Implementation of the DDR scheme for the Reissner-Mindlin plate problem. More...

Classes
struct	HArDCore2D::RMParameters
	Structure to store model data. More...

struct	HArDCore2D::RMNorms
	Structure to store component norms (for rotation, displacement, Kirchoff term and total energy) More...

struct	HArDCore2D::ReissnerMindlin
	Assemble a RM problem. More...

Typedefs
typedef Eigen::SparseMatrix< double >	HArDCore2D::ReissnerMindlin::SystemMatrixType

typedef std::function< double(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::ForcingTermType

typedef std::function< Eigen::Vector2d(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::SolutionRotationType

typedef std::function< Eigen::Matrix2d(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::GradientRotationType

typedef std::function< double(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::SolutionDisplacementType

Functions
	HArDCore2D::RMParameters::RMParameters (const double thickness, const double young_modulus, const double poisson_ratio)
	Constructor.

	HArDCore2D::RMNorms::RMNorms (double norm_rotation, double norm_displacement, double norm_kirchoff)
	Constructor.

	HArDCore2D::ReissnerMindlin::ReissnerMindlin (const DDRCore &ddrcore, const RMParameters &para, const BoundaryConditions &BC_theta, const BoundaryConditions &BC_u, bool use_threads, std::ostream &output=std::cout)
	Constructor.

void	HArDCore2D::ReissnerMindlin::assembleLinearSystem (const ForcingTermType &f, const SolutionRotationType &theta, const GradientRotationType &grad_theta, const SolutionDisplacementType &u)
	Assemble the global system

size_t	HArDCore2D::ReissnerMindlin::dimensionSpace () const
	Returns the dimension of the rotation + displacement space (with BC)

size_t	HArDCore2D::ReissnerMindlin::nb_bdryDOFs () const
	Returns the nb of DOFs for BC.

size_t	HArDCore2D::ReissnerMindlin::sizeSystem () const
	Returns the size of the system without BC.

const std::vector< std::pair< size_t, size_t > > &	HArDCore2D::ReissnerMindlin::locUKN () const
	Returns the location of the unknowns among the DOFs.

std::vector< size_t >	HArDCore2D::ReissnerMindlin::globalDOFIndices (const Cell &T) const
	Create the vector of DOF indices for cell T, which combines the DOFs for the spaces EXcurl and Xgrad.

const RMParameters &	HArDCore2D::ReissnerMindlin::para () const
	Returns the parameters.

const EXCurl &	HArDCore2D::ReissnerMindlin::exCurl () const
	Returns the space EXCurl.

const XGrad &	HArDCore2D::ReissnerMindlin::xGrad () const
	Returns the space XGrad.

const SystemMatrixType &	HArDCore2D::ReissnerMindlin::systemMatrix () const
	Returns the linear system matrix.

SystemMatrixType &	HArDCore2D::ReissnerMindlin::systemMatrix ()
	Returns the linear system matrix.

const Eigen::VectorXd &	HArDCore2D::ReissnerMindlin::systemVector () const
	Returns the linear system right-hand side vector.

Eigen::VectorXd &	HArDCore2D::ReissnerMindlin::systemVector ()
	Returns the linear system right-hand side vector.

const SystemMatrixType &	HArDCore2D::ReissnerMindlin::bdryMatrix () const
	Returns the Matrix for BC.

const Eigen::VectorXd &	HArDCore2D::ReissnerMindlin::bdryValues () const
	Returns the boundary values.

const double &	HArDCore2D::ReissnerMindlin::stabilizationParameter () const
	Returns the stabilization parameter.

double &	HArDCore2D::ReissnerMindlin::stabilizationParameter ()
	Returns the stabilization parameter.

RMNorms	HArDCore2D::ReissnerMindlin::computeNorms (const Eigen::VectorXd &v) const
	Compute the discrete norms: rotation, displacement, Kirchoff term, and complete energy.

template<typename outValue , typename Fct >
std::function< outValue(const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::contractPara (const Fct &F) const
	Takes a function dependent on RMParameter and a position x, and returns a function depending only on x (using the parameters of this class)

Variables
double	HArDCore2D::RMParameters::t

double	HArDCore2D::RMParameters::E

double	HArDCore2D::RMParameters::nu

double	HArDCore2D::RMParameters::beta0

double	HArDCore2D::RMParameters::beta1

double	HArDCore2D::RMParameters::kappa

double	HArDCore2D::RMNorms::rotation
	Norm of rotation.

