void draw() {
for (float i = 0; i < sx; i++) {
for (float j = 0; j < sy; j++) {
glBegin(GL_QUADS);
glNormal3f(getx((i+0.5)/sx,(j+0.5)/sy),
gety((i+0.5)/sx, (j+0.5)/sy),
getz((i+0.5)/sx,(j+0.5)/sy));
glVertex3f(getx(i/sx, j/sy),
gety(i/sx, j/sy),
getz(i/sx, j/sy));
glVertex3f(getx((i+1)/sx, j/sy),
gety((i+1)/sx, j/sy),
getz((i+1)/sx, j/sy));
glVertex3f(getx((i+1)/sx, (j+1)/sy),
gety((i+1)/sx, (j+1)/sy),
getz((i+1)/sx, (j+1)/sy));
glVertex3f(getx(i/sx, (j+1)/sy),
gety(i/sx, (j+1)/sy),
getz(i/sx, (j+1)/sy));
glEnd();
}
}
}
double getchi2(double dof, double alpha)
{
double tol = 1.0E-3;
double ac, lm, rm, eps, chi2, za, x;
int i, itmax = 100;
if (dof > 30.0) {
/* approximate a value if degrees of freedom are > 30 based on eqn 1. Sachs, 1984 */
za = -getz(alpha); /* NB: Eq. requires change of sign for percentile */
x = 2.0 / 9.0 / dof;
chi2 = pow((dof * (1.0 - x + za * sqrt(x))), 3.0);
} else{
lm = 0.0;
rm = 1000.0;
if (alpha > 0.5)
eps = (1.0 - alpha) * tol;
else
eps = alpha * tol;
for (i = 1; i <= itmax; i++) {
chi2 = 0.5 * (lm + rm);
ac = 1.0 - gammp(0.5 * dof, 0.5 * chi2);
if (fabs(ac - alpha) <= eps)
return (chi2);
if (ac > alpha){
lm = chi2;
}else {
rm = chi2;
}
}
}
return (chi2);
}
double Plane::getzbound(Area* limit, vect2d pt, double rad, double height, bool clipsolid)
{
PROBEGIN(checkz_fast);
PROBEGIN(checkz_slow);
if (slope==0 && !clipsolid) {
// Special case: slope is zero, so bound is z [+-] height.
return cpt.z+(ceil?-height:height);
}
if (rad == 0) {
return getz(pt)+(ceil?-height:height);
}
// Calculate the highest (or lowest) point where the cylinder
// intersects with the plane. This is always <px, py> [+-] <ix, iy>*rad
vect2d tpt = pt;
if ((slope>0) == ceil) {
tpt -= dir*rad;
} else {
tpt += dir*rad;
}
// If the limit area is not specified, or <tpx, tpy> is in the
// area, simply return the value of the plane at that point [+-] height.
if ((limit == NULL) || limit->pointin(tpt)) {
PROEND(checkz_fast);
double ret = getz(tpt);
if (ceil) {
ret -= height;
} else {
ret += height;
}
return ret;
}
// Ok, so the point is not in the area. So, we have to find some
// other point to be the (max|min)imum. This point will either be
// 1. a vertex of the area, or
// 2. a point along one of the walls.
//
// We start out with the value at [+-]infinity, and then check all
// possible points. We loop through the walls, checking the vertex
// if the vertex is inside the circle, then check the points where
// the circle intersects the wall.
double cz = (ceil?INFINITY:-INFINITY);
#define ckz(pt) { \
double tz=getz(pt) + (ceil?-height:height); \
if (ceil == (tz<cz)) cz = tz; \
}
double rad2 = sqr(rad);
FOREACHW(w, limit) {
double a, ta;
// Check the vertex.
if (vlen2(w->v1-pt) < rad2) {
ckz(w->v1);
}
// Transform the point to wall coordinate space.
double doti = ~w->j*(pt-w->v1);
double dotj = w->j*(pt-w->v1);
// Circle does not intersect.
if (fabs(doti)>rad+EPSILON) continue;
// Check intersection points.
