void
NineNodeMixedQuad::formResidAndTangent( int tang_flag )
{
//strains ordered : eps11, eps22, eps33, 2*eps12
//volumtric strains projected onto {1, \xi, \eta} natural coordinates
static const int ndm = 2 ;
static const int ndf = 2 ;
static const int nstress = 4 ;
static const int numberNodes = 9 ;
static const int numberGauss = 9 ;
static const int nShape = 3 ;
static const int nMixed = 3 ;
int i, j, k, p, q, r, s ;
int jj, kk ;
int success ;
static double volume ;
static double xsj ; // determinant jacaobian matrix
static double dvol[numberGauss] ; //volume element
static double gaussPoint[ndm] ;
static double natCoorArray[ndm][numberGauss] ;
static Vector strain(nstress) ; //strain
static double shp[nShape][numberNodes] ; //shape functions at a gauss point
static double Shape[nShape][numberNodes][numberGauss] ; //all the shape functions
static double shpBar[nShape][numberNodes][nMixed] ; //mean value of shape functions
static double rightHandSide[nShape][numberNodes][nMixed] ;
static Vector residJ(ndf) ; //nodeJ residual
static Matrix stiffJK(ndf,ndf) ; //nodeJK stiffness
static Vector stress(nstress) ; //stress
static Matrix dd(nstress,nstress) ; //material tangent
static double interp[nMixed] ;
static Matrix Proj(3,3) ; //projection matrix
static Matrix ProjInv(3,3) ;
static Matrix Iden(3,3) ;
Iden(0,0) = 1.0 ;
Iden(1,1) = 1.0 ;
Iden(2,2) = 1.0 ;
//---------B-matrices------------------------------------
static Matrix BJ(nstress,ndf) ; // B matrix node J
static Matrix BJtran(ndf,nstress) ;
static Matrix BK(nstress,ndf) ; // B matrix node k
static Matrix BJtranD(ndf,nstress) ;
//-------------------------------------------------------
//zero stiffness and residual
stiff.Zero( ) ;
resid.Zero( ) ;
//node coordinates
computeBasis() ;
//zero mean shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ ) {
for (r=0; r<nMixed; r++ ) {
shpBar[p][q][r] = 0.0 ;
rightHandSide[p][q][r] = 0.0 ;
}
}//end for q
} // end for p
//zero volume
volume = 0.0 ;
//zero projection matrix
Proj.Zero( ) ;
ProjInv.Zero( ) ;
//gauss loop to compute and save shape functions
int count = 0 ;
for ( i = 0; i < 3; i++ ) {
for ( j = 0; j < 3; j++ ) {
gaussPoint[0] = sg[i] ;
gaussPoint[1] = sg[j] ;
//save gauss point locations
natCoorArray[0][count] = gaussPoint[0] ;
natCoorArray[1][count] = gaussPoint[1] ;
//get shape functions
shape2dNine( gaussPoint, xl, shp, xsj ) ;
//save shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ )
Shape[p][q][count] = shp[p][q] ;
} // end for p
//volume element to also be saved
dvol[count] = ( wg[i]*wg[j] ) * xsj ;
//add to projection matrix
interp[0] = 1.0 ;
interp[1] = gaussPoint[0] ;
interp[2] = gaussPoint[1] ;
for ( r=0; r<nMixed; r++ ) {
for ( s=0; s<nMixed; s++ )
Proj(r,s) += ( interp[r]*interp[s] * dvol[count] ) ;
}//end for r
volume += dvol[count] ;
//add to mean shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ ) {
for ( s=0; s<nMixed; s++ )
rightHandSide[p][q][s] += ( shp[p][q] * interp[s] * dvol[count] ) ;
}//end for q
} // end for p
//increment gauss point counter
count++ ;
} //end for j
} // end for i
//invert projection matrix
//int Solve(const Matrix &M, Matrix &res) const;
Proj.Solve( Iden, ProjInv ) ;
//mean value of shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ ) {
for (r=0; r<nMixed; r++ ) {
for (s=0; s<nMixed; s++ )
