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element_class_kirchhoff_shell_inline_impl.cc
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element_class_kirchhoff_shell_inline_impl.cc
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/**
* @file element_class_kirchhoff_shell_inline_impl.cc
*
* @author Damien Spielmann <damien.spielmann@epfl.ch>
*
* @date creation: Fri Jul 04 2014
* @date last modification: Fri Jul 04 2014
*
* @brief Element class Kirchhoff Shell
*
* @section LICENSE
*
* Copyright (©) 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_STRUCTURAL_ELEMENT_CLASS_PROPERTY(_kirchhoff_shell,
_gt_triangle_3,
_itp_kirchhoff_shell,
_triangle_3,
_ek_structural,
3,
_git_triangle, 2);
/* -------------------------------------------------------------------------- */
//cf. element_class_bernoulli...
//element_class_triangle_3_inline... (pour compute Jacobian)
template <>
inline void
InterpolationElement<_itp_kirchhoff_shell>::computeShapes(const Vector<Real> & natural_coords,
Vector<Real> & N,
const Matrix<Real> & projected_coord,
UInt id) {
// projected_coord (x1 x2 x3) (y1 y2 y3)
// natural coordinate
Real xi = natural_coords(0);
Real eta = natural_coords(1);
Real x21=projected_coord(0,0)-projected_coord(0,1); //x1-x2
Real x32=projected_coord(0,1)-projected_coord(0,2);
Real x13=projected_coord(0,2)-projected_coord(0,0);
Real y21=projected_coord(1,0)-projected_coord(1,1); //y1-y2
Real y32=projected_coord(1,1)-projected_coord(1,2);
Real y13=projected_coord(1,2)-projected_coord(1,0);
/* Real x21=projected_coord(0,1)-projected_coord(0,0);
Real x32=projected_coord(0,2)-projected_coord(0,1);
Real x13=projected_coord(0,0)-projected_coord(0,2);
Real y21=projected_coord(1,1)-projected_coord(1,0);
Real y32=projected_coord(1,2)-projected_coord(1,1);
Real y13=projected_coord(1,0)-projected_coord(1,2);*/
// natural triangle side length
Real L4=sqrt(x21*x21+y21*y21);
Real L5=sqrt(x32*x32+y32*y32);
Real L6=sqrt(x13*x13+y13*y13);
// sinus and cosinus
Real C4=x21/L4; //1
Real C5=x32/L5; //-1/sqrt(2);
Real C6=x13/L6; //0
Real S4=y21/L4; //0;
Real S5=y32/L5; //1/sqrt(2);
Real S6=y13/L6; //-1;
Real N1 = 1-xi-eta;
Real N2 = xi;
Real N3 = eta;
Real P4 = 4*xi*(1-xi-eta);
Real P5 = 4*xi*eta;
Real P6 = 4*eta*(1-xi-eta);
switch (id) {
case 0: { // N
N(0) = N1;
N(1) = N2;
N(2) = N3;
break;
}
case 1: { // Nwi2
N(0) = -(1/8)*P4*L4*C4+(1/8)*P6*L6*C6;
N(1) = -(1/8)*P5*L5*C5+(1/8)*P4*L4*C4;
N(2) = -(1/8)*P6*L6*C6+(1/8)*P5*L5*C5;
break;
}
case 2: { // Nwi3
N(0) = -(1/8)*P4*L4*S4+(1/8)*P6*L6*S6;
N(1) = -(1/8)*P5*L5*S5+(1/8)*P4*L4*S4;
