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zeroboundary.cpp
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#define EIGEN_NO_DEBUG
#include <iostream>
#include <cmath>
#include <stdlib.h>
#include <vector>
#include <iomanip>
#include "spline.h"
#include <eigen3/Eigen/Dense>
#include <eigen3/Eigen/Sparse>
#include <eigen3/unsupported/Eigen/KroneckerProduct>
using namespace std;
using namespace spline;
using namespace Eigen;
typedef Eigen::SparseVector<double> SpVec;
typedef Eigen::SparseMatrix<double> SpMat;
MatrixXd globalExtraction(double* knot, int p, int m) {
vector<double> knots;
MatrixXd CC = MatrixXd::Identity(m - p, m - p);
for (int i = 0; i < m + 1; i++)
knots.push_back(knot[i]);
int delay = 0, cont = 0, conts = 0;
for (int i = 0; i < m + 1 - 2 * (p + 1); i++) {
if (knot[i + p + 1] == knot[i + p + 2]) {
cont++;
delay++;
continue;
}
int k = (i - delay + 1) * (p + 1);
for (int j = 0; j < p - cont; j++) {
MatrixXd C = MatrixXd::Zero(m - p + (i - delay) * p - conts + j + 1,
m - p + (i - delay) * p - conts + j);
for (int ii = 0; ii < k - p + 1; ii++)
C(ii, ii) = 1;
for (int ii = k - p + 1; ii <= k; ii++) {
C(ii, ii) = (knot[i + p + 1] - knots[ii]) / (knots[ii + p] - knots[ii]);
C(ii, ii - 1) = 1 - (knot[i + p + 1] - knots[ii]) / (knots[ii + p] - knots[ii]);
}
for (int ii = k + 1; ii < m - p + (i - delay) * p - conts + j + 1; ii++)
C(ii, ii - 1) = 1;
CC *= C.transpose();
knots.insert(knots.begin() + (i - delay) * (p + 1) + p + 1, knot[i + p + 1]);
}
conts = delay;
cont = 0;
}
return CC;
}
void GenerateKnot(int order, int refine, int insert, double* insert_knot,
double* & knot, int& m);
void CombineKnot(double* knot1, int m1, double* knot2, int m2, double* & knot,
int& m);
void Geometry(double xi, double eta, double& pxpxi, double& pxpeta,
double& pypxi, double& pypeta);
void CompToPhy(double xi, double eta, double& x, double& y);
void AnalyticalDeformation(double x, double y, double L, double D, double I,
double P, double E,
double nu,
Vector2d& deformation);
void AnalyticalStress(double x, double y, double L, double D, double I,
double P, Vector3d& stress);
int main() {
double kkkkk[] = {0, 0, 0, 0, 0, .5, 1, 1, 1, 1, 1};
cout << globalExtraction(kkkkk, 4, 10) << endl;
double P = -1000;
double E = 1000;
double nu = 0.3;
double L = 4;
double D = 2;
double I = D * D * D / 12;
double* gaussian = x6;
double* weight = w6;
int gaussian_points = 6;
MatrixXd DD(3, 3);
DD << 1 - nu, nu, 0, nu, 1 - nu, 0, 0, 0, (1.0 - 2 * nu) / 2;
DD *= E / (1 + nu) / (1 - 2 * nu);
int order = 4;
int refine = 4;
int m_x_patch1, m_y_patch1;
int m_x_patch2, m_y_patch2;
int p_x = order, p_y = order;
double* knots_x_patch1, *knots_y_patch1;
double* knots_x_patch2, *knots_y_patch2;
double insertion_patch1[] = {.5};
double insertion_patch2[] = {1.0/4, .5, 3.0/4, };
GenerateKnot(p_x, refine, 1, insertion_patch1, knots_x_patch1, m_x_patch1);