shpBar[p][q][r] += ( ProjInv(r,s) * rightHandSide[p][q][s] ) ;
}//end for r
}//end for q
}//end for p
//gauss loop
for ( i=0; i<numberGauss; i++ ) {
//extract gauss point location
gaussPoint[0] = natCoorArray[0][i] ;
gaussPoint[1] = natCoorArray[1][i] ;
//extract shape functions from saved array
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ )
shp[p][q] = Shape[p][q][i] ;
} // end for p
//zero the strains
strain.Zero( ) ;
// j-node loop to compute strain
for ( j=0; j<numberNodes; j++ ) {
//compute B matrix
BJ = computeBbar( j, gaussPoint, shp, shpBar ) ;
//nodal displacements
const Vector &ul = nodePointers[j]->getTrialDisp( ) ;
//compute the strain
//strain += (BJ*ul) ;
strain.addMatrixVector(1.0, BJ,ul,1.0 ) ;
} // end for j
//send the strain to the material
success = materialPointers[i]->setTrialStrain( strain ) ;
//compute the stress
stress = materialPointers[i]->getStress( ) ;
//multiply by volume element
stress *= dvol[i] ;
if ( tang_flag == 1 ) {
dd = materialPointers[i]->getTangent( ) ;
dd *= dvol[i] ;
} //end if tang_flag
//residual and tangent calculations node loops
jj = 0 ;
for ( j=0; j<numberNodes; j++ ) {
BJ = computeBbar( j, gaussPoint, shp, shpBar ) ;
//transpose
//BJtran = transpose( nstress, ndf, BJ ) ;
for (p=0; p<ndf; p++) {
for (q=0; q<nstress; q++)
BJtran(p,q) = BJ(q,p) ;
}//end for p
//residual
//residJ = BJtran * stress ;
residJ.addMatrixVector(0.0, BJtran,stress,1.0);
//residual
for ( p=0; p<ndf; p++ )
resid( jj + p ) += residJ(p) ;
if ( tang_flag == 1 ) {
//BJtranD = BJtran * dd ;
BJtranD.addMatrixProduct(0.0, BJtran,dd,1.0);
kk = 0 ;
for ( k=0; k<numberNodes; k++ ) {
BK = computeBbar( k, gaussPoint, shp, shpBar ) ;
//stiffJK = BJtranD * BK ;
stiffJK.addMatrixProduct(0.0, BJtranD,BK,1.0) ;
for ( p=0; p<ndf; p++ ) {
for ( q=0; q<ndf; q++ )
stiff( jj+p, kk+q ) += stiffJK( p, q ) ;
} //end for p
kk += ndf ;
}//end for k loop
}//end if tang_flag
jj += ndf ;
}//end for j loop
}//end for i gauss loop
return ;
}
//return secant matrix
const Matrix&
NineNodeMixedQuad::getInitialStiff( )
{
if (Ki != 0)
return *Ki;
static const int ndm = 2 ;
static const int ndf = 2 ;
static const int nstress = 4 ;
static const int numberNodes = 9 ;
static const int numberGauss = 9 ;
static const int nShape = 3 ;
static const int nMixed = 3 ;
int i, j, k, p, q, r, s ;
int jj, kk ;
static double volume ;
static double xsj ; // determinant jacaobian matrix
static double dvol[numberGauss] ; //volume element
static double gaussPoint[ndm] ;
static double natCoorArray[ndm][numberGauss] ;
static Vector strain(nstress) ; //strain
static double shp[nShape][numberNodes] ; //shape functions at a gauss point
static double Shape[nShape][numberNodes][numberGauss] ; //all the shape functions
static double shpBar[nShape][numberNodes][nMixed] ; //mean value of shape functions
static double rightHandSide[nShape][numberNodes][nMixed] ;
static Vector residJ(ndf) ; //nodeJ residual
static Matrix stiffJK(ndf,ndf) ; //nodeJK stiffness
static Vector stress(nstress) ; //stress
static Matrix dd(nstress,nstress) ; //material tangent
static double interp[nMixed] ;
static Matrix Proj(3,3) ; //projection matrix
static Matrix ProjInv(3,3) ;
static Matrix Iden(3,3) ;
Iden(0,0) = 1.0 ;
Iden(1,1) = 1.0 ;
Iden(2,2) = 1.0 ;
//---------B-matrices------------------------------------
static Matrix BJ(nstress,ndf) ; // B matrix node J
