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gsThinShellAssembler.hpp
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/** @file gsThinShellAssembler.hpp
@brief Provides linear and nonlinear assemblers for thin shells
This file is part of the G+Smo library.
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
Author(s):
H.M. Verhelst (2019-..., TU Delft)
A. Mantzaflaris (2019-..., Inria)
*/
#pragma once
#include <gsKLShell/gsThinShellAssembler.h>
#include <gsKLShell/gsMaterialMatrix.h>
#include <gsKLShell/gsMaterialMatrixBase.h>
#include <gsKLShell/gsMaterialMatrixIntegrate.h>
#include <gsPde/gsBoundaryConditions.h>
#include <gsCore/gsFunctionExpr.h>
#include <gsCore/gsPiecewiseFunction.h>
#include <gsIO/gsWriteParaview.h>
#include <gsMSplines/gsWeightMapper.h>
namespace gismo
{
template <short_t d, class T, bool bending>
gsThinShellAssembler<d, T, bending>::gsThinShellAssembler(const gsMultiPatch<T> & patches,
const gsMultiBasis<T> & basis,
const gsBoundaryConditions<T> & bconditions,
const gsFunction<T> & surface_force,
const gsMaterialMatrixContainer<T> & materialMatrices
)
:
m_patches(patches),
m_basis(basis),
m_spaceBasis(&basis),
m_bcs(bconditions),
m_forceFun(&surface_force),
m_materialMatrices(materialMatrices)
{
this->_defaultOptions();
this->_getOptions();
this->_initialize();
}
template <short_t d, class T, bool bending>
gsThinShellAssembler<d, T, bending>::gsThinShellAssembler(const gsMultiPatch<T> & patches,
const gsMultiBasis<T> & basis,
const gsBoundaryConditions<T> & bconditions,
const gsFunction<T> & surface_force,
gsMaterialMatrixBase<T> * materialMatrix
)
:
m_patches(patches),
m_basis(basis),
m_spaceBasis(&basis),
m_bcs(bconditions),
m_forceFun(&surface_force)
{
m_materialMatrices = gsMaterialMatrixContainer<T>(m_patches.nPatches());
for (size_t p=0; p!=m_patches.nPatches(); p++)
m_materialMatrices.add(materialMatrix);
this->_defaultOptions();
this->_getOptions();
this->_initialize();
}
template <short_t d, class T, bool bending>
gsThinShellAssembler<d, T, bending>& gsThinShellAssembler<d, T, bending>::operator=( const gsThinShellAssembler& other )
{
if (this!=&other)
{
m_patches=other.m_patches;
m_basis=other.m_basis;
m_spaceBasis=other.m_spaceBasis;
m_bcs=other.m_bcs;
m_forceFun=other.m_forceFun;
m_materialMatrices=other.m_materialMatrices;
m_options=other.m_options;
m_alpha_d_bc=other.m_alpha_d_bc;
m_alpha_r_bc=other.m_alpha_r_bc;
m_alpha_d_ifc=other.m_alpha_d_ifc;
m_alpha_r_ifc=other.m_alpha_r_ifc;
m_continuity=other.m_continuity;
m_IfcDefault=other.m_IfcDefault;
// m_assembler=other.m_assembler;
m_ddofs=other.m_ddofs;
m_mapper=other.m_mapper;
m_foundInd=other.m_foundInd;
m_pressInd=other.m_pressInd;
// To do: make copy constructor for the gsExprAssembler
m_assembler.setIntegrationElements(m_basis);
m_assembler.setOptions(m_options);
}
return *this;
}
template <short_t d, class T, bool bending>
gsThinShellAssembler<d, T, bending>& gsThinShellAssembler<d, T, bending>::operator=( gsThinShellAssembler&& other )