GenerateKnot(p_y, refine, 3, insertion_patch2, knots_y_patch1, m_y_patch1);
GenerateKnot(p_x, refine, 3, insertion_patch2, knots_x_patch2, m_x_patch2);
GenerateKnot(p_y, refine, 3, insertion_patch2, knots_y_patch2, m_y_patch2);
double* knots_y_coupling;
int m_y_coupling;
CombineKnot(knots_y_patch1, m_y_patch1, knots_y_patch2, m_y_patch2,
knots_y_coupling,
m_y_coupling);
int dof_x_patch1 = m_x_patch1 - p_x, dof_y_patch1 = m_y_patch1 - p_y,
dof_x_patch2 = m_x_patch2 - p_x,
dof_y_patch2 = m_y_patch2 - p_y;
int dof_patch1 = dof_x_patch1 * dof_y_patch1,
dof_patch2 = dof_x_patch2 * dof_y_patch2;
int elements_x_patch1 = m_x_patch1 - 2 * p_x,
elements_y_patch1 = m_y_patch1 - 2 * p_y,
elements_x_patch2 = m_x_patch2 - 2 * p_x,
elements_y_patch2 = m_y_patch2 - 2 * p_y;
int elements_y_coupling = m_y_coupling - 2 * p_y;
MatrixXd M = MatrixXd::Zero(dof_y_patch2, dof_y_patch2),
N2N1 = MatrixXd::Zero(dof_y_patch2, dof_y_patch1);
for (int ii_y = 0; ii_y < elements_y_coupling; ii_y++) {
double J_y = (knots_y_coupling[ii_y + p_y + 1] - knots_y_coupling[ii_y + p_y]) /
2;
double Middle_y = (knots_y_coupling[ii_y + p_y + 1] + knots_y_coupling[ii_y +
p_y]) / 2;
int i_y_patch1 = Findspan(m_y_patch1, p_y, knots_y_patch1, Middle_y);
int i_y_patch2 = Findspan(m_y_patch2, p_y, knots_y_patch2, Middle_y);
for (int jj_y = 0; jj_y < gaussian_points; jj_y++) {
double eta = Middle_y + J_y * gaussian[jj_y];
double** ders_y_patch1, **ders_y_patch2;
DersBasisFuns(i_y_patch1, eta, p_y, knots_y_patch1, 0, ders_y_patch1);
DersBasisFuns(i_y_patch2, eta, p_y, knots_y_patch2, 0, ders_y_patch2);
VectorXd Neta_patch1 = VectorXd::Zero(dof_y_patch1),
Neta_patch2 = VectorXd::Zero(dof_y_patch2);
for (int kk_y = 0; kk_y < p_y + 1; kk_y++) {
Neta_patch1(i_y_patch1 - p_y + kk_y) = ders_y_patch1[0][kk_y];
Neta_patch2(i_y_patch2 - p_y + kk_y) = ders_y_patch2[0][kk_y];
}
for (int k = 0; k < 1; k++)
delete ders_y_patch1[k];
delete[] ders_y_patch1;
for (int k = 0; k < 1; k++)
delete ders_y_patch2[k];
delete[] ders_y_patch2;
M += weight[jj_y] * Neta_patch2 * Neta_patch2.transpose() * J_y;;
N2N1 += weight[jj_y] * Neta_patch2 * Neta_patch1.transpose() * J_y;
}
}
MatrixXd MN2N1 = M.fullPivHouseholderQr().solve(N2N1);
MatrixXd Iden = MatrixXd::Identity(2, 2);
MatrixXd couplingMatrix = MatrixXd::Zero(2 * dof_patch2,
2 * (dof_patch2 - dof_y_patch2 + dof_y_patch1));
couplingMatrix.block(0, 0, 2 * dof_y_patch2,
2 * dof_y_patch1) = kroneckerProduct(MN2N1, Iden);
couplingMatrix.block(2 * dof_y_patch2, 2 * dof_y_patch1,
2 * (dof_patch2 - dof_y_patch2),
2 * (dof_patch2 - dof_y_patch2)) = MatrixXd::Identity(2 *
(dof_patch2 - dof_y_patch2), 2 * (dof_patch2 - dof_y_patch2));
MatrixXd K_patch1 = MatrixXd::Zero(2 * dof_patch1, 2 * dof_patch1);
for (int ii_x = 0; ii_x < elements_x_patch1; ii_x++) {
double J_x = (knots_x_patch1[ii_x + p_x + 1] - knots_x_patch1[ii_x + p_x]) / 2;
double Middle_x = (knots_x_patch1[ii_x + p_x + 1] + knots_x_patch1[ii_x +