static Matrix BJtran(ndf,nstress) ;
static Matrix BK(nstress,ndf) ; // B matrix node k
static Matrix BJtranD(ndf,nstress) ;
//-------------------------------------------------------
//zero stiffness and residual
stiff.Zero( ) ;
//node coordinates
computeBasis() ;
//zero mean shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ ) {
for (r=0; r<nMixed; r++ ) {
shpBar[p][q][r] = 0.0 ;
rightHandSide[p][q][r] = 0.0 ;
}
}//end for q
} // end for p
//zero volume
volume = 0.0 ;
//zero projection matrix
Proj.Zero( ) ;
ProjInv.Zero( ) ;
//gauss loop to compute and save shape functions
int count = 0 ;
for ( i = 0; i < 3; i++ ) {
for ( j = 0; j < 3; j++ ) {
gaussPoint[0] = sg[i] ;
gaussPoint[1] = sg[j] ;
//save gauss point locations
natCoorArray[0][count] = gaussPoint[0] ;
natCoorArray[1][count] = gaussPoint[1] ;
//get shape functions
shape2dNine( gaussPoint, xl, shp, xsj ) ;
//save shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ )
Shape[p][q][count] = shp[p][q] ;
} // end for p
//volume element to also be saved
dvol[count] = ( wg[i]*wg[j] ) * xsj ;
//add to projection matrix
interp[0] = 1.0 ;
interp[1] = gaussPoint[0] ;
interp[2] = gaussPoint[1] ;
for ( r=0; r<nMixed; r++ ) {
for ( s=0; s<nMixed; s++ )
Proj(r,s) += ( interp[r]*interp[s] * dvol[count] ) ;
}//end for r
volume += dvol[count] ;
//add to mean shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ ) {
for ( s=0; s<nMixed; s++ )
rightHandSide[p][q][s] += ( shp[p][q] * interp[s] * dvol[count] ) ;
}//end for q
} // end for p
//increment gauss point counter
count++ ;
} //end for j
} // end for i
//invert projection matrix
//int Solve(const Matrix &M, Matrix &res) const;
Proj.Solve( Iden, ProjInv ) ;
//mean value of shape functions
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ ) {
for (r=0; r<nMixed; r++ ) {
for (s=0; s<nMixed; s++ )
shpBar[p][q][r] += ( ProjInv(r,s) * rightHandSide[p][q][s] ) ;
}//end for r
}//end for q
}//end for p
//gauss loop
for ( i=0; i<numberGauss; i++ ) {
//extract gauss point location
gaussPoint[0] = natCoorArray[0][i] ;
gaussPoint[1] = natCoorArray[1][i] ;
//extract shape functions from saved array
for ( p=0; p<nShape; p++ ) {
for ( q=0; q<numberNodes; q++ )
shp[p][q] = Shape[p][q][i] ;
} // end for p
dd = materialPointers[i]->getInitialTangent( ) ;
dd *= dvol[i] ;
//residual and tangent calculations node loops
jj = 0 ;
for ( j=0; j<numberNodes; j++ ) {
BJ = computeBbar( j, gaussPoint, shp, shpBar ) ;
//transpose
//BJtran = transpose( nstress, ndf, BJ ) ;
for (p=0; p<ndf; p++) {
for (q=0; q<nstress; q++)
BJtran(p,q) = BJ(q,p) ;
}//end for p
//BJtranD = BJtran * dd ;
BJtranD.addMatrixProduct(0.0, BJtran,dd,1.0);
kk = 0 ;
for ( k=0; k<numberNodes; k++ ) {
BK = computeBbar( k, gaussPoint, shp, shpBar ) ;
//stiffJK = BJtranD * BK ;
stiffJK.addMatrixProduct(0.0, BJtranD,BK,1.0) ;
for ( p=0; p<ndf; p++ ) {
for ( q=0; q<ndf; q++ )
stiff( jj+p, kk+q ) += stiffJK( p, q ) ;
} //end for p
kk += ndf ;
}//end for k loop
jj += ndf ;
}//end for j loop
}//end for i gauss loop
Ki = new Matrix(stiff);
return stiff;
}
//form residual and tangent
void
ShellMITC9::formResidAndTangent( int tang_flag )
{
//
// six(6) nodal dof's ordered :
//
// - -
// | u1 | <---plate membrane
// | u2 |
// |----------|
// | w = u3 | <---plate bending
// | theta1 |
// | theta2 |
// |----------|
// | theta3 | <---drill
// - -
//
// membrane strains ordered :