a = sqrt(rad2-sqr(doti));
if (isnan(a)) a = 0;
ta = dotj+a;
if (ta >= 0 && ta <= w->len) {
ckz(w->v1+w->j*ta);
}
ta = dotj-a;
if (ta >= 0 && ta <= w->len) {
ckz(w->v1+w->j*ta);
}
}
//================================================================================
const tensor& DM04_PF::Dm_Dkin2(const stresstensor &Stre,
const straintensor &Stra,
const MaterialParameter &MaterialParameter_in) const
{
const double oneOver3 = 1.0/3.0;
const double rt23 = sqrt(2.0/3.0);
tensor I2("I", 2, def_dim_2);
double e0 = gete0(MaterialParameter_in);
double e_r = gete_r(MaterialParameter_in);
double lambda_c = getlambda_c(MaterialParameter_in);
double xi = getxi(MaterialParameter_in);
double Pat = getPat(MaterialParameter_in);
//double m = getm(MaterialParameter_in);
double M_cal = getM_cal(MaterialParameter_in);
double cc = getcc(MaterialParameter_in);
double A0 = getA0(MaterialParameter_in);
double nd = getnd(MaterialParameter_in);
stresstensor alpha = getalpha(MaterialParameter_in);
stresstensor z = getz(MaterialParameter_in);
stresstensor n;
stresstensor alpha_d;
stresstensor alpha_d_alpha;
double g = 0.0;
double ec = e_r;
double stateParameter = 0.0;
double expnd = 1.0;
//double ad = 0.0;
double D0 = 0.0;
stresstensor s_bar;
double norm_s = 0.0;
double epsilon_v = 0.0;
double e = e0;
double J3D;
double cos3theta = 0.0;
double z_n = 0.0;
double alpha_n = 0.0;
double s_n = 0.0;
double p = Stre.p_hydrostatic();
stresstensor s = Stre.deviator();
s_bar = s - (alpha *p);
norm_s = sqrt( (s_bar("ij")*s_bar("ij")).trace() );
if (p > 0.0 && norm_s > 0.0)
n = s_bar * (1.0/norm_s);
J3D = n.Jinvariant3();
cos3theta = -3.0*sqrt(6.0) *J3D;
if (cos3theta > 1.0)
cos3theta = 1.0;
if (cos3theta < -1.0)
cos3theta = -1.0;
g = getg(cc, cos3theta);
if ( (p/Pat) >= 0.0 )
ec = getec(e_r, lambda_c, xi, Pat, p);
epsilon_v = Stra.Iinvariant1();
e = e0 + (1.0 + e0) *epsilon_v;
stateParameter = e - ec;
expnd = exp(nd*stateParameter);
alpha_n = (alpha("ij")*n("ij")).trace();
s_n = (s("ij")*n("ij")).trace();
// way 1
//ad = g*M_cal*expnd - m;
//D0 = rt23 * ad - alpha_n;
// way 2
D0 = rt23*g*M_cal*expnd - s_n /p;
tensor dD_dz(2, def_dim_2, 0.0);
// dD_dz:
if (z_n > 0.0)
dD_dz = n *A0;
// dm_da:
tensor tensor1 = I2("ij")*dD_dz("mn");
tensor1.null_indices();
PlasticFlow::PF_tensorR4 = tensor1 *(-D0*oneOver3);
return PlasticFlow::PF_tensorR4;
}
//================================================================================
const tensor& DM04_PF::Dm_Dkin(const stresstensor &Stre,
const straintensor &Stra,
const MaterialParameter &MaterialParameter_in) const
{
const double oneOver3 = 1.0/3.0;
const double rt23 = sqrt(2.0/3.0);
tensor I2("I", 2, def_dim_2);
tensor I4 = I2("ij")*I2("kl");
tensor I4s = ( I4.transpose0110() + I4.transpose0111() ) *0.5;
double e0 = gete0(MaterialParameter_in);
double e_r = gete_r(MaterialParameter_in);
double lambda_c = getlambda_c(MaterialParameter_in);
double xi = getxi(MaterialParameter_in);