p_x]) / 2;
int i_x = Findspan(m_x_patch1, p_x, knots_x_patch1, Middle_x);
for (int ii_y = 0; ii_y < elements_y_patch1; ii_y++) {
double J_y = (knots_y_patch1[ii_y + p_y + 1] - knots_y_patch1[ii_y + p_y]) / 2;
double Middle_y = (knots_y_patch1[ii_y + p_y + 1] + knots_y_patch1[ii_y +
p_y]) / 2;
int i_y = Findspan(m_y_patch1, p_y, knots_y_patch1, Middle_y);
for (int jj_x = 0; jj_x < gaussian_points; jj_x++) {
for (int jj_y = 0; jj_y < gaussian_points; jj_y++) {
double xi = Middle_x + J_x * gaussian[jj_x];
double eta = Middle_y + J_y * gaussian[jj_y];
double** ders_x, **ders_y;
DersBasisFuns(i_x, xi, p_x, knots_x_patch1, 1, ders_x);
DersBasisFuns(i_y, eta, p_y, knots_y_patch1, 1, ders_y);
VectorXd Nxi(p_x + 1), Nxi_xi(p_x + 1), Neta(p_y + 1), Neta_eta(p_y + 1);
for (int kk_x = 0; kk_x < p_x + 1; kk_x++) {
Nxi(kk_x) = ders_x[0][kk_x];
Nxi_xi(kk_x) = ders_x[1][kk_x];
}
for (int kk_y = 0; kk_y < p_y + 1; kk_y++) {
Neta(kk_y) = ders_y[0][kk_y];
Neta_eta(kk_y) = ders_y[1][kk_y];
}
for (int k = 0; k < 2; k++)
delete ders_x[k];
delete[] ders_x;
for (int k = 0; k < 2; k++)
delete ders_y[k];
delete[] ders_y;
VectorXd Nxi_xiNeta, NxiNeta_eta;
Nxi_xiNeta = kroneckerProduct(Nxi_xi, Neta);
NxiNeta_eta = kroneckerProduct(Nxi, Neta_eta);
double pxpxi, pxpeta, pypxi, pypeta;
Geometry(xi, eta, pxpxi, pxpeta, pypxi, pypeta);
double Jacobian = pxpxi * pypeta - pxpeta * pypxi;
VectorXd Nx_xNy, NxNy_y;
Nx_xNy = 1.0 / Jacobian * (Nxi_xiNeta * pypeta - NxiNeta_eta * pypxi);
NxNy_y = 1.0 / Jacobian * (-Nxi_xiNeta * pxpeta + NxiNeta_eta * pxpxi);
for (int kkx = 0; kkx < (p_x + 1) * (p_y + 1); kkx++) {
for (int kky = 0; kky < (p_x + 1) * (p_y + 1); kky++) {
MatrixXd Bx(3, 2);
MatrixXd By(3, 2);
Bx << Nx_xNy(kkx), 0, 0, NxNy_y(kkx), NxNy_y(kkx), Nx_xNy(kkx);
By << Nx_xNy(kky), 0, 0, NxNy_y(kky), NxNy_y(kky), Nx_xNy(kky);
K_patch1.block(2 * ((m_y_patch1 - p_y) * (kkx / (p_y + 1) + i_x - p_x) + kkx %
(p_y + 1) + i_y - p_y), 2 * ((m_y_patch1 - p_y) * (kky /
(p_y + 1) + i_x - p_x) + kky
% (p_y + 1) + i_y - p_y), 2,
2) += weight[jj_x] * weight[jj_y] * Jacobian * Bx.transpose() * DD * By * J_x *
J_y;
}
}
}
}
}
}
MatrixXd K_patch2 = MatrixXd::Zero(2 * dof_patch2, 2 * dof_patch2);
for (int ii_x = 0; ii_x < elements_x_patch2; ii_x++) {
double J_x = (knots_x_patch2[ii_x + p_x + 1] - knots_x_patch2[ii_x + p_x]) / 2;
double Middle_x = (knots_x_patch2[ii_x + p_x + 1] + knots_x_patch2[ii_x +
p_x]) / 2;
int i_x = Findspan(m_x_patch2, p_x, knots_x_patch2, Middle_x);
for (int ii_y = 0; ii_y < elements_y_patch2; ii_y++) {
double J_y = (knots_y_patch2[ii_y + p_y + 1] - knots_y_patch2[ii_y + p_y]) / 2;
double Middle_y = (knots_y_patch2[ii_y + p_y + 1] + knots_y_patch2[ii_y +
p_y]) / 2;
int i_y = Findspan(m_y_patch2, p_y, knots_y_patch2, Middle_y);
for (int jj_x = 0; jj_x < gaussian_points; jj_x++) {
for (int jj_y = 0; jj_y < gaussian_points; jj_y++) {