//
// strain(0) = eps00 i.e. (11)-strain
// strain(1) = eps11 i.e. (22)-strain
// strain(2) = gamma01 i.e. (12)-shear
//
// curvatures and shear strains ordered :
//
// strain(3) = kappa00 i.e. (11)-curvature
// strain(4) = kappa11 i.e. (22)-curvature
// strain(5) = 2*kappa01 i.e. 2*(12)-curvature
//
// strain(6) = gamma02 i.e. (13)-shear
// strain(7) = gamma12 i.e. (23)-shear
//
// same ordering for moments/shears but no 2
//
// Then,
// epsilon00 = -z * kappa00 + eps00_membrane
// epsilon11 = -z * kappa11 + eps11_membrane
// gamma01 = 2*epsilon01 = -z * (2*kappa01) + gamma01_membrane
//
// Shear strains gamma02, gamma12 constant through cross section
//
static const int ndf = 6 ; //two membrane plus three bending plus one drill
static const int nstress = 8 ; //three membrane, three moment, two shear
static const int ngauss = 9 ;
static const int numnodes = 9 ;
int i, j, k, p, q ;
int jj, kk ;
int node ;
int success ;
double volume = 0.0 ;
static double xsj ; // determinant jacaobian matrix
static double dvol[ngauss] ; //volume element
static Vector strain(nstress) ; //strain
static double shp[3][numnodes] ; //shape functions at a gauss point
static Vector residJ(ndf) ; //nodeJ residual
static Matrix stiffJK(ndf,ndf) ; //nodeJK stiffness
static Vector stress(nstress) ; //stress resultants
static Matrix dd(nstress,nstress) ; //material tangent
double epsDrill = 0.0 ; //drilling "strain"
double tauDrill = 0.0 ; //drilling "stress"
//---------B-matrices------------------------------------
static Matrix BJ(nstress,ndf) ; // B matrix node J
static Matrix BJtran(ndf,nstress) ;
static Matrix BK(nstress,ndf) ; // B matrix node k
static Matrix BJtranD(ndf,nstress) ;
static Matrix Bbend(3,3) ; // bending B matrix
static Matrix Bshear(2,3) ; // shear B matrix
static Matrix Bmembrane(3,2) ; // membrane B matrix
static double BdrillJ[ndf] ; //drill B matrix
static double BdrillK[ndf] ;
double *drillPointer ;
static double saveB[nstress][ndf][numnodes] ;
//-------------------------------------------------------
//zero stiffness and residual
stiff.Zero( ) ;
resid.Zero( ) ;
//compute Jacobian and inverse at center
double L1 = 0.0 ;
double L2 = 0.0 ;
//gauss loop
for ( i = 0; i < ngauss; i++ ) {
//get shape functions
shape2d( sg[i], tg[i], xl, shp, xsj ) ;
//volume element to also be saved
dvol[i] = wg[i] * xsj ;
volume += dvol[i] ;
//zero the strains
strain.Zero( ) ;
epsDrill = 0.0 ;
// j-node loop to compute strain
for ( j = 0; j < numnodes; j++ ) {
//compute B matrix
Bmembrane = computeBmembrane( j, shp ) ;
Bbend = computeBbend( j, shp ) ;
Bshear = computeBshear( j, shp ) ;
BJ = assembleB( Bmembrane, Bbend, Bshear ) ;
//save the B-matrix
for (p=0; p<nstress; p++) {
for (q=0; q<ndf; q++ ) {
saveB[p][q][j] = BJ(p,q) ;
}//end for q
}//end for p
//nodal "displacements"
const Vector &ul = nodePointers[j]->getTrialDisp( ) ;
//compute the strain
//strain += (BJ*ul) ;
strain.addMatrixVector(1.0, BJ,ul,1.0 ) ;
//drilling B matrix
drillPointer = computeBdrill( j, shp ) ;
for (p=0; p<ndf; p++ ) {
//BdrillJ[p] = *drillPointer++ ;
BdrillJ[p] = *drillPointer ; //set p-th component
drillPointer++ ; //pointer arithmetic
}//end for p
//drilling "strain"
for ( p = 0; p < ndf; p++ )
epsDrill += BdrillJ[p]*ul(p) ;
} // end for j
//send the strain to the material
success = materialPointers[i]->setTrialSectionDeformation( strain ) ;