{
m_patches=give(other.m_patches);
m_basis=give(other.m_basis);
m_spaceBasis=give(other.m_spaceBasis);
m_bcs=give(other.m_bcs);
m_forceFun=give(other.m_forceFun);
m_materialMatrices=give(other.m_materialMatrices);
m_options=give(other.m_options);
m_alpha_d_bc=give(other.m_alpha_d_bc);
m_alpha_r_bc=give(other.m_alpha_r_bc);
m_alpha_d_ifc=give(other.m_alpha_d_ifc);
m_alpha_r_ifc=give(other.m_alpha_r_ifc);
m_continuity=give(other.m_continuity);
m_IfcDefault=give(other.m_IfcDefault);
// m_assembler=give(other.m_assembler);
m_ddofs=give(other.m_ddofs);
m_mapper=give(other.m_mapper);
m_foundInd=give(other.m_foundInd);
m_pressInd=give(other.m_pressInd);
// To do: make copy constructor for the gsExprAssembler
m_assembler.setIntegrationElements(m_basis);
m_assembler.setOptions(m_options);
return *this;
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::_defaultOptions()
{
m_options.addReal("WeakDirichlet","Penalty parameter weak dirichlet conditions",1e3);
m_options.addReal("WeakClamped","Penalty parameter weak clamped conditions",1e3);
m_options.addInt("Continuity","Set the continuity for the space",-1);
m_options.addReal("IfcDirichlet","Penalty parameter weak dirichlet conditions on the interface",1e3);
m_options.addReal("IfcClamped","Penalty parameter weak clamped conditions on the interface",1e3);
m_options.addInt("IfcDefault","Default weak(!) interface coupling; C^k, k={-1,0,1}",1);
// Assembler options
m_options.addInt("DirichletStrategy","Method for enforcement of Dirichlet BCs [11..14]",11);
m_options.addInt("DirichletValues","Method for computation of Dirichlet DoF values [100..103]",101);
m_options.addInt("InterfaceStrategy","Method of treatment of patch interfaces [0..3]",1);
m_options.addReal("bdA","Estimated nonzeros per column of the matrix: bdA*deg + bdB",2);
m_options.addInt("bdB","Estimated nonzeros per column of the matrix: bdA*deg + bdB",1);
m_options.addReal("bdO","Overhead of sparse mem. allocation: (1+bdO)(bdA*deg + bdB) [0..1]",0.333);
m_options.addReal("quA","Number of quadrature points: quA*deg + quB",1);
m_options.addInt("quB","Number of quadrature points: quA*deg + quB",1);
m_options.addInt("quRule","Quadrature rule [1:GaussLegendre,2:GaussLobatto]",1);
m_options.addString("Solver","Sparse linear solver", "CGDiagonal");
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::_getOptions() const
{
m_alpha_d_bc = m_options.getReal("WeakDirichlet");
m_alpha_r_bc = m_options.getReal("WeakClamped");
m_continuity = m_options.getInt("Continuity");
m_alpha_d_ifc = m_options.getReal("IfcDirichlet");
m_alpha_r_ifc = m_options.getReal("IfcClamped");
m_IfcDefault = m_options.getInt("IfcDefault");
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::setOptions(gsOptionList & options)
{
// Check if the continuity option changed
// Get old continuity
index_t continuity = m_options.getInt("Continuity");
m_options.update(options,gsOptionList::addIfUnknown);
// If the continuity changed, we need to re-initialize the space.
