// // Created by Wei Chen on 3/2/22 // #include #include #include "Material.hpp" namespace da::sha { namespace top { Material::Material(double p_YM, double p_PR, double p_density, double p_alpha) : YM(p_YM), PR(p_PR), density(p_density), alpha(p_alpha) { D.setZero(); D(0, 0) = 1.0 - PR; D(0, 1) = PR; D(0, 2) = PR; D(1, 0) = PR; D(1, 1) = 1.0 - PR; D(1, 2) = PR; D(2, 0) = PR; D(2, 1) = PR; D(2, 2) = 1.0 - PR; D(3, 3) = (1.0 - 2.0 * PR) / 2.0; D(4, 4) = (1.0 - 2.0 * PR) / 2.0; D(5, 5) = (1.0 - 2.0 * PR) / 2.0; D = YM / (1.0 + PR) / (1.0 - 2.0 * PR) * D; spdlog::info( "linear elastic material: Young's modulus = {}, Poisson's ratio = {}, density = {}, scaling factor alpha = {}", YM, PR, density, alpha); } // a, b, c: **half** size of hex element void Material::computeKe(double a, double b, double c, const Eigen::Matrix &D, Eigen::Matrix &Ke) { Eigen::Vector2d GP(-1.0 / sqrt(3.0), 1.0 / sqrt(3.0)); Eigen::Vector2d GW(1.0, 1.0); Ke.setZero(); Eigen::Matrix L = Eigen::Matrix::Zero(); L(0, 0) = 1.0; L(1, 4) = 1.0; L(2, 8) = 1.0; L(3, 1) = 1.0; L(3, 3) = 1.0; L(4, 5) = 1.0; L(4, 7) = 1.0; L(5, 2) = 1.0; L(5, 6) = 1.0; Eigen::Matrix tmp{ {-a, -b, -c}, {a, -b, -c}, {a, b, -c}, {-a, b, -c}, {-a, -b, c}, {a, -b, c}, {a, b, c}, {-a, b, c} }; for (int i = 0; i < 2; ++i) { for (int j = 0; j < 2; ++j) { for (int k = 0; k < 2; ++k) { double x = GP(i), y = GP(j), z = GP(k); Eigen::RowVector dNx{-(1.0 - y) * (1.0 - z) / 8.0, (1.0 - y) * (1.0 - z) / 8.0, (1.0 + y) * (1.0 - z) / 8.0, -(1.0 + y) * (1.0 - z) / 8.0, -(1.0 - y) * (1.0 + z) / 8.0, (1.0 - y) * (1.0 + z) / 8.0, (1.0 + y) * (1.0 + z) / 8.0, -(1.0 + y) * (1.0 + z) / 8.0}; Eigen::RowVector dNy{-(1.0 - x) * (1.0 - z) / 8.0, -(1.0 + x) * (1.0 - z) / 8.0, (1.0 + x) * (1.0 - z) / 8.0, (1.0 - x) * (1.0 - z) / 8.0, -(1.0 - x) * (1.0 + z) / 8.0, -(1.0 + x) * (1.0 + z) / 8.0, (1.0 + x) * (1.0 + z) / 8.0, (1.0 - x) * (1.0 + z) / 8.0}; Eigen::RowVector dNz{-(1.0 - x) * (1.0 - y) / 8.0, -(1.0 + x) * (1.0 - y) / 8.0, -(1.0 + x) * (1.0 + y) / 8.0, -(1.0 - x) * (1.0 + y) / 8.0, (1.0 - x) * (1.0 - y) / 8.0, (1.0 + x) * (1.0 - y) / 8.0, (1.0 + x) * (1.0 + y) / 8.0, (1.0 - x) * (1.0 + y) / 8.0}; Eigen::Matrix tmp1; tmp1(0, Eigen::all) = dNx; tmp1(1, Eigen::all) = dNy; tmp1(2, Eigen::all) = dNz; Eigen::Matrix3d J = tmp1 * tmp; Eigen::Matrix3d JInv = J.inverse(); double JDet = J.determinant(); Eigen::Matrix G = Eigen::Matrix::Zero(); G(Eigen::seq(0, 2), Eigen::seq(0, 2)) = JInv; G(Eigen::seq(3, 5), Eigen::seq(3, 5)) = JInv; G(Eigen::seq(6, 8), Eigen::seq(6, 8)) = JInv; Eigen::Matrix dN = Eigen::Matrix::Zero(); dN(0, Eigen::seq(0, 23, 3)) = dNx; dN(1, Eigen::seq(0, 23, 3)) = dNy; dN(2, Eigen::seq(0, 23, 3)) = dNz; dN(3, Eigen::seq(1, 23, 3)) = dNx; dN(4, Eigen::seq(1, 23, 3)) = dNy; dN(5, Eigen::seq(1, 23, 3)) = dNz; dN(6, Eigen::seq(2, 23, 3)) = dNx; dN(7, Eigen::seq(2, 23, 3)) = dNy; dN(8, Eigen::seq(2, 23, 3)) = dNz; Eigen::Matrix Be = L * G * dN; Ke = Ke + GW(i) * GW(j) * GW(k) * JDet * (Be.transpose() * D * Be); } } } } void Material::computeBe(double a, double b, double c, std::vector> &Be) { assert(Be.size() == 8); // 8 Gauss Points int gcnt = 0; // count for Gauss Points Eigen::Vector2d GP(-1.0 / sqrt(3.0), 1.0 / sqrt(3.0)); Eigen::Matrix L = Eigen::Matrix::Zero(); L(0, 0) = 1.0; L(1, 4) = 1.0; L(2, 8) = 1.0; L(3, 1) = 1.0; L(3, 3) = 1.0; L(4, 5) = 1.0; L(4, 7) = 1.0; L(5, 2) = 1.0; L(5, 6) = 1.0; Eigen::Matrix tmp{ {-a, -b, -c}, {a, -b, -c}, {a, b, -c}, {-a, b, -c}, {-a, -b, c}, {a, -b, c}, {a, b, c}, {-a, b, c} }; for (int i = 0; i < 2; ++i) { for (int j = 0; j < 2; ++j) { for (int k = 0; k < 2; ++k) { double x = GP(i), y = GP(j), z = GP(k); Eigen::RowVector dNx{-(1.0 - y) * (1.0 - z) / 8.0, (1.0 - y) * (1.0 - z) / 8.0, (1.0 + y) * (1.0 - z) / 8.0, -(1.0 + y) * (1.0 - z) / 8.0, -(1.0 - y) * (1.0 + z) / 8.0, (1.0 - y) * (1.0 + z) / 8.0, (1.0 + y) * (1.0 + z) / 8.0, -(1.0 + y) * (1.0 + z) / 8.0}; Eigen::RowVector dNy{-(1.0 - x) * (1.0 - z) / 8.0, -(1.0 + x) * (1.0 - z) / 8.0, (1.0 + x) * (1.0 - z) / 8.0, (1.0 - x) * (1.0 - z) / 8.0, -(1.0 - x) * (1.0 + z) / 8.0, -(1.0 + x) * (1.0 + z) / 8.0, (1.0 + x) * (1.0 + z) / 8.0, (1.0 - x) * (1.0 + z) / 8.0}; Eigen::RowVector dNz{-(1.0 - x) * (1.0 - y) / 8.0, -(1.0 + x) * (1.0 - y) / 8.0, -(1.0 + x) * (1.0 + y) / 8.0, -(1.0 - x) * (1.0 + y) / 8.0, (1.0 - x) * (1.0 - y) / 8.0, (1.0 + x) * (1.0 - y) / 8.0, (1.0 + x) * (1.0 + y) / 8.0, (1.0 - x) * (1.0 + y) / 8.0}; Eigen::Matrix tmp1; tmp1(0, Eigen::all) = dNx; tmp1(1, Eigen::all) = dNy; tmp1(2, Eigen::all) = dNz; Eigen::Matrix3d J = tmp1 * tmp; Eigen::Matrix3d JInv = J.inverse(); Eigen::Matrix G = Eigen::Matrix::Zero(); G(Eigen::seq(0, 