//compute the stress
stress = materialPointers[i]->getStressResultant( ) ;
//drilling "stress"
tauDrill = Ktt * epsDrill ;
//multiply by volume element
stress *= dvol[i] ;
tauDrill *= dvol[i] ;
if ( tang_flag == 1 ) {
dd = materialPointers[i]->getSectionTangent( ) ;
dd *= dvol[i] ;
} //end if tang_flag
//residual and tangent calculations node loops
jj = 0 ;
for ( j = 0; j < numnodes; j++ ) {
//extract BJ
for (p=0; p<nstress; p++) {
for (q=0; q<ndf; q++ )
BJ(p,q) = saveB[p][q][j] ;
}//end for p
//multiply bending terms by (-1.0) for correct statement
// of equilibrium
for ( p = 3; p < 6; p++ ) {
for ( q = 3; q < 6; q++ )
BJ(p,q) *= (-1.0) ;
} //end for p
//transpose
//BJtran = transpose( 8, ndf, BJ ) ;
for (p=0; p<ndf; p++) {
for (q=0; q<nstress; q++)
BJtran(p,q) = BJ(q,p) ;
}//end for p
//residJ = BJtran * stress ;
residJ.addMatrixVector(0.0, BJtran,stress,1.0 ) ;
//drilling B matrix
drillPointer = computeBdrill( j, shp ) ;
for (p=0; p<ndf; p++ ) {
BdrillJ[p] = *drillPointer ;
drillPointer++ ;
}//end for p
//residual including drill
for ( p = 0; p < ndf; p++ )
resid( jj + p ) += ( residJ(p) + BdrillJ[p]*tauDrill ) ;
if ( tang_flag == 1 ) {
//BJtranD = BJtran * dd ;
BJtranD.addMatrixProduct(0.0, BJtran,dd,1.0 ) ;
for (p=0; p<ndf; p++) {
BdrillJ[p] *= ( Ktt*dvol[i] ) ;
}//end for p
kk = 0 ;
for ( k = 0; k < numnodes; k++ ) {
//extract BK
for (p=0; p<nstress; p++) {
for (q=0; q<ndf; q++ ){
BK(p,q) = saveB[p][q][k];
}//end for q
}//end for p
//drilling B matrix
drillPointer = computeBdrill( k, shp ) ;
for (p=0; p<ndf; p++ ) {
BdrillK[p] = *drillPointer ;
drillPointer++ ;
}//end for p
//stiffJK = BJtranD * BK ;
// + transpose( 1,ndf,BdrillJ ) * BdrillK ;
stiffJK.addMatrixProduct(0.0, BJtranD,BK,1.0 ) ;
for ( p = 0; p < ndf; p++ ) {
for ( q = 0; q < ndf; q++ ) {
stiff( jj+p, kk+q ) += stiffJK(p,q)
+ ( BdrillJ[p]*BdrillK[q] ) ;
}//end for q
}//end for p
kk += ndf ;
} // end for k loop
} // end if tang_flag
jj += ndf ;
} // end for j loop
} //end for i gauss loop
return ;
}
//return secant matrix
const Matrix& ShellMITC9::getInitialStiff( )
{
if (Ki != 0)
return *Ki;
static const int ndf = 6 ; //two membrane plus three bending plus one drill
static const int nstress = 8 ; //three membrane, three moment, two shear
static const int ngauss = 9 ;
static const int numnodes = 9 ;
int i, j, k, p, q ;
int jj, kk ;
int node ;
double volume = 0.0 ;
static double xsj ; // determinant jacaobian matrix
static double dvol[ngauss] ; //volume element
static double shp[3][numnodes] ; //shape functions at a gauss point
static Matrix stiffJK(ndf,ndf) ; //nodeJK stiffness
static Matrix dd(nstress,nstress) ; //material tangent
//static Matrix J0(2,2) ; //Jacobian at center
//static Matrix J0inv(2,2) ; //inverse of Jacobian at center
//---------B-matrices------------------------------------
static Matrix BJ(nstress,ndf) ; // B matrix node J
static Matrix BJtran(ndf,nstress) ;
static Matrix BK(nstress,ndf) ; // B matrix node k
static Matrix BJtranD(ndf,nstress) ;
static Matrix Bbend(3,3) ; // bending B matrix
static Matrix Bshear(2,3) ; // shear B matrix
static Matrix Bmembrane(3,2) ; // membrane B matrix
static double BdrillJ[ndf] ; //drill B matrix
static double BdrillK[ndf] ;
double *drillPointer ;
static double saveB[nstress][ndf][numnodes] ;
//-------------------------------------------------------