if (continuity != m_options.getInt("Continuity"))
this->_initialize();
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::_initialize()
{
//gsInfo<<"Active options:\n"<< m_assembler.options() <<"\n";
// Elements used for numerical integration
m_assembler.setIntegrationElements(m_basis);
m_assembler.setOptions(m_options);
GISMO_ASSERT(m_bcs.hasGeoMap(),"No geometry map was assigned to the boundary conditions. Use bc.setGeoMap to assign one!");
// Initialize the geometry maps
// geometryMap m_ori = m_assembler.getMap(m_patches);
// geometryMap m_def = m_assembler.getMap(*m_defpatches);
// Set the discretization space
space m_space = m_assembler.getSpace(*m_spaceBasis, d, 0); // last argument is the space ID
this->_assembleDirichlet();
m_ddofs = m_space.fixedPart();
m_mapper = m_space.mapper();
// foundation is off by default
m_foundInd = false;
// pressure is off by default
m_pressInd = false;
GISMO_ASSERT(m_forceFun->targetDim()==d,"Force must have " << d<<" dimensions but has "<<m_forceFun->targetDim());
// test interfaces on in-plane and out-of-plane connection and put them in respective containers
_ifcTest();
// match interfaces where needed
// todo
// Put the interfaces in the right container depending on the
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::addStrongC0(const gsBoxTopology::ifContainer & interfaces)
{
m_strongC0 = interfaces;
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::addStrongC1(const gsBoxTopology::ifContainer & interfaces)
{
m_strongC1 = interfaces;
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::addWeakC0(const gsBoxTopology::ifContainer & interfaces)
{
m_weakC0 = interfaces;
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::addWeakC1(const gsBoxTopology::ifContainer & interfaces)
{
m_weakC1 = interfaces;
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::addUncoupled(const gsBoxTopology::ifContainer & interfaces)
{
m_uncoupled = interfaces;
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::initInterfaces()
{
// Find unassigned interfaces and add them to the right containers
for (gsBoxTopology::const_iiterator it = m_patches.topology().iBegin(); it!=m_patches.topology().iEnd(); it++)
{
if (
std::find(m_strongC0.begin(), m_strongC0.end(), *it) == m_strongC0.end() // m_strongC0 does not contain *it
&& std::find(m_strongC1.begin(), m_strongC1.end(), *it) == m_strongC1.end() // m_strongC1 does not contain *it
&& std::find(m_weakC0.begin(), m_weakC0.end(), *it) == m_weakC0.end() // m_weakC0 does not contain *it
&& std::find(m_weakC1.begin(), m_weakC1.end(), *it) == m_weakC1.end() // m_weakC1 does not contain *it
&& std::find(m_uncoupled.begin(), m_uncoupled.end(), *it) == m_uncoupled.end() // m_uncoupled does not contain *it
)
{
if (m_IfcDefault==-1)
continue;
else if (m_IfcDefault==0)
m_weakC0.push_back(*it);
else if (m_IfcDefault==1)
m_weakC1.push_back(*it);
else
GISMO_ERROR("Option unknown");
}
}
// Set strong C0 using the setup function.
}
template <short_t d, class T, bool bending>
void gsThinShellAssembler<d, T, bending>::_assembleNeumann()
{
_assembleNeumann_impl<d>();
}
template <short_t d, class T, bool bending>
template<int _d>
typename std::enable_if<_d==3, void>::type
gsThinShellAssembler<d, T, bending>::_assembleNeumann_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto g_N = m_assembler.getBdrFunction(m_ori);
m_assembler.assembleBdr(m_bcs.get("Neumann"),m_space * g_N * tv(m_ori).norm());
}
template <short_t d, class T, bool bending>
template<int _d>
typename std::enable_if<!(_d==3), void>::type
gsThinShellAssembler<d, T, bending>::_assembleNeumann_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto g_N = m_assembler.getBdrFunction(m_ori);
m_assembler.assembleBdr(m_bcs.get("Neumann"), m_space * g_N * tv(m_ori).norm());
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assemblePressure()
