mkse

2026-09-01 10:00:04 +03:00
parent 2168b2200a
commit 8be40ef77c
18 changed files with 3646 additions and 0 deletions
@@ -0,0 +1,115 @@
+#pragma once
+
+// Axisymmetric finite-element integration kernels.
+
+#include <array>
+#include <cmath>
+
+#include "Elasticity.h"
+
+namespace fem_axisymmetric {
+
+constexpr double kTwoPi = 6.28318530717958647692;
+
+struct TriangleQuadraturePoint {
+	double weight;
+	std::array<double, 3> phi;
+};
+
+inline const std::array<TriangleQuadraturePoint, 3> kTriangleQuadrature = { {
+	{ 1.0 / 3.0, { 1.0 / 6.0, 1.0 / 6.0, 2.0 / 3.0 } },
+	{ 1.0 / 3.0, { 1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0 } },
+	{ 1.0 / 3.0, { 2.0 / 3.0, 1.0 / 6.0, 1.0 / 6.0 } }
+} };
+
+inline double signed_double_area(const Point& p1, const Point& p2, const Point& p3) {
+	return (p2.x - p1.x) * (p3.y - p1.y) - (p3.x - p1.x) * (p2.y - p1.y);
+}
+
+inline void assemble(
+	Matrix& A,
+	std::vector<double>& F,
+	const std::vector<Point>& points,
+	const std::vector<Triangle>& triangles,
+	double,
+	double E,
+	double nu,
+	const vec_function& f) {
+
+	const double lambda = (E * nu) / ((1.0 + nu) * (1.0 - 2.0 * nu));
+	const double mu = E / (2.0 * (1.0 + nu));
+	const Matrix C({
+		{ lambda + 2.0 * mu, lambda, lambda, 0.0 },
+		{ lambda, lambda + 2.0 * mu, lambda, 0.0 },
+		{ lambda, lambda, lambda + 2.0 * mu, 0.0 },
+		{ 0.0, 0.0, 0.0, mu }
+	});
+
+	for (const Triangle& T : triangles) {
+		const Point& p1 = points[T.a];
+		const Point& p2 = points[T.b];
+		const Point& p3 = points[T.c];
+		const double two_area = signed_double_area(p1, p2, p3);
+		const double area = 0.5 * std::fabs(two_area);
+
+		const Matrix grad_phi({
+			{ (p2.y - p3.y) / two_area, (p3.x - p2.x) / two_area },
+			{ (p3.y - p1.y) / two_area, (p1.x - p3.x) / two_area },
+			{ (p1.y - p2.y) / two_area, (p2.x - p1.x) / two_area }
+		});
+
+		Matrix Ae(6ull);
+		std::vector<double> Fe(6, 0.0);
+		for (const auto& qp : kTriangleQuadrature) {
+			const Point q = qp.phi[0] * p1 + qp.phi[1] * p2 + qp.phi[2] * p3;
+			const double r_q = q.x;
+
+			Matrix B(4ull, 6ull);
+			for (size_t p = 0; p < 3; ++p) {
+				const double dphi_dr = grad_phi[p][0];
+				const double dphi_dz = grad_phi[p][1];
+				const double phi = qp.phi[p];
+
+				B[0][2 * p] = dphi_dr;
+				B[1][2 * p + 1] = dphi_dz;
+				B[2][2 * p] = phi / r_q;
+				B[3][2 * p] = dphi_dz;
+				B[3][2 * p + 1] = dphi_dr;
+			}
+
+			const Matrix stiffness_q = B.T().dot(C).dot(B);
+			const double weight = kTwoPi * area * qp.weight * r_q;
+			for (size_t i = 0; i < 6; ++i)
+				for (size_t j = 0; j < 6; ++j)
+					Ae[i][j] += weight * stiffness_q[i][j];
+
+			const Point body_force = f(q);
+			for (size_t p = 0; p < 3; ++p) {
+				const double shape_value = qp.phi[p];
+				Fe[2 * p] += weight * shape_value * body_force.x;
+				Fe[2 * p + 1] += weight * shape_value * body_force.y;
+			}
+		}
+
+		auto dof = [T](size_t i) -> size_t {
+			if (i == 0) return 2 * T.a;
+			if (i == 1) return 2 * T.a + 1;
+			if (i == 2) return 2 * T.b;
+			if (i == 3) return 2 * T.b + 1;
+			if (i == 4) return 2 * T.c;
+			return 2 * T.c + 1;
+		};
+
+		for (size_t i = 0; i < 6; ++i) {
+			F[dof(i)] += Fe[i];
+			for (size_t j = 0; j < 6; ++j)
+				A[dof(i)][dof(j)] += Ae[i][j];
+		}
+	}
+}
+
+inline double boundary_segment_weight(const Point& midpoint, double len) {
+	return 0.5 * kTwoPi * midpoint.x * len;
+}
+
+} // namespace fem_axisymmetric