stiff.Zero( ) ;
//compute Jacobian and inverse at center
double L1 = 0.0 ;
double L2 = 0.0 ;
//computeJacobian( L1, L2, xl, J0, J0inv ) ;
//gauss loop
for ( i = 0; i < ngauss; i++ ) {
//get shape functions
shape2d( sg[i], tg[i], xl, shp, xsj ) ;
//volume element to also be saved
dvol[i] = wg[i] * xsj ;
volume += dvol[i] ;
// j-node loop to compute strain
for ( j = 0; j < numnodes; j++ ) {
//compute B matrix
Bmembrane = computeBmembrane( j, shp ) ;
Bbend = computeBbend( j, shp ) ;
Bshear = computeBshear( j, shp ) ;
BJ = assembleB( Bmembrane, Bbend, Bshear ) ;
//save the B-matrix
for (p=0; p<nstress; p++) {
for (q=0; q<ndf; q++ )
saveB[p][q][j] = BJ(p,q) ;
}//end for p
//drilling B matrix
drillPointer = computeBdrill( j, shp ) ;
for (p=0; p<ndf; p++ ) {
//BdrillJ[p] = *drillPointer++ ;
BdrillJ[p] = *drillPointer ; //set p-th component
drillPointer++ ; //pointer arithmetic
}//end for p
} // end for j
dd = materialPointers[i]->getInitialTangent( ) ;
dd *= dvol[i] ;
//residual and tangent calculations node loops
jj = 0 ;
for ( j = 0; j < numnodes; j++ ) {
//extract BJ
for (p=0; p<nstress; p++) {
for (q=0; q<ndf; q++ )
BJ(p,q) = saveB[p][q][j] ;
}//end for p
//multiply bending terms by (-1.0) for correct statement
// of equilibrium
for ( p = 3; p < 6; p++ ) {
for ( q = 3; q < 6; q++ )
BJ(p,q) *= (-1.0) ;
} //end for p
//transpose
//BJtran = transpose( 8, ndf, BJ ) ;
for (p=0; p<ndf; p++) {
for (q=0; q<nstress; q++)
BJtran(p,q) = BJ(q,p) ;
}//end for p
//drilling B matrix
drillPointer = computeBdrill( j, shp ) ;
for (p=0; p<ndf; p++ ) {
BdrillJ[p] = *drillPointer ;
drillPointer++ ;
}//end for p
//BJtranD = BJtran * dd ;
BJtranD.addMatrixProduct(0.0, BJtran,dd,1.0 ) ;
for (p=0; p<ndf; p++)
BdrillJ[p] *= ( Ktt*dvol[i] ) ;
kk = 0 ;
for ( k = 0; k < numnodes; k++ ) {
//extract BK
for (p=0; p<nstress; p++) {
for (q=0; q<ndf; q++ )
BK(p,q) = saveB[p][q][k] ;
}//end for p
//drilling B matrix
drillPointer = computeBdrill( k, shp ) ;
for (p=0; p<ndf; p++ ) {
BdrillK[p] = *drillPointer ;
drillPointer++ ;
}//end for p
//stiffJK = BJtranD * BK ;
// + transpose( 1,ndf,BdrillJ ) * BdrillK ;
stiffJK.addMatrixProduct(0.0, BJtranD,BK,1.0 ) ;
for ( p = 0; p < ndf; p++ ) {
for ( q = 0; q < ndf; q++ ) {
stiff( jj+p, kk+q ) += stiffJK(p,q)
+ ( BdrillJ[p]*BdrillK[q] ) ;
}//end for q
}//end for p
kk += ndf ;
} // end for k loop
jj += ndf ;
} // end for j loop
} //end for i gauss loop
Ki = new Matrix(stiff);
return stiff ;
}
//*********************************************************************
//form residual and tangent
void BbarBrick::formResidAndTangent( int tang_flag )
{
//strains ordered : eps11, eps22, eps33, 2*eps12, 2*eps23, 2*eps31
static const int ndm = 3 ;
static const int ndf = 3 ;
static const int nstress = 6 ;
static const int numberNodes = 8 ;
static const int numberGauss = 8 ;
static const int nShape = 4 ;
int i, j, k, p, q ;
int jj, kk ;
int success ;
static double volume ;
static double xsj ; // determinant jacaobian matrix
static double dvol[numberGauss] ; //volume element
static double gaussPoint[ndm] ;
static Vector strain(nstress) ; //strain
static double shp[nShape][numberNodes] ; //shape functions at a gauss point
static double Shape[nShape][numberNodes][numberGauss] ; //all the shape functions
static double shpBar[nShape][numberNodes] ; //mean value of shape functions
