);
|
||||
appendDiagnostics(result.diagnostics, direct_b.diagnostics);
|
||||
appendDiagnostics(result.diagnostics, direct_c.diagnostics);
|
||||
appendDiagnostics(result.diagnostics, direct_d.diagnostics);
|
||||
if (hasError(result.diagnostics)) {
|
||||
return result;
|
||||
}
|
||||
const std::size_t gamma23 = strainComponentIndex(MITC4StrainComponent::Gamma23);
|
||||
const std::size_t gamma13 = strainComponentIndex(MITC4StrainComponent::Gamma13);
|
||||
for (std::size_t dof = 0; dof < 24; ++dof) {
|
||||
result.rows[gamma13][dof] = 0.5 * (1.0 - eta) * direct_a.rows[gamma13][dof] +
|
||||
0.5 * (1.0 + eta) * direct_c.rows[gamma13][dof];
|
||||
result.rows[gamma23][dof] = 0.5 * (1.0 - xi) * direct_b.rows[gamma23][dof] +
|
||||
0.5 * (1.0 + xi) * direct_d.rows[gamma23][dof];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
inline std::array<MITC4IntegrationPoint, 8> mitc4GaussQuadrature2x2x2() {
|
||||
const Real gauss = 1.0 / std::sqrt(3.0);
|
||||
const std::array<Real, 2> points = {-gauss, gauss};
|
||||
@@ -739,15 +320,6 @@ inline MITC4MaterialIntegrationData mitc4BuildMaterialIntegrationData(const MITC
|
||||
return data;
|
||||
}
|
||||
|
||||
inline LocalBasis computeLocalBasis(const std::array<Vec3, 4>& coordinates) {
|
||||
const MITC4Geometry geometry = buildMITC4Geometry(coordinates, 1.0);
|
||||
if (!geometry.ok()) {
|
||||
throw std::runtime_error("invalid MITC4 geometry");
|
||||
}
|
||||
const MITC4DirectorFrame& frame = geometry.nodal_frames[0];
|
||||
return {frame.v1, frame.v2, frame.vn};
|
||||
}
|
||||
|
||||
struct ElementStiffnessOptions {
|
||||
Real drilling_stiffness_scale = 1.0e-3;
|
||||
};
|
||||
|
||||
Reference in New Issue
Block a user