{
this->_getOptions();
_assemblePressure_impl<d,matrix>();
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assemblePressure_impl()
{
// No matrix contribution for the linear case
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assemblePressure_impl()
{
if (m_pressInd)
{
gsMultiPatch<T> & defpatches = m_patches;
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(defpatches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto m_pressure = m_assembler.getCoeff(*m_pressFun, m_ori);
GISMO_ASSERT(m_pressFun->targetDim()==1,"Pressure function has dimension "<<m_pressFun->targetDim()<<", but expected 1");
m_assembler.assemble(
m_pressure.val() * m_space * usn(m_def) * meas(m_ori)
);
}
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3), void>::type
gsThinShellAssembler<d, T, bending>::_assemblePressure_impl()
{
// Since pressure works out-of-plane, this function has no effect
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assemblePressure(const gsFunctionSet<T> & deformed)
{
this->_getOptions();
_assemblePressure_impl<d,matrix>(deformed);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assemblePressure_impl(const gsFunctionSet<T> & deformed)
{
if (m_pressInd)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto m_pressure = m_assembler.getCoeff(*m_pressFun, m_ori);
GISMO_ASSERT(m_pressFun->targetDim()==1,"Pressure function has dimension "<<m_pressFun->targetDim()<<", but expected 1");
m_assembler.assemble(
-m_pressure.val() * m_space * var1(m_space,m_def).tr()* meas(m_ori)
);
}
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assemblePressure_impl(const gsFunctionSet<T> & deformed)
{
if (m_pressInd)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto m_pressure = m_assembler.getCoeff(*m_pressFun, m_ori);
GISMO_ASSERT(m_pressFun->targetDim()==1,"Pressure function has dimension "<<m_pressFun->targetDim()<<", but expected 1");
// Assemble vector
m_assembler.assemble(
m_pressure.val() * m_space * sn(m_def).normalized() * meas(m_ori)
);
}
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3), void>::type
gsThinShellAssembler<d, T, bending>::_assemblePressure_impl(const gsFunctionSet<T> & deformed)
{
// Since pressure works out-of-plane, this function has no effect
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assembleFoundation()
{
this->_getOptions();
_assembleFoundation_impl<d,matrix>();
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleFoundation_impl()
{
// No matrix contribution for the linear case
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleFoundation_impl()
{
if (m_foundInd)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto m_foundation = m_assembler.getCoeff(*m_foundFun, m_ori);
GISMO_ASSERT(m_foundFun->targetDim()==3,"Foundation function has dimension "<<m_foundFun->targetDim()<<", but expected 3");
m_assembler.assemble(
m_space * m_foundation.asDiag() * m_space.tr() * meas(m_ori)
);
}
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3), void>::type
gsThinShellAssembler<d, T, bending>::_assembleFoundation_impl()
{
// Since foundation works out-of-plane, this function has no effect
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assembleFoundation(const gsFunctionSet<T> & deformed)
{
this->_getOptions();
_assembleFoundation_impl<d,matrix>(deformed);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleFoundation_impl(const gsFunctionSet<T> & deformed)
{
if (m_foundInd)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto m_foundation = m_assembler.getCoeff(*m_foundFun, m_ori);
GISMO_ASSERT(m_foundFun->targetDim()==3,"Foundation function has dimension "<<m_foundFun->targetDim()<<", but expected 3");
m_assembler.assemble(
m_space * m_foundation.asDiag() * m_space.tr() * meas(m_ori)
);
}
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleFoundation_impl(const gsFunctionSet<T> & deformed)