N(2) = -(1/8)*P6*L6*S6+(1/8)*P5*L5*S5;
break;
}
case 3: { // Nxi1
N(0) = 3/(2*L4)*P4*C4-3/(2*L6)*P6*C6;
N(1) = 3/(2*L5)*P5*C5-3/(2*L4)*P4*C4;
N(2) = 3/(2*L6)*P6*C6-3/(2*L5)*P5*C5;
break;
}
case 4: { // Nxi2
N(0) = N1-(3./4.)*P4*C4*C4-(3./4.)*P6*C6*C6;
N(1) = N2-(3./4.)*P5*C5*C5-(3./4.)*P4*C4*C4;
N(2) = N3-(3./4.)*P6*C6*C6-(3./4.)*P5*C5*C5;
break;
}
case 5: { // Nxi3
N(0) = -(3./4.)*P4*C4*S4-(3./4.)*P6*C6*S6;
N(1) = -(3./4.)*P5*C5*S5-(3./4.)*P4*C4*S4;
N(2) = -(3./4.)*P6*C6*S6-(3./4.)*P5*C5*S5;
break;
}
case 6: { // Nyi1
N(0) = 3/(2*L4)*P4*S4-3/(2*L6)*P6*S6;
N(1) = 3/(2*L5)*P5*S5-3/(2*L4)*P4*S4;
N(2) = 3/(2*L6)*P6*S6-3/(2*L5)*P5*S5;
break;
}
case 7: { // Nyi2
N(0) = -(3./4.)*P4*C4*S4-(3./4.)*P6*C6*S6;
N(1) = -(3./4.)*P5*C5*S5-(3./4.)*P4*C4*S4;
N(2) = -(3./4.)*P6*C6*S6-(3./4.)*P5*C5*S5;
break;
}
case 8: { // Nyi3
N(0) = N1-(3./4.)*P4*S4*S4-(3./4.)*P6*S6*S6;
N(1) = N2-(3./4.)*P5*S5*S5-(3./4.)*P4*S4*S4;
N(2) = N3-(3./4.)*P6*S6*S6-(3./4.)*P5*S5*S5;
break;
}
}
}
/* -------------------------------------------------------------------------- */
template <>
inline void
InterpolationElement<_itp_kirchhoff_shell>::computeDNDS(const Vector<Real> & natural_coords,
Matrix<Real> & dnds,
const Matrix<Real> & projected_coord,
UInt id) {
// natural coordinate
Real xi = natural_coords(0);
Real eta = natural_coords(1);
// projected_coord (x1 x2 x3) (y1 y2 y3)
// donne juste pour pour le patch test 4_5_5 mais donne quelque changement de signe dans la matrice de rotation
Real x21=projected_coord(0,0)-projected_coord(0,1); //x1-x2
Real x32=projected_coord(0,1)-projected_coord(0,2);
Real x13=projected_coord(0,2)-projected_coord(0,0);
Real y21=projected_coord(1,0)-projected_coord(1,1); //y1-y2
Real y32=projected_coord(1,1)-projected_coord(1,2);
Real y13=projected_coord(1,2)-projected_coord(1,0);
// donne juste pour la matrice de rigidité... mais pas pour le patch test 4_5_5
/* Real x21=projected_coord(0,1)-projected_coord(0,0);
Real x32=projected_coord(0,2)-projected_coord(0,1);
Real x13=projected_coord(0,0)-projected_coord(0,2);
Real y21=projected_coord(1,1)-projected_coord(1,0);
Real y32=projected_coord(1,2)-projected_coord(1,1);
Real y13=projected_coord(1,0)-projected_coord(1,2);*/
// natural triangle side length
Real L4=sqrt(x21*x21+y21*y21);
Real L5=sqrt(x32*x32+y32*y32);
Real L6=sqrt(x13*x13+y13*y13);
// sinus and cosinus
Real C4=x21/L4;
Real C5=x32/L5;
Real C6=x13/L6;
Real S4=y21/L4;
Real S5=y32/L5;
Real S6=y13/L6;
Real dN1xi = -1;
Real dN2xi = 1;
Real dN3xi = 0;
Real dN1eta = -1;
Real dN2eta = 0;
Real dN3eta = 1;
