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solver.cpp
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solver.cpp
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#include "solver.h"
#include "math.h"
Solver::Solver()
{
setParameters(1.0, 1.0, 10., BC::free, BC::free);
}
void Solver::setParameters(double E, double I, double L, BC lBC, BC rBC)
{
m_E = E;
m_I = I;
m_length = L;
leftBC = lBC;
rightBC = rBC;
}
bool Solver::doAnalysis(double w, double P, double xP)
{
bool retval = true;
// set up results containers
X.clear();
M.clear();
V.clear();
th.clear();
d.clear();
double kfu, kf0, kmu, km0;
double Pe, Me;
const int N = 6;
double Pvector[N];
double Kmatrix[N][N];
for (int i=0; i<N; i++) {
Pvector[i] = 0.0;
for (int j=0; j<N; j++) {
Kmatrix[i][j] = 0.0;
}
}
// element 1
double L = xP;
if (L < m_length/100.) L = m_length/100.;
kfu = 12. * m_E * m_I / pow(L, 3) ;
kf0 = 6. * m_E * m_I / pow(L, 2) ;
kmu = kf0 ;
km0 = 4. * m_E * m_I / L ;
Pe = w * L / 2.;
Me = -Pe * L / 6.0;
Kmatrix[0][0] += kfu;
Kmatrix[1][0] += kmu;
Kmatrix[1][1] += km0;
Kmatrix[2][0] += -kfu;
Kmatrix[2][1] += -kf0;
Kmatrix[2][2] += kfu;
Kmatrix[3][0] += kmu;
Kmatrix[3][1] += km0/2.;
Kmatrix[3][2] += -kmu;
Kmatrix[3][3] += km0;
Pvector[0] -= Pe;
Pvector[1] += Me;
Pvector[2] -= Pe;
Pvector[3] -= Me;
// element 2
L = m_length - xP;
if (L < m_length/100.) L = m_length/100.;
kfu = 12. * m_E * m_I / pow(L, 3) ;
kf0 = 6. * m_E * m_I / pow(L, 2) ;
kmu = kf0 ;
km0 = 4. * m_E * m_I / L ;
Pe = w * L / 2.;
Me = -Pe * L / 6.0;
Kmatrix[2][2] += kfu;
Kmatrix[3][2] += kmu;
Kmatrix[3][3] += km0;
Kmatrix[4][2] += -kfu;
Kmatrix[4][3] += -kf0;
Kmatrix[4][4] += kfu;
Kmatrix[5][2] += kmu;
Kmatrix[5][3] += km0/2.;
Kmatrix[5][4] += -kmu;
Kmatrix[5][5] += km0;
Pvector[2] -= Pe;
Pvector[3] += Me;
Pvector[4] -= Pe;
Pvector[5] -= Me;
if (P != 0.0) Pvector[2] -= P;
for (int i=0; i<N; i++)
for (int j=i+1; j<N; j++)
Kmatrix[i][j] = Kmatrix[j][i];
// apply left BC
if (leftBC == BC::fixed || leftBC == BC::pinned)
{
Kmatrix[0][0] = 1.0;
Kmatrix[1][0] = 0.0;
Kmatrix[2][0] = 0.0;
Kmatrix[3][0] = 0.0;
Kmatrix[4][0] = 0.0;
Kmatrix[5][0] = 0.0;
Kmatrix[0][1] = 0.0;
Kmatrix[0][2] = 0.0;
Kmatrix[0][3] = 0.0;
Kmatrix[0][4] = 0.0;
Kmatrix[0][5] = 0.0;
Pvector[0] = 0.0;
}
if (leftBC == BC::fixed || leftBC == BC::sliding)
{
Kmatrix[0][1] = 0.0;
Kmatrix[1][1] = 1.0;
Kmatrix[2][1] = 0.0;
Kmatrix[3][1] = 0.0;
Kmatrix[4][1] = 0.0;
Kmatrix[5][1] = 0.0;
Kmatrix[1][0] = 0.0;
Kmatrix[1][2] = 0.0;
Kmatrix[1][3] = 0.0;
Kmatrix[1][4] = 0.0;
Kmatrix[1][5] = 0.0;
Pvector[1] = 0.0;
}
// apply right BC
if (rightBC == BC::fixed || rightBC == BC::pinned)
{
Kmatrix[0][4] = 0.0;
Kmatrix[1][4] = 0.0;
Kmatrix[2][4] = 0.0;
Kmatrix[3][4] = 0.0;
Kmatrix[4][4] = 1.0;
Kmatrix[5][4] = 0.0;
Kmatrix[4][0] = 0.0;
Kmatrix[4][1] = 0.0;
Kmatrix[4][2] = 0.0;
Kmatrix[4][3] = 0.0;
Kmatrix[4][5] = 0.0;
Pvector[4] = 0.0;
}
if (rightBC == BC::fixed || rightBC == BC::sliding)
{
Kmatrix[0][5] = 0.0;
Kmatrix[1][5] = 0.0;
Kmatrix[2][5] = 0.0;
Kmatrix[3][5] = 0.0;
Kmatrix[4][5] = 0.0;
Kmatrix[5][5] = 1.0;
Kmatrix[5][0] = 0.0;
Kmatrix[5][1] = 0.0;
Kmatrix[5][2] = 0.0;
Kmatrix[5][3] = 0.0;
Kmatrix[5][4] = 0.0;
Pvector[5] = 0.0;
}
// solve system
// ... LDL^t matrix decomposition
for (int i=0; i<N; i++)
{
for (int k=0; k<i; k++) Kmatrix[i][i] -= Kmatrix[i][k]*Kmatrix[i][k]*Kmatrix[k][k];
// singularity check ...