{
if (m_foundInd)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto m_foundation = m_assembler.getCoeff(*m_foundFun, m_ori);
GISMO_ASSERT(m_foundFun->targetDim()==3,"Foundation function has dimension "<<m_foundFun->targetDim()<<", but expected 3");
// Assemble vector
m_assembler.assemble(
m_space * m_foundation.asDiag() * (m_def - m_ori) * meas(m_ori) // [v_x,v_y,v_z] diag([k_x,k_y,k_z]) [u_x; u_y; u_z]
);
}
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3), void>::type
gsThinShellAssembler<d, T, bending>::_assembleFoundation_impl(const gsFunctionSet<T> & deformed)
{
// Since foundation works out-of-plane, this function has no effect
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assembleWeakBCs()
{
this->_getOptions();
_assembleWeakBCs_impl<d,matrix>();
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
// auto g_N = m_assembler.getBdrFunction(m_ori);
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
-(m_alpha_d_bc * m_space * m_space.tr()) * tv(m_ori).norm()
);
// for weak clamped
m_assembler.assembleBdr
(
m_bcs.get("Weak Clamped")
,
(
m_alpha_r_bc * ( ( var1(m_space,m_ori) * unv(m_ori) ) * ( var1(m_space,m_ori) * unv(m_ori) ).tr() )
) * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto g_N = m_assembler.getBdrFunction(m_ori);
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
-(m_alpha_d_bc * m_space * g_N ) * tv(m_ori).norm()
);
// for weak clamped
// do nothing
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3) && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
// auto g_N = m_assembler.getBdrFunction(m_ori);
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
-(m_alpha_d_bc * m_space * m_space.tr()) * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3) && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto g_N = m_assembler.getBdrFunction(m_ori);
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
(m_alpha_d_bc * (m_space * (m_ori - m_ori) - m_space * (g_N) )) * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assembleWeakBCs(const gsFunctionSet<T> & deformed)
{
this->_getOptions();
_assembleWeakBCs_impl<d,matrix>(deformed);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl(const gsFunctionSet<T> & deformed)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
// auto g_N = m_assembler.getBdrFunction(m_ori);
auto du = m_def - m_ori;
auto dnN = ( usn(m_def).tr()*unv(m_ori) - usn(m_ori).tr()*unv(m_ori) ).val();
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
-m_alpha_d_bc * m_space * m_space.tr() * tv(m_ori).norm()
);
// for weak clamped
m_assembler.assembleBdr
(
m_bcs.get("Weak Clamped")
,
(
m_alpha_r_bc * dnN * ( var2deriv2(m_space,m_space,m_def,unv(m_ori).tr()) )
+
m_alpha_r_bc * ( ( var1(m_space,m_def) * unv(m_ori) ) * ( var1(m_space,m_def) * unv(m_ori) ).tr() )
) * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl(const gsFunctionSet<T> & deformed)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto g_N = m_assembler.getBdrFunction(m_ori);
auto du = m_def - m_ori;
auto dnN = ( usn(m_def).tr()*unv(m_ori) - usn(m_ori).tr()*unv(m_ori) ).val();
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
m_alpha_d_bc * (m_space * du - m_space * (g_N) ) * tv(m_ori).norm()
);
// for weak clamped
m_assembler.assembleBdr
(
m_bcs.get("Weak Clamped")
,
(
- m_alpha_r_bc * dnN * ( var1(m_space,m_def) * usn(m_ori) )
) * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3) && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl(const gsFunctionSet<T> & deformed)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
// geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
// auto g_N = m_assembler.getBdrFunction(m_ori);
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