Real dP4xi = 4-8*xi-4*eta;
Real dP5xi = 4*eta;
Real dP6xi = -4*eta;
Real dP4eta = -4*xi;
Real dP5eta = 4*xi;
Real dP6eta = 4-4*xi-8*eta;
switch (id) {
case 0: { // N'xi N'eta
dnds(0,0) = dN1xi;
dnds(0,1) = dN2xi;
dnds(0,2) = dN3xi;
dnds(1,0) = dN1eta;
dnds(1,1) = dN2eta;
dnds(1,2) = dN3eta;
break;
}
case 1: { // Nxi1'xi Nxi1'eta
dnds(0,0) = 3/(2*L4)*dP4xi*C4-3/(2*L6)*dP6xi*C6;
dnds(0,1) = 3/(2*L5)*dP5xi*C5-3/(2*L4)*dP4xi*C4;
dnds(0,2) = 3/(2*L6)*dP6xi*C6-3/(2*L5)*dP5xi*C5;
dnds(1,0) = 3/(2*L4)*dP4eta*C4-3/(2*L6)*dP6eta*C6;
dnds(1,1) = 3/(2*L5)*dP5eta*C5-3/(2*L4)*dP4eta*C4;
dnds(1,2) = 3/(2*L6)*dP6eta*C6-3/(2*L5)*dP5eta*C5;
break;
}
case 2: { // Nxi2'xi Nxi2'eta
dnds(0,0) = -1-(3./4.)*dP4xi*C4*C4-(3./4.)*dP6xi*C6*C6;
dnds(0,1) = 1-(3./4.)*dP5xi*C5*C5-(3./4.)*dP4xi*C4*C4;
dnds(0,2) =-(3./4.)*dP6xi*C6*C6-(3./4.)*dP5xi*C5*C5;
dnds(1,0) = -1-(3./4.)*dP4eta*C4*C4-(3./4.)*dP6eta*C6*C6;
dnds(1,1) = -(3./4.)*dP5eta*C5*C5-(3./4.)*dP4eta*C4*C4;
dnds(1,2) = 1-(3./4.)*dP6eta*C6*C6-(3./4.)*dP5eta*C5*C5;
break;
}
case 3: { // Nxi3'xi Nxi3'eta
dnds(0,0) = -(3./4.)*dP4xi*C4*S4-(3./4.)*dP6xi*C6*S6;
dnds(0,1) = -(3./4.)*dP5xi*C5*S5-(3./4.)*dP4xi*C4*S4;
dnds(0,2) = -(3./4.)*dP6xi*C6*S6-(3./4.)*dP5xi*C5*S5;
dnds(1,0) = -(3./4.)*dP4eta*C4*S4-(3./4.)*dP6eta*C6*S6;
dnds(1,1) = -(3./4.)*dP5eta*C5*S5-(3./4.)*dP4eta*C4*S4;
dnds(1,2) = -(3./4.)*dP6eta*C6*S6-(3./4.)*dP5eta*C5*S5;
break;
}
case 4: { // Nyi1'xi Nyi1'eta
dnds(0,0) = 3/(2*L4)*dP4xi*S4-3/(2*L6)*dP6xi*S6;
dnds(0,1) = 3/(2*L5)*dP5xi*S5-3/(2*L4)*dP4xi*S4;
dnds(0,2) = 3/(2*L6)*dP6xi*S6-3/(2*L5)*dP5xi*S5;
dnds(1,0) = 3/(2*L4)*dP4eta*S4-3/(2*L6)*dP6eta*S6;
dnds(1,1) = 3/(2*L5)*dP5eta*S5-3/(2*L4)*dP4eta*S4;
dnds(1,2) = 3/(2*L6)*dP6eta*S6-3/(2*L5)*dP5eta*S5;
break;
}
case 5: { // Nyi2'xi Nyi2'eta
dnds(0,0) = -(3./4.)*dP4xi*C4*S4-(3./4.)*dP6xi*C6*S6;
dnds(0,1) = -(3./4.)*dP5xi*C5*S5-(3./4.)*dP4xi*C4*S4;
dnds(0,2) = -(3./4.)*dP6xi*C6*S6-(3./4.)*dP5xi*C5*S5;
dnds(1,0) = -(3./4.)*dP4eta*C4*S4-(3./4.)*dP6eta*C6*S6;
dnds(1,1) = -(3./4.)*dP5eta*C5*S5-(3./4.)*dP4eta*C4*S4;
dnds(1,2) = -(3./4.)*dP6eta*C6*S6-(3./4.)*dP5eta*C5*S5;
break;
}
case 6: { // Nyi3'xi Nyi3'eta
dnds(0,0) = dN1xi-(3./4.)*dP4xi*S4*S4-(3./4.)*dP6xi*S6*S6;
dnds(0,1) = dN2xi-(3./4.)*dP5xi*S5*S5-(3./4.)*dP4xi*S4*S4;
dnds(0,2) = dN3xi-(3./4.)*dP6xi*S6*S6-(3./4.)*dP5xi*S5*S5;
dnds(1,0) = dN1eta-(3./4.)*dP4eta*S4*S4-(3./4.)*dP6eta*S6*S6;
dnds(1,1) = dN2eta-(3./4.)*dP5eta*S5*S5-(3./4.)*dP4eta*S4*S4;
dnds(1,2) = dN3eta-(3./4.)*dP6eta*S6*S6-(3./4.)*dP5eta*S5*S5;
break;
}
}
}

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