2), Eigen::seq(0, 2)) = JInv; G(Eigen::seq(3, 5), Eigen::seq(3, 5)) = JInv; G(Eigen::seq(6, 8), Eigen::seq(6, 8)) = JInv; Eigen::Matrix dN = Eigen::Matrix::Zero(); dN(0, Eigen::seq(0, 23, 3)) = dNx; dN(1, Eigen::seq(0, 23, 3)) = dNy; dN(2, Eigen::seq(0, 23, 3)) = dNz; dN(3, Eigen::seq(1, 23, 3)) = dNx; dN(4, Eigen::seq(1, 23, 3)) = dNy; dN(5, Eigen::seq(1, 23, 3)) = dNz; dN(6, Eigen::seq(2, 23, 3)) = dNx; dN(7, Eigen::seq(2, 23, 3)) = dNy; dN(8, Eigen::seq(2, 23, 3)) = dNz; Be[gcnt].setZero(6, 24); Be[gcnt] = L * G * dN; ++gcnt; } } } } void Material::computeN(const Eigen::RowVector3d &P, Eigen::Matrix &N) { N.setZero(); double x = P(0), y = P(1), z = P(2); // TODO: eps?? assert(x >= -1.0 && x <= 1.0 && y >= -1.0 && y <= 1.0 && z >= -1.0 && z <= 1.0); Eigen::RowVector tmp; tmp(0) = 0.125 * (1.0 - x) * (1.0 - y) * (1.0 - z); tmp(1) = 0.125 * (1.0 + x) * (1.0 - y) * (1.0 - z); tmp(2) = 0.125 * (1.0 + x) * (1.0 + y) * (1.0 - z); tmp(3) = 0.125 * (1.0 - x) * (1.0 + y) * (1.0 - z); tmp(4) = 0.125 * (1.0 - x) * (1.0 - y) * (1.0 + z); tmp(5) = 0.125 * (1.0 + x) * (1.0 - y) * (1.0 + z); tmp(6) = 0.125 * (1.0 + x) * (1.0 + y) * (1.0 + z); tmp(7) = 0.125 * (1.0 - x) * (1.0 + y) * (1.0 + z); N(0, Eigen::seq(0, 23, 3)) = tmp; N(1, Eigen::seq(1, 23, 3)) = tmp; N(2, Eigen::seq(2, 23, 3)) = tmp; } void Material::computeB(double a, double b, double c, const Eigen::RowVector3d &P, Eigen::Matrix &B) { B.setZero(); double x = P(0), y = P(1), z = P(2); // TODO: eps?? assert(x >= -1.0 && x <= 1.0 && y >= -1.0 && y <= 1.0 && z >= -1.0 && z <= 1.0); Eigen::Matrix tmp; tmp(0, 0) = -0.125 * (1.0 - y) * (1.0 - z); tmp(0, 1) = 0.125 * (1.0 - y) * (1.0 - z); tmp(0, 2) = 0.125 * (1.0 + y) * (1.0 - z); tmp(0, 3) = -0.125 * (1.0 + y) * (1.0 - z); tmp(0, 4) = -0.125 * (1.0 - y) * (1.0 + z); tmp(0, 5) = 0.125 * (1.0 - y) * (1.0 + z); tmp(0, 6) = 0.125 * (1.0 + y) * (1.0 + z); tmp(0, 7) = -0.125 * (1.0 + y) * (1.0 + z); tmp(1, 0) = -0.125 * (1.0 - x) * (1.0 - z); tmp(1, 1) = -0.125 * (1.0 + x) * (1.0 - z); tmp(1, 2) = 0.125 * (1.0 + x) * (1.0 - z); tmp(1, 3) = 0.125 * (1.0 - x) * (1.0 - z); tmp(1, 4) = -0.125 * (1.0 - x) * (1.0 + z); tmp(1, 5) = -0.125 * (1.0 + x) * (1.0 + z); tmp(1, 6) = 0.125 * (1.0 + x) * (1.0 + z); tmp(1, 7) = 0.125 * (1.0 - x) * (1.0 + z); tmp(2, 0) = -0.125 * (1.0 - x) * (1.0 - y); tmp(2, 1) = -0.125 * (1.0 + x) * (1.0 - y); tmp(2, 2) = -0.125 * (1.0 + x) * (1.0 + y); tmp(2, 3) = -0.125 * (1.0 - x) * (1.0 + y); tmp(2, 4) = 0.125 * (1.0 - x) * (1.0 - y); tmp(2, 5) = 0.125 * (1.0 + x) * (1.0 - y); tmp(2, 6) = 0.125 * (1.0 + x) * (1.0 + y); tmp(2, 7) = 0.125 * (1.0 - x) * (1.0 + y); tmp.row(0) /= a; tmp.row(1) /= b; tmp.row(2) /= c; B(0, Eigen::seq(0, 23, 3)) = tmp.row(0); B(1, Eigen::seq(1, 23, 3)) = tmp.row(1); B(2, Eigen::seq(2, 23, 3)) = tmp.row(2); B(3, Eigen::seq(0, 23, 3)) = tmp.row(1); B(3, Eigen::seq(1, 23, 3)) = tmp.row(0); B(4, Eigen::seq(1, 23, 3)) = tmp.row(2); B(4, Eigen::seq(2, 23, 3)) = tmp.row(1); B(5, Eigen::seq(0, 23, 3)) = tmp.row(2); B(5, Eigen::seq(2, 23, 3)) = tmp.row(0); } Eigen::Matrix Material::computeHeatKe(double a,double b,double c,double k0){ Eigen::Vector2d GP(-1.0 / sqrt(3.0), 1.0 / sqrt(3.0)); Eigen::Vector2d GW(1.0, 1.0); Eigen::Matrix heatKe; heatKe.setZero(); Eigen::Matrix tmp{ {-a, -b, -c}, {a, -b, -c}, {a, b, -c}, {-a, b, -c}, {-a, -b, c}, {a, -b, c}, {a, b, c}, {-a, b, c} }; for (int i = 0; i < 2; ++i) { for (int j = 0; j < 2; ++j) { for (int k = 0; k < 2; ++k) { double x = GP(i), y = GP(j), z = GP(k); Eigen::RowVector dNx{-(1.0 - y) * (1.0 - z) / 8.0, (1.0 - y) * (1.0 - z) / 8.0, (1.0 + y) * (1.0 - z) / 8.0, -(1.0 + y) * (1.0 - z) / 8.0, -(1.0 - y) * (1.0 + z) / 8.0, (1.0 - y) * (1.0 + z) / 8.0, (1.0 + y) * (1.0 + z) / 8.0, -(1.0 + y) * (1.0 + z) / 8.0}; Eigen::RowVector dNy{-(1.0 - x) * (1.0 - z) / 8.0, -(1.0 + x) * (1.0 - z) / 8.0, (1.0 + x) * (1.0 - z) / 8.0, (1.0 - x) * (1.0 - z) / 8.0, -(1.0 - x) * (1.0 + z) / 8.0, -(1.0 + x) * (1.0 + z) / 8.0, (1.0 + x) * (1.0 + z) / 8.0, (1.0 - x) * (1.0 + z) / 8.0}; Eigen::RowVector dNz{-(1.0 - x) * (1.0 - y) / 8.0, -(1.0 + x) * (1.0 - y) / 8.0, -(1.0 + x) * (1.0 + y) / 8.0, -(1.0 - x) * (1.0 + y) / 8.0, (1.0 - x) * (1.0 - y) / 8.0, (1.0 + x) * (1.0 - y) / 8.0, (1.0 + x) * (1.0 + y) / 8.0, (1.0 - x) * (1.0 + y) / 8.0}; Eigen::Matrix tmp1; tmp1(0, Eigen::all) = dNx; tmp1(1, Eigen::all) = dNy; tmp1(2, Eigen::all) = dNz; Eigen::Matrix3d J = tmp1 * tmp; Eigen::Matrix3d JInv = J.inverse(); double JDet = J.determinant(); heatKe = heatKe + GW(i) * GW(j) * GW(k) * JDet * k0 *(dNx.transpose()*dNx+dNy.transpose()*dNy+dNz.transpose()*dNz); } } } return heatKe; } } // top } // da::sha