-m_alpha_d_bc * m_space * m_space.tr() * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3) && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakBCs_impl(const gsFunctionSet<T> & deformed)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto g_N = m_assembler.getBdrFunction(m_ori);
// Weak BCs
m_assembler.assembleBdr
(
m_bcs.get("Weak Dirichlet")
,
m_alpha_d_bc * (m_space * (m_def - m_ori) - m_space * (g_N) ) * tv(m_ori).norm()
);
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assembleWeakIfc()
{
this->_getOptions();
_assembleWeakIfc_impl<d,matrix>();
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakIfc_impl()
{
geometryMap m_ori = m_assembler.getMap(m_patches);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
// C^0 coupling
m_assembler.assembleIfc(m_weakC0,
m_alpha_d_ifc * m_space.left() * m_space.left().tr()
,
-m_alpha_d_ifc * m_space.right()* m_space.left() .tr()
,
-m_alpha_d_ifc * m_space.left() * m_space.right().tr()
,
m_alpha_d_ifc * m_space.right()* m_space.right().tr()
);
// C^1 coupling
// Penalty of out-of-plane coupling
// dW^pr / du_r --> second line
m_assembler.assembleIfc(m_weakC1,
m_alpha_r_ifc * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ) * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ).tr() // left left
,
m_alpha_r_ifc * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ) * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ).tr() // left right
,
m_alpha_r_ifc * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ) * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ).tr() // right left
,
m_alpha_r_ifc * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ) * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ).tr() // right right
,
// Symmetry
m_alpha_r_ifc * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ) * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ).tr() // right right
,
m_alpha_r_ifc * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ) * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ).tr() // right left
,
m_alpha_r_ifc * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ) * ( var1(m_space.right(),m_ori.right()) * usn(m_ori.left()) ).tr() // left right
,
m_alpha_r_ifc * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ) * ( var1(m_space.left(),m_ori.left()) * usn(m_ori.right()) ).tr() // left left
);
// Penalty of in-plane coupling
// dW^pr / du_r --> fourth line
m_assembler.assembleIfc(m_weakC1,
m_alpha_r_ifc * ( ovar1(m_space.left() ,m_ori.left() ) * usn(m_ori.right()) ) * ( ovar1(m_space.left() ,m_ori.left() ) * usn(m_ori.right()) ).tr() // left left
+ // Symmetry
m_alpha_r_ifc * ( var1(m_space.left() ,m_ori.left() ) * unv(m_ori.right()) ) * ( var1(m_space.left() ,m_ori.left() ) * unv(m_ori.right()) ).tr() // left left
,
m_alpha_r_ifc * ( ovar1(m_space.left() ,m_ori.left() ) * usn(m_ori.right()) ) * ( var1(m_space.right(),m_ori.right()) * unv(m_ori.left() ) ).tr() // left right
+ // Symmetry
m_alpha_r_ifc * ( var1(m_space.left() ,m_ori.left() ) * unv(m_ori.right()) ) * ( ovar1(m_space.right(),m_ori.right()) * usn(m_ori.left() ) ).tr() // left right
,
m_alpha_r_ifc * ( var1(m_space.right(),m_ori.right()) * unv(m_ori.left() ) ) * ( ovar1(m_space.left() ,m_ori.left() ) * usn(m_ori.right()) ).tr() // right left
+ // Symmetry
m_alpha_r_ifc * ( ovar1(m_space.right(),m_ori.right()) * usn(m_ori.left() ) ) * ( var1(m_space.left() ,m_ori.left() ) * unv(m_ori.right()) ).tr() // right left
,
m_alpha_r_ifc * ( var1(m_space.right(),m_ori.right()) * unv(m_ori.left() ) ) * ( var1(m_space.right(),m_ori.right()) * unv(m_ori.left() ) ).tr() // right right
+ // Symmetry
m_alpha_r_ifc * ( ovar1(m_space.right(),m_ori.right()) * usn(m_ori.left() ) ) * ( ovar1(m_space.right(),m_ori.right()) * usn(m_ori.left() ) ).tr() // right right
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakIfc_impl()
{
/*
empty
*/
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3) && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakIfc_impl()