if (abs(Kmatrix[i][i]) < 1.e-10)
{
retval = false;
return retval;
}
// not singular
for (int j=i+1; j<N; j++)
{
for (int k=0; k<i; k++) Kmatrix[j][i] -= Kmatrix[i][k]*Kmatrix[j][k]*Kmatrix[k][k];
Kmatrix[j][i] /= Kmatrix[i][i];
}
}
// .. back substitution
for (int j=0; j<N; j++)
for (int k=0; k<j; k++)
Pvector[j] -= Kmatrix[j][k]*Pvector[k];
for (int m=0; m<N; m++)
Pvector[m] /= Kmatrix[m][m];
for (int j=N-1; j>=0; j--)
for (int m=j+1; m<N; m++)
Pvector[j] -= Kmatrix[m][j] * Pvector[m];
double vi, vj, thetai, thetaj;
double x0;
// ... element 1
x0 = 0.0;
vi = Pvector[0];
thetai = Pvector[1];
vj = Pvector[2];
thetaj = Pvector[3];
L = xP;
if (L < m_length/100.) L = m_length/100.;
kfu = 12. * m_E * m_I / pow(L, 3) ;
kf0 = 6. * m_E * m_I / pow(L, 2) ;
kmu = kf0 ;
km0 = 4. * m_E * m_I / L ;
Pe = w * L / 2.;
Me = -Pe * L / 6.0;
for (int k=0; k<=20; k++)
{
// position
double x = L*double(k)/20;
// compute moment
double moment = ( kmu - kfu * x ) * (vj - vi)
+ (-km0 + kf0 * x ) * thetai + (-0.5*km0 + kf0 * x) * thetaj
- w / 12. * (L*L - 6.*x*L + 6.*x*x);
// compute shear
double shear = kfu * (vi - vj) + kf0 * (thetai + thetaj)
- w * (x - 0.5*L);
// compute slope
double slope = 6.*x/L*(1.0 - x/L) * (vj - vi) / L
+ (1. - 4.*x/L + 3.*x*x/(L*L)) * thetai + (-2.*x/L + 3.*x*x/(L*L)) * thetaj
- w * x* (L*L - 3.*L*x + 2.*x*x)/(12.*m_E*m_I);
// compute deflection
double disp = vj * (3. - 2.*x/L)*x*x/(L*L) + vi * (1. - 3.*x*x/(L*L) + 2.*x*x*x/(L*L*L))
+ x*(1. - 2.*x/L + x*x/(L*L)) * thetai + x*(-x/L + x*x/(L*L)) * thetaj
- w * (L - x)*(L - x)*x*x/(24.*m_E*m_I) ;
X.append((x0+x)/12.);
M.append(moment/12.);
V.append(shear);
th.append(slope);
d.append(disp);
}
// ... element 2
x0 = xP;
if (x0 < m_length/100.) x0 = m_length/100.;
vi = Pvector[2];
thetai = Pvector[3];
vj = Pvector[4];
thetaj = Pvector[5];
L = m_length - xP;
if (L < m_length/100.) L = m_length/100.;
kfu = 12. * m_E * m_I / pow(L, 3) ;
kf0 = 6. * m_E * m_I / pow(L, 2) ;
kmu = kf0 ;
km0 = 4. * m_E * m_I / L ;
Pe = w * L / 2.;
Me = -Pe * L / 6.0;
for (int k=0; k<=20; k++)
{
// position
double x = L*double(k)/20;
// compute moment
double moment = ( kmu - kfu * x ) * (vj - vi)
+ (-km0 + kf0 * x ) * thetai + (-0.5*km0 + kf0 * x) * thetaj
- w / 12. * (L*L - 6.*x*L + 6.*x*x);
// compute shear
double shear = kfu * (vi - vj) + kf0 * (thetai + thetaj)
- w * (x - 0.5*L);
// compute slope
double slope = 6.*x/L*(1.0 - x/L) * (vj - vi) / L
+ (1. - 4.*x/L + 3.*x*x/(L*L)) * thetai + (-2.*x/L + 3.*x*x/(L*L)) * thetaj
- w * x* (L*L - 3.*L*x + 2.*x*x)/(12.*m_E*m_I);
// compute deflection
double disp = vj * (3. - 2.*x/L)*x*x/(L*L) + vi * (1. - 3.*x*x/(L*L) + 2.*x*x*x/(L*L*L))
+ x*(1. - 2.*x/L + x*x/(L*L)) * thetai + x*(-x/L + x*x/(L*L)) * thetaj
- w * (L - x)*(L - x)*x*x/(24.*m_E*m_I) ;
X.append((x0+x)/12.);
M.append(moment/12.);
V.append(shear);
th.append(slope);
d.append(disp);
}
return retval;
}
QVector<double> *Solver::getX()
{
return &X;
}
QVector<double> *Solver::getMoment()
{
return &M;
}
QVector<double> *Solver::getShear()
{
return &V;
}
QVector<double> *Solver::getRotation()
{
return &th;
}
QVector<double> *Solver::getDeflection()
{
return &d;
}