double xi = Middle_x + J_x * gaussian[jj_x];
double eta = Middle_y + J_y * gaussian[jj_y];
double** ders_x, **ders_y;
DersBasisFuns(i_x, xi, p_x, knots_x_patch2, 1, ders_x);
DersBasisFuns(i_y, eta, p_y, knots_y_patch2, 1, ders_y);
VectorXd Nxi(p_x + 1), Nxi_xi(p_x + 1), Neta(p_y + 1), Neta_eta(p_y + 1);
for (int kk_x = 0; kk_x < p_x + 1; kk_x++) {
Nxi(kk_x) = ders_x[0][kk_x];
Nxi_xi(kk_x) = ders_x[1][kk_x];
}
for (int kk_y = 0; kk_y < p_y + 1; kk_y++) {
Neta(kk_y) = ders_y[0][kk_y];
Neta_eta(kk_y) = ders_y[1][kk_y];
}
for (int k = 0; k < 2; k++)
delete ders_x[k];
delete[] ders_x;
for (int k = 0; k < 2; k++)
delete ders_y[k];
delete[] ders_y;
VectorXd Nxi_xiNeta, NxiNeta_eta;
Nxi_xiNeta = kroneckerProduct(Nxi_xi, Neta);
NxiNeta_eta = kroneckerProduct(Nxi, Neta_eta);
double pxpxi, pxpeta, pypxi, pypeta;
Geometry(xi, eta, pxpxi, pxpeta, pypxi, pypeta);
double Jacobian = pxpxi * pypeta - pxpeta * pypxi;
VectorXd Nx_xNy, NxNy_y;
Nx_xNy = 1.0 / Jacobian * (Nxi_xiNeta * pypeta - NxiNeta_eta * pypxi);
NxNy_y = 1.0 / Jacobian * (-Nxi_xiNeta * pxpeta + NxiNeta_eta * pxpxi);
for (int kkx = 0; kkx < (p_x + 1) * (p_y + 1); kkx++) {
for (int kky = 0; kky < (p_x + 1) * (p_y + 1); kky++) {
MatrixXd Bx(3, 2);
MatrixXd By(3, 2);
Bx << Nx_xNy(kkx), 0, 0, NxNy_y(kkx), NxNy_y(kkx), Nx_xNy(kkx);
By << Nx_xNy(kky), 0, 0, NxNy_y(kky), NxNy_y(kky), Nx_xNy(kky);
K_patch2.block(2 * ((m_y_patch2 - p_y) * (kkx / (p_y + 1) + i_x - p_x) + kkx %
(p_y + 1) + i_y - p_y), 2 * ((m_y_patch2 - p_y) * (kky /
(p_y + 1) + i_x - p_x) + kky
% (p_y + 1) + i_y - p_y), 2,
2) += weight[jj_x] * weight[jj_y] * Jacobian * Bx.transpose() * DD * By * J_x *
J_y;
}
}
}
}
}
}
MatrixXd K = MatrixXd::Zero(2 * (dof_patch1 + dof_patch2 -
dof_y_patch2), 2 * (dof_patch1 + dof_patch2 - dof_y_patch2));
K.block(0, 0, 2 * dof_patch1, 2 * dof_patch1) = K_patch1;
K.block(2 * (dof_patch1 - dof_y_patch1), 2 * (dof_patch1 - dof_y_patch1),
2 * (dof_patch2 - dof_y_patch2 + dof_y_patch1),
2 * (dof_patch2 - dof_y_patch2 + dof_y_patch1)) += couplingMatrix.transpose()
* K_patch2 * couplingMatrix;
VectorXd FT = VectorXd::Zero(2 * (dof_patch1 + dof_patch2 -
dof_y_patch2));
for (int ii_y = 0; ii_y < elements_y_patch2; ii_y++) {
double J_y = (knots_y_patch2[ii_y + p_y + 1] - knots_y_patch2[ii_y + p_y]) / 2;
double Middle_y = (knots_y_patch2[ii_y + p_y + 1] + knots_y_patch2[ii_y +
p_y]) / 2;
int i_y = Findspan(m_y_patch2, p_y, knots_y_patch2, Middle_y);
for (int jj_y = 0; jj_y < gaussian_points; jj_y++) {
double xi = 0.9999999999999999999999;
double eta = Middle_y + J_y * gaussian[jj_y];
double** ders_y;
DersBasisFuns(i_y, eta, p_y, knots_y_patch2, 0, ders_y);
VectorXd Nxi = VectorXd::Zero(dof_x_patch2),
Neta = VectorXd::Zero(dof_y_patch2);
for (int kk_y = 0; kk_y < p_y + 1; kk_y++) {
Neta(i_y - p_y + kk_y) = ders_y[0][kk_y];
}
Nxi(dof_x_patch2 - 1) = 1;
for (int k = 0; k < 1; k++)
delete ders_y[k];
