77 lines
1.9 KiB
C++
77 lines
1.9 KiB
C++
|
#pragma once
|
||
|
|
|
||
|
|
// Cartesian finite-element integration kernels.
|
||
|
|
|
||
|
|
#include "Elasticity.h"
|
||
|
|
|
||
|
|
namespace fem_cartesian {
|
||
|
|
|
||
|
|
inline void assemble(
|
||
|
|
Matrix& A,
|
||
|
|
std::vector<double>& F,
|
||
|
|
const std::vector<Point>& points,
|
||
|
|
const std::vector<Triangle>& triangles,
|
||
|
|
double triangle_area,
|
||
|
|
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, 0.0 },
|
||
|
|
{ lambda, lambda + 2.0 * mu, 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 Matrix grad_phi({
|
||
|
|
{ (p2.y - p3.y) / (2.0 * triangle_area), (p3.x - p2.x) / (2.0 * triangle_area) },
|
||
|
|
{ (p3.y - p1.y) / (2.0 * triangle_area), (p1.x - p3.x) / (2.0 * triangle_area) },
|
||
|
|
{ (p1.y - p2.y) / (2.0 * triangle_area), (p2.x - p1.x) / (2.0 * triangle_area) }
|
||
|
|
});
|
||
|
|
|
||
|
|
Matrix R(3, 6ull);
|
||
|
|
for (size_t p = 0; p < 3; ++p) {
|
||
|
|
R[0][2 * p] = grad_phi[p][0];
|
||
|
|
R[1][2 * p + 1] = grad_phi[p][1];
|
||
|
|
R[2][2 * p] = grad_phi[p][1];
|
||
|
|
R[2][2 * p + 1] = grad_phi[p][0];
|
||
|
|
}
|
||
|
|
|
||
|
|
Matrix Ae = triangle_area * R.T().dot(C).dot(R);
|
||
|
|
|
||
|
|
std::vector<double> Fe(6, 0.0);
|
||
|
|
const Point center = (p1 + p2 + p3) / 3.0;
|
||
|
|
const Point body_force = f(center);
|
||
|
|
for (size_t p = 0; p < 3; ++p) {
|
||
|
|
Fe[2 * p] = body_force.x * triangle_area / 3.0;
|
||
|
|
Fe[2 * p + 1] = body_force.y * triangle_area / 3.0;
|
||
|
|
}
|
||
|
|
|
||
|
|
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&, double len) {
|
||
|
|
return 0.5 * len;
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace fem_cartesian
|