double Pat = getPat(MaterialParameter_in);
//double m = getm(MaterialParameter_in);
double M_cal = getM_cal(MaterialParameter_in);
double cc = getcc(MaterialParameter_in);
double A0 = getA0(MaterialParameter_in);
double nd = getnd(MaterialParameter_in);
stresstensor alpha = getalpha(MaterialParameter_in);
stresstensor z = getz(MaterialParameter_in);
stresstensor n;
stresstensor alpha_d;
stresstensor alpha_d_alpha;
double g = 0.0;
double ec = e_r;
double stateParameter = 0.0;
double expnd = 1.0;
//double ad = 0.0;
double A_d = 0.0;
double B = 1.0;
double C = 0.0;
double D0 = 0.0;
stresstensor s_bar;
double norm_s = 0.0;
double epsilon_v = 0.0;
double e = e0;
double J3D;
double cos3theta = 0.0;
double z_n = 0.0;
double alpha_n = 0.0;
double s_n = 0.0;
double p = Stre.p_hydrostatic();
stresstensor s = Stre.deviator();
s_bar = s - (alpha *p);
norm_s = sqrt( (s_bar("ij")*s_bar("ij")).trace() );
if (p > 0.0 && norm_s > 0.0)
n = s_bar * (1.0/norm_s);
J3D = n.Jinvariant3();
cos3theta = -3.0*sqrt(6.0) *J3D;
if (cos3theta > 1.0)
cos3theta = 1.0;
if (cos3theta < -1.0)
cos3theta = -1.0;
g = getg(cc, cos3theta);
if ( (p/Pat) >= 0.0 )
ec = getec(e_r, lambda_c, xi, Pat, p);
epsilon_v = Stra.Iinvariant1();
e = e0 + (1.0 + e0) *epsilon_v;
stateParameter = e - ec;
expnd = exp(nd*stateParameter);
alpha_n = (alpha("ij")*n("ij")).trace();
s_n = (s("ij")*n("ij")).trace();
// way 1
//ad = g*M_cal*expnd - m;
//D0 = rt23 * ad - alpha_n;
// way 2
D0 = rt23*g*M_cal*expnd - s_n /p;
z_n = (z("ij")*n("ij")).trace();
if (z_n < 0.0)
z_n = 0.0;
A_d = A0 * (1.0 + z_n);
B = 1.0 + 1.5 *((1.0-cc)/cc) *g *cos3theta;
C = 3.0 *sqrt(1.5) *((1.0-cc)/cc) *g;
tensor n_n = n("ik")*n("kj");
n_n.null_indices();
tensor nt_nt = n("ij")*n("kl");
nt_nt.null_indices();
tensor alpha_I = alpha("ij")*I2("kl");
alpha_I.null_indices();
tensor n_I = n("ij")*I2("kl");
n_I.null_indices();
// dn_dalpha:
tensor dn_da = nt_nt - I4s;
dn_da = dn_da *(p/norm_s);
// dcos3theta_dalpha:
tensor dcos3theta_da = dn_da("ijmn")*n_n("ji");
dcos3theta_da.null_indices();
dcos3theta_da = dcos3theta_da *(-3.0*sqrt(6.0));
// dg_da:
tensor dg_da = dcos3theta_da *(g*g*(1.0-cc)/(2.0*cc));
// dB_da:
tensor dB_da = (dg_da*cos3theta + dcos3theta_da*g) *(1.5*(1.0-cc)/cc);
// dC_ds:
tensor dC_da = dg_da *(3.0*sqrt(1.5)*(1.0-cc)/cc);
// dR_da:
tensor tensor1 = n("ij")*dB_da("mn");
tensor1.null_indices();
tensor tensor2 = n_n - I2 *oneOver3;
tensor tensor3 = tensor2("ij")*dC_da("mn");
tensor3.null_indices();
tensor tensor4 = n("kj")*dn_da("ikmn");
tensor4.null_indices();
tensor4.transpose1100();
tensor dR_da = dn_da *B + tensor1 + tensor4 *(2.0*C) + tensor3;
// dad_da:
tensor dad_da = dg_da *(M_cal*expnd);
// dD_da:
// way 1
//tensor tensor5 = alpha("pq")*dn_da("pqmn");
// tensor5.null_indices();
//tensor dD_da = (dad_da *rt23 - n - tensor5) *(-A_d);
// way 2
tensor tensor5 = s("pq")*dn_da("pqmn");
tensor5.null_indices();