static Vector residJ(ndf) ; //nodeJ residual
static Matrix stiffJK(ndf,ndf) ; //nodeJK stiffness
static Vector stress(nstress) ; //stress
static Matrix dd(nstress,nstress) ; //material tangent
//---------B-matrices------------------------------------
static Matrix BJ(nstress,ndf) ; // B matrix node J
static Matrix BJtran(ndf,nstress) ;
static Matrix BK(nstress,ndf) ; // B matrix node k
static Matrix BJtranD(ndf,nstress) ;
//-------------------------------------------------------
//zero stiffness and residual
stiff.Zero( ) ;
resid.Zero( ) ;
//compute basis vectors and local nodal coordinates
computeBasis( ) ;
//zero mean shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shpBar[p][q] = 0.0 ;
} // end for p
//zero volume
volume = 0.0 ;
//gauss loop to compute and save shape functions
int count = 0 ;
for ( i = 0; i < 2; i++ ) {
for ( j = 0; j < 2; j++ ) {
for ( k = 0; k < 2; k++ ) {
gaussPoint[0] = sg[i] ;
gaussPoint[1] = sg[j] ;
gaussPoint[2] = sg[k] ;
//get shape functions
shp3d( gaussPoint, xsj, shp, xl ) ;
//save shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
Shape[p][q][count] = shp[p][q] ;
} // end for p
//volume element to also be saved
dvol[count] = wg[count] * xsj ;
//add to volume
volume += dvol[count] ;
//add to mean shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shpBar[p][q] += ( dvol[count] * shp[p][q] ) ;
} // end for p
count++ ;
} //end for k
} //end for j
} // end for i
//mean value of shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shpBar[p][q] /= volume ;
} // end for p
//gauss loop
for ( i = 0; i < numberGauss; i++ ) {
//extract shape functions from saved array
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shp[p][q] = Shape[p][q][i] ;
} // end for p
//zero the strains
strain.Zero( ) ;
// j-node loop to compute strain
for ( j = 0; j < numberNodes; j++ ) {
//compute B matrix
BJ = computeBbar( j, shp, shpBar ) ;
//nodal displacements
const Vector &ul = nodePointers[j]->getTrialDisp( ) ;
//compute the strain
//strain += (BJ*ul) ;
strain.addMatrixVector(1.0, BJ,ul,1.0 ) ;
} // end for j
//send the strain to the material
success = materialPointers[i]->setTrialStrain( strain ) ;
//compute the stress
stress = materialPointers[i]->getStress( ) ;
//multiply by volume element
stress *= dvol[i] ;
if ( tang_flag == 1 ) {
dd = materialPointers[i]->getTangent( ) ;
dd *= dvol[i] ;
} //end if tang_flag
//residual and tangent calculations node loops
jj = 0 ;
for ( j = 0; j < numberNodes; j++ ) {
BJ = computeBbar( j, shp, shpBar ) ;
//transpose
//BJtran = transpose( nstress, ndf, BJ ) ;
for (p=0; p<ndf; p++) {
for (q=0; q<nstress; q++)
BJtran(p,q) = BJ(q,p) ;
}//end for p
//residual
//residJ = BJtran * stress ;
residJ.addMatrixVector(0.0, BJtran,stress,1.0);
//residual
for ( p = 0; p < ndf; p++ ) {
resid( jj + p ) += residJ(p) ;
if (applyLoad == 0) {
resid( jj + p ) -= dvol[i]*b[p]*shp[3][j];
} else {
resid( jj + p ) -= dvol[i]*appliedB[p]*shp[3][j];
}
}
if ( tang_flag == 1 ) {
//BJtranD = BJtran * dd ;
BJtranD.addMatrixProduct(0.0, BJtran,dd,1.0);
kk = 0 ;
for ( k = 0; k < numberNodes; k++ ) {
BK = computeBbar( k, shp, shpBar ) ;
//stiffJK = BJtranD * BK ;
stiffJK.addMatrixProduct(0.0, BJtranD,BK,1.0) ;
for ( p = 0; p < ndf; p++ ) {
for ( q = 0; q < ndf; q++ )
stiff( jj+p, kk+q ) += stiffJK( p, q ) ;
} //end for p
kk += ndf ;
} // end for k loop
} // end if tang_flag