delete[] ders_y;
VectorXd NxiNetaY, NxiNeta;
VectorXd Y(2);
Y(1) = 1, Y(0) = 0;
NxiNeta = kroneckerProduct(Nxi, Neta);
NxiNetaY = kroneckerProduct(NxiNeta, Y);
double pxpxi, pxpeta, pypxi, pypeta;
Geometry(xi, eta, pxpxi, pxpeta, pypxi, pypeta);
double x, y;
CompToPhy(xi, eta, x, y);
Vector3d stress;
AnalyticalStress(x, y, L, D, I, P, stress);
FT.segment(2 * (dof_patch1 - dof_y_patch1),
2 * (dof_patch2 - dof_y_patch2 + dof_y_patch1)) += weight[jj_y] * (stress(
2) * NxiNetaY) * J_y * pypeta;
}
}
MatrixXd K_compute = K.block(2 * dof_y_patch1, 2 * dof_y_patch1,
2 * (dof_patch1 + dof_patch2 -
dof_y_patch2 - dof_y_patch1), 2 * (dof_patch1 + dof_patch2 -
dof_y_patch2 - dof_y_patch1));
VectorXd F_compute = FT.segment(2 * dof_y_patch1, 2 * (dof_patch1 + dof_patch2 -
dof_y_patch2 - dof_y_patch1));
VectorXd U_result = K_compute.partialPivLu().solve(F_compute);
cout<<U_result<<endl;
return 0;
}
void GenerateKnot(int order, int refine, int insert, double* insert_knot,
double* & knot, int& m) {
vector<double> Knot;
for (int i = 0; i <= order; i++) {
Knot.push_back(0);
}
for (int i = 0; i < insert; i++) {
Knot.push_back(insert_knot[i]);
}
for (int i = 0; i <= order; i++) {
Knot.push_back(1);
}
for (int i = 0; i < refine; i++) {
for (int j = 0; j < Knot.end() - Knot.begin() - 1; j++) {
double insertion;
if (Knot[j] != Knot[j + 1]) {
insertion = (Knot[j] + Knot[j + 1]) / 2;
Knot.insert(Knot.begin() + j + 1, insertion);
j++;
}
}
}
m = Knot.end() - Knot.begin() - 1;
knot = new double[m + 1];
for (int i = 0; i < m + 1; i++)
knot[i] = Knot[i];
}
void CombineKnot(double* knot1, int m1, double* knot2, int m2, double* & knot,
int& m) {
vector<double> Knot;
int i1 = 0, i2 = 0;
while (i1 <= m1) {
if (knot1[i1] == knot2[i2]) {
Knot.push_back(knot1[i1]);
i1++, i2++;
} else if (knot1[i1] < knot2[i2]) {
Knot.push_back(knot1[i1]);
i1++;
} else {
Knot.push_back(knot2[i2]);
i2++;
}
}
m = Knot.end() - Knot.begin() - 1;
knot = new double[m + 1];
for (int i = 0; i < m + 1; i++)
knot[i] = Knot[i];
}
void AnalyticalDeformation(double x, double y, double L, double D, double I,
double P, double E,
double nu,
Vector2d& deformation) {
double E_bar = E / (1 - pow(nu, 2));
double nu_bar = nu / (1 - nu);
deformation(0) = -P * y / 6 / E_bar / I * ((6 * L - 3 * x) * x +
(2 + nu_bar) * (pow(y,
2) - pow(D / 2, 2)));
deformation(1) = P / 6 / E_bar / I * (3 * nu_bar * pow(y,
2) * (L - x) + (4 + 5 * nu_bar) * D * D * x / 4 + (3 * L - x) * x * x);
}
void AnalyticalStress(double x, double y, double L, double D, double I,
double P,
Vector3d& stress) {
stress(0) = -P * (L - x) * y / I;
stress(1) = 0;
stress(2) = P / 2 / I * (pow(D / 2, 2) - pow(y, 2));
}
void Geometry(double xi, double eta, double& pxpxi, double& pxpeta,
double& pypxi, double& pypeta) {
pxpxi = 2;
pxpeta = 0;
pypxi = 0;
pypeta = 2;
}
void CompToPhy(double xi, double eta, double& x, double& y) {
y = (eta - 0.5) * 2;
x = xi * 4;
}