tensor dD_da = (dad_da *rt23 - tensor5 *(1.0/p)) *(-A_d);
if (z_n > 0.0) {
tensor tensor6 = z("pq")*dn_da("pqmn");
tensor6.null_indices();
dD_da += tensor6 *(-A0*D0);
}
// dm_da:
tensor tensor7 = I2("ij")*dD_da("mn");
tensor7.null_indices();
PlasticFlow::PF_tensorR4 = dR_da + tensor7 *oneOver3;
return PlasticFlow::PF_tensorR4;
}
//================================================================================
const straintensor& DM04_PF::PlasticFlowTensor(const stresstensor& Stre,
const straintensor& Stra,
const MaterialParameter &MaterialParameter_in) const
{
const double oneOver3 = 1.0/3.0;
const double rt23 = sqrt(2.0/3.0);
tensor I2("I", 2, def_dim_2);
double e0 = gete0(MaterialParameter_in);
double e_r = gete_r(MaterialParameter_in);
double lambda_c = getlambda_c(MaterialParameter_in);
double xi = getxi(MaterialParameter_in);
double Pat = getPat(MaterialParameter_in);
//double m = getm(MaterialParameter_in);
double M_cal = getM_cal(MaterialParameter_in);
double cc = getcc(MaterialParameter_in);
double A0 = getA0(MaterialParameter_in);
double nd = getnd(MaterialParameter_in);
stresstensor alpha = getalpha(MaterialParameter_in);
stresstensor z = getz(MaterialParameter_in);
stresstensor n;
stresstensor alpha_d;
stresstensor alpha_d_alpha;
double g = 0.0;
double ec = e_r;
double stateParameter = 0.0;
double expnd = 1.0;
//double ad = 0.0;
double A_d = 0.0;
double B = 1.0;
double C = 0.0;
double D = 0.0;
double D0 = 0.0;
stresstensor s_bar;
double norm_s = 0.0;
double epsilon_v = 0.0;
double e = e0;
double J3D;
double cos3theta = 0.0;
double z_n = 0.0;
double alpha_n = 0.0;
double s_n = 0.0;
double p = Stre.p_hydrostatic();
stresstensor s = Stre.deviator();
s_bar = s - (alpha *p);
norm_s = sqrt( (s_bar("ij")*s_bar("ij")).trace() );
if (p > 0.0 && norm_s > 0.0)
n = s_bar * (1.0/norm_s);
J3D = n.Jinvariant3();
cos3theta = -3.0*sqrt(6.0) *J3D;
if (p <= 0.0)
cos3theta = 1.0;
if (cos3theta > 1.0)
cos3theta = 1.0;
if (cos3theta < -1.0)
cos3theta = -1.0;
g = getg(cc, cos3theta);
if ( (p/Pat) >= 0.0 )
ec = getec(e_r, lambda_c, xi, Pat, p);
epsilon_v = Stra.Iinvariant1();
e = e0 + (1.0 + e0) *epsilon_v;
stateParameter = e - ec;
expnd = exp(nd*stateParameter);
alpha_n = (alpha("ij")*n("ij")).trace();
s_n = (s("ij")*n("ij")).trace();
// way 1
//ad = g*M_cal*expnd - m;
//D0 = rt23 *ad - alpha_n;
// way 2, better use this when "p" is small
D0 = rt23*g*M_cal*expnd - s_n /p;
z_n = (z("ij")*n("ij")).trace();
if (z_n < 0.0)
z_n = 0.0;
A_d = A0 * (1.0 + z_n);
D = D0 *(-A_d);
B = 1.0 + 1.5 *((1.0-cc)/cc) *g *cos3theta;
C = 3.0 *sqrt(1.5) *((1.0-cc)/cc) *g;
stresstensor n_n = n("ik")*n("kj");
n_n.null_indices();
// note different 'positive-negative' since we assume extension (dilation) positive
// which is different from the Ref.
DM04_PF::DM04m = n *B + n_n *C + I2 *((D-C)*oneOver3);
return DM04_PF::DM04m;
}
void Matrix::addscale (float x,float y,float z)
{
getx ()->mul (x);
gety ()->mul (y);
getz ()->mul (z);
}