jj += ndf ;
} // end for j loop
} //end for i gauss loop
return ;
}
//return stiffness matrix
const Matrix& BbarBrick::getInitialStiff( )
{
if (Ki != 0)
return *Ki;
//strains ordered : eps11, eps22, eps33, 2*eps12, 2*eps23, 2*eps31
static const int ndm = 3 ;
static const int ndf = 3 ;
static const int nstress = 6 ;
static const int numberNodes = 8 ;
static const int numberGauss = 8 ;
static const int nShape = 4 ;
int i, j, k, p, q ;
int jj, kk ;
static double volume ;
static double xsj ; // determinant jacaobian matrix
static double dvol[numberGauss] ; //volume element
static double gaussPoint[ndm] ;
static Vector strain(nstress) ; //strain
static double shp[nShape][numberNodes] ; //shape functions at a gauss point
static double Shape[nShape][numberNodes][numberGauss] ; //all the shape functions
static double shpBar[nShape][numberNodes] ; //mean value of shape functions
static Matrix stiffJK(ndf,ndf) ; //nodeJK stiffness
static Matrix dd(nstress,nstress) ; //material tangent
//---------B-matrices------------------------------------
static Matrix BJ(nstress,ndf) ; // B matrix node J
static Matrix BJtran(ndf,nstress) ;
static Matrix BK(nstress,ndf) ; // B matrix node k
static Matrix BJtranD(ndf,nstress) ;
//-------------------------------------------------------
//zero stiffness and residual
stiff.Zero( ) ;
//compute basis vectors and local nodal coordinates
computeBasis( ) ;
//zero mean shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shpBar[p][q] = 0.0 ;
} // end for p
//zero volume
volume = 0.0 ;
//gauss loop to compute and save shape functions
int count = 0 ;
for ( i = 0; i < 2; i++ ) {
for ( j = 0; j < 2; j++ ) {
for ( k = 0; k < 2; k++ ) {
gaussPoint[0] = sg[i] ;
gaussPoint[1] = sg[j] ;
gaussPoint[2] = sg[k] ;
//get shape functions
shp3d( gaussPoint, xsj, shp, xl ) ;
//save shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
Shape[p][q][count] = shp[p][q] ;
} // end for p
//volume element to also be saved
dvol[count] = wg[count] * xsj ;
//add to volume
volume += dvol[count] ;
//add to mean shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shpBar[p][q] += ( dvol[count] * shp[p][q] ) ;
} // end for p
count++ ;
} //end for k
} //end for j
} // end for i
//mean value of shape functions
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shpBar[p][q] /= volume ;
} // end for p
//gauss loop
for ( i = 0; i < numberGauss; i++ ) {
//extract shape functions from saved array
for ( p = 0; p < nShape; p++ ) {
for ( q = 0; q < numberNodes; q++ )
shp[p][q] = Shape[p][q][i] ;
} // end for p
dd = materialPointers[i]->getInitialTangent( ) ;
dd *= dvol[i] ;
//residual and tangent calculations node loops
jj = 0 ;
for ( j = 0; j < numberNodes; j++ ) {
BJ = computeBbar( j, shp, shpBar ) ;
//transpose
//BJtran = transpose( nstress, ndf, BJ ) ;
for (p=0; p<ndf; p++) {
for (q=0; q<nstress; q++)
BJtran(p,q) = BJ(q,p) ;
}//end for p
//BJtranD = BJtran * dd ;
BJtranD.addMatrixProduct(0.0, BJtran,dd,1.0);
kk = 0 ;
for ( k = 0; k < numberNodes; k++ ) {
BK = computeBbar( k, shp, shpBar ) ;
//stiffJK = BJtranD * BK ;
stiffJK.addMatrixProduct(0.0, BJtranD,BK,1.0) ;
for ( p = 0; p < ndf; p++ ) {
for ( q = 0; q < ndf; q++ )
stiff( jj+p, kk+q ) += stiffJK( p, q ) ;
} //end for p
kk += ndf ;
} // end for k loop
jj += ndf ;
} // end for j loop
} //end for i gauss loop
Ki = new Matrix(stiff);
return stiff ;
}