{
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
// C^0 coupling
m_assembler.assembleIfc(m_weakC0,
m_alpha_d_ifc * m_space.left() * m_space.left().tr()
,
-m_alpha_d_ifc * m_space.right()* m_space.left() .tr()
,
-m_alpha_d_ifc * m_space.left() * m_space.right().tr()
,
m_alpha_d_ifc * m_space.right()* m_space.right().tr()
);
// C^1 coupling DOES NOT CONTRIBUTE IN 2D PROBLEMS
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<!(_d==3) && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakIfc_impl()
{
/*
empty
*/
}
template <short_t d, class T, bool bending>
template <bool matrix>
void gsThinShellAssembler<d, T, bending>::_assembleWeakIfc(const gsFunctionSet<T> & deformed)
{
this->_getOptions();
_assembleWeakIfc_impl<d,matrix>(deformed);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakIfc_impl(const gsFunctionSet<T> & deformed)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto du = ((m_def.left()-m_ori.left()) - (m_def.right()-m_ori.right()));
auto dN_lr = (usn(m_def.left()).tr()*usn(m_def.right())
- usn(m_ori.left()).tr()*usn(m_ori.right())).val();
auto dN_rl = (usn(m_def.right()).tr()*usn(m_def.left())
- usn(m_ori.right()).tr()*usn(m_ori.left())).val();
auto dnN_lr= (unv(m_def.left()).tr()*usn(m_def.right())
- unv(m_ori.left()).tr()*usn(m_ori.right())).val();
auto dnN_rl= (unv(m_def.right()).tr()*usn(m_def.left())
- unv(m_ori.right()).tr()*usn(m_ori.left())).val();
// C^0 coupling
m_assembler.assembleIfc(m_weakC0,
m_alpha_d_ifc * m_space.left() * m_space.left().tr()
,
-m_alpha_d_ifc * m_space.right()* m_space.left() .tr()
,
-m_alpha_d_ifc * m_space.left() * m_space.right().tr()
,
m_alpha_d_ifc * m_space.right()* m_space.right().tr()
);
// C^1 coupling
// Penalty of out-of-plane coupling
// dW^pr / du_r --> first line
m_assembler.assembleIfc(m_weakC1,
m_alpha_r_ifc * dN_lr * var2(m_space.left() ,m_space.left() ,m_def.left() ,usn(m_def.right()).tr() ) // left left
,
m_alpha_r_ifc * dN_lr * ( var1(m_space.left() ,m_def.left() ) * var1(m_space.right(),m_def.right()).tr() )// left right
,
m_alpha_r_ifc * dN_lr * ( var1(m_space.right(),m_def.right()) * var1(m_space.left() ,m_def.left() ).tr() )// right left
,
m_alpha_r_ifc * dN_lr * var2( m_space.right(),m_space.right(),m_def.right(),usn(m_def.left() ).tr() ) // right right
,
// Symmetry
m_alpha_r_ifc * dN_rl * var2(m_space.right() ,m_space.right() ,m_def.right() ,usn(m_def.left()).tr() ) // right right
,
m_alpha_r_ifc * dN_rl * ( var1(m_space.right() ,m_def.right() ) * var1(m_space.left(),m_def.left()).tr() )// right left
,
m_alpha_r_ifc * dN_rl * ( var1(m_space.left(),m_def.left()) * var1(m_space.right() ,m_def.right() ).tr() )// left right
,
m_alpha_r_ifc * dN_rl * var2( m_space.left(),m_space.left(),m_def.left(),usn(m_def.right() ).tr() ) // left left
);
// Penalty of out-of-plane coupling
// dW^pr / du_r --> second line
m_assembler.assembleIfc(m_weakC1,
m_alpha_r_ifc * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ) * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ).tr() // left left
,
m_alpha_r_ifc * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ) * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ).tr() // left right
,
m_alpha_r_ifc * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ) * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ).tr() // right left
,
m_alpha_r_ifc * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ) * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ).tr() // right right
,
// Symmetry
m_alpha_r_ifc * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ) * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ).tr() // right right
,
m_alpha_r_ifc * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ) * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ).tr() // right left
,
m_alpha_r_ifc * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ) * ( var1(m_space.right(),m_def.right()) * usn(m_def.left()) ).tr() // left right
,
m_alpha_r_ifc * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ) * ( var1(m_space.left(),m_def.left()) * usn(m_def.right()) ).tr() // left left
);
// Penalty of in-plane coupling
// dW^pr / du_r --> third line
m_assembler.assembleIfc(m_weakC1,
m_alpha_r_ifc * dnN_lr * ovar2(m_space.left(),m_space.left(),m_def.left(),usn(m_def.right()).tr()) // left left
+ // Symmetry
m_alpha_r_ifc * dnN_rl * ovar2(m_space.left(),m_space.left(),m_def.left(),usn(m_def.right()).tr()) // left left
,
m_alpha_r_ifc * dnN_lr * ( ovar1(m_space.left() ,m_def.left() ) * var1(m_space.right(),m_def.right()).tr() ) // left right
+ // Symmetry
m_alpha_r_ifc * dnN_rl * ( ovar1(m_space.left() ,m_def.left() ) * var1(m_space.right(),m_def.right()).tr() ) // right left
,
m_alpha_r_ifc * dnN_lr * ( ovar1(m_space.right(),m_def.right()) * var1(m_space.left() ,m_def.left() ).tr() ) // right left
+ // Symmetry
m_alpha_r_ifc * dnN_rl * ( ovar1(m_space.right(),m_def.right()) * var1(m_space.left() ,m_def.left() ).tr() ) // right left
,
m_alpha_r_ifc * dnN_lr * ovar2(m_space.right(),m_space.right(),m_def.right(),usn(m_def.left()).tr()) // right right
+ // Symmetry
m_alpha_r_ifc * dnN_rl * ovar2(m_space.right(),m_space.right(),m_def.right(),usn(m_def.left()).tr()) // right right
);
// Penalty of in-plane coupling
// dW^pr / du_r --> fourth line
m_assembler.assembleIfc(m_weakC1,
m_alpha_r_ifc * ( ovar1(m_space.left() ,m_def.left() ) * usn(m_def.right()) ) * ( ovar1(m_space.left() ,m_def.left() ) * usn(m_def.right()) ).tr() // left left
+ // Symmetry
m_alpha_r_ifc * ( var1(m_space.left() ,m_def.left() ) * unv(m_def.right()) ) * ( var1(m_space.left() ,m_def.left() ) * unv(m_def.right()) ).tr() // left left
,
m_alpha_r_ifc * ( ovar1(m_space.left() ,m_def.left() ) * usn(m_def.right()) ) * ( var1(m_space.right(),m_def.right()) * unv(m_def.left() ) ).tr() // left right
+ // Symmetry
m_alpha_r_ifc * ( var1(m_space.left() ,m_def.left() ) * unv(m_def.right()) ) * ( ovar1(m_space.right(),m_def.right()) * usn(m_def.left() ) ).tr() // left right
,
m_alpha_r_ifc * ( var1(m_space.right(),m_def.right()) * unv(m_def.left() ) ) * ( ovar1(m_space.left() ,m_def.left() ) * usn(m_def.right()) ).tr() // right left
+ // Symmetry
m_alpha_r_ifc * ( ovar1(m_space.right(),m_def.right()) * usn(m_def.left() ) ) * ( var1(m_space.left() ,m_def.left() ) * unv(m_def.right()) ).tr() // right left
,
m_alpha_r_ifc * ( var1(m_space.right(),m_def.right()) * unv(m_def.left() ) ) * ( var1(m_space.right(),m_def.right()) * unv(m_def.left() ) ).tr() // right right
+ // Symmetry
m_alpha_r_ifc * ( ovar1(m_space.right(),m_def.right()) * usn(m_def.left() ) ) * ( ovar1(m_space.right(),m_def.right()) * usn(m_def.left() ) ).tr() // right right
);
}
template <short_t d, class T, bool bending>
template<int _d, bool matrix>
typename std::enable_if<_d==3 && !matrix, void>::type
gsThinShellAssembler<d, T, bending>::_assembleWeakIfc_impl(const gsFunctionSet<T> & deformed)
{
geometryMap m_ori = m_assembler.getMap(m_patches);
geometryMap m_def = m_assembler.getMap(deformed);
space m_space = m_assembler.trialSpace(0); // last argument is the space ID
auto du = ((m_def.left()-m_ori.left()) - (m_def.right()-m_ori.right()));
auto dN_lr = (usn(m_def.left()).tr()*usn(m_def.right())
- usn(m_ori.left()).tr()*usn(m_ori.right())).val();
auto dN_rl = (usn(m_def.right()).tr()*usn(m_def.left())
- usn(m_ori.right()).tr()*usn(m_ori.left())).val();
auto dnN_lr= (unv(m_def.left()).tr()*usn(m_def.right())
- unv(m_ori.left()).tr()*usn(m_ori.right())).val();
auto dnN_rl= (unv(m_def.right()).tr()*usn(m_def.left())
- unv(m_ori.right()).tr()*usn(m_ori.left())).val();
// C^0 coupling
m_assembler.assembleIfc(m_weakC0,
-m_alpha_d_ifc * m_space.left() * du
,