double	HArDCore2D::RMNorms::displacement
	Norm of displacement.

double	HArDCore2D::RMNorms::kirchoff
	Norm of kirchoff term.

double	HArDCore2D::RMNorms::energy
	Total energy.

static const double	HArDCore2D::PI = boost::math::constants::pi<double>()

static ReissnerMindlin::SolutionRotationType	HArDCore2D::constant_theta

static ReissnerMindlin::GradientRotationType	HArDCore2D::constant_grad_theta

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::constant_u

static ReissnerMindlin::ForcingTermType	HArDCore2D::constant_f

static ReissnerMindlin::SolutionRotationType	HArDCore2D::polynomial_theta

static ReissnerMindlin::GradientRotationType	HArDCore2D::polynomial_grad_theta

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::polynomial_u

static ReissnerMindlin::ForcingTermType	HArDCore2D::polynomial_f

static std::function< double(const VectorRd &)>	HArDCore2D::an_g = [](const VectorRd &x)->double { return sin(PIx(0))sin(PI*x(1)); }

static std::function< VectorRd(const VectorRd &)>	HArDCore2D::an_GRAD_g

static std::function< MatrixRd(const VectorRd &)>	HArDCore2D::an_HESS_g

static std::function< double(const VectorRd &)>	HArDCore2D::an_LAPL_g = [](const VectorRd &x)->double { return -2pow(PI,2)sin(PIx(0))sin(PI*x(1)); }

static std::function< double(const VectorRd &)>	HArDCore2D::an_V = [](const VectorRd &x)->double { return x(0) * exp(-x(0))*cos(x(1)); }

static std::function< VectorRd(const VectorRd &)>	HArDCore2D::an_GRAD_V

static std::function< MatrixRd(const VectorRd &)>	HArDCore2D::an_HESS_V

static std::function< double(const VectorRd &)>	HArDCore2D::an_LAPL_V = [](const VectorRd &x)->double { return -2.* exp(-x(0))*cos(x(1)); }

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::an_v

static ReissnerMindlin::SolutionRotationType	HArDCore2D::an_GRAD_v

static ReissnerMindlin::GradientRotationType	HArDCore2D::an_HESS_v

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::an_LAPL_v

static ReissnerMindlin::SolutionRotationType	HArDCore2D::analytical_theta = an_GRAD_v

static ReissnerMindlin::GradientRotationType	HArDCore2D::analytical_grad_theta = an_HESS_v

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::analytical_u

static ReissnerMindlin::ForcingTermType	HArDCore2D::analytical_f

static ReissnerMindlin::SolutionRotationType	HArDCore2D::ukn_theta

static ReissnerMindlin::GradientRotationType	HArDCore2D::ukn_grad_theta

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::ukn_u

static ReissnerMindlin::ForcingTermType	HArDCore2D::ukn_f

static ReissnerMindlin::SolutionRotationType	HArDCore2D::kir_theta

static ReissnerMindlin::GradientRotationType	HArDCore2D::kir_grad_theta

static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::kir_u

static ReissnerMindlin::ForcingTermType	HArDCore2D::kir_f

Detailed Description

Implementation of the DDR scheme for the Reissner-Mindlin plate problem.

Typedef Documentation

◆ ForcingTermType

typedef std::function<double(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::ForcingTermType

◆ GradientRotationType

typedef std::function<Eigen::Matrix2d(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::GradientRotationType

◆ SolutionDisplacementType

typedef std::function<double(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::SolutionDisplacementType

◆ SolutionRotationType

typedef std::function<Eigen::Vector2d(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::SolutionRotationType

◆ SystemMatrixType

typedef Eigen::SparseMatrix<double> HArDCore2D::ReissnerMindlin::SystemMatrixType

Function Documentation

◆ assembleLinearSystem()

void ReissnerMindlin::assembleLinearSystem	(	const ForcingTermType &	f,
		const SolutionRotationType &	theta,
		const GradientRotationType &	grad_theta,
		const SolutionDisplacementType &	u
	)

Assemble the global system

Parameters

f	Forcing term
theta	Boundary value
grad_theta	Boundary value
u	Boundary value

◆ bdryMatrix()

const SystemMatrixType & HArDCore2D::ReissnerMindlin::bdryMatrix ( ) const

inline

Returns the Matrix for BC.

◆ bdryValues()

const Eigen::VectorXd & HArDCore2D::ReissnerMindlin::bdryValues ( ) const

inline

Returns the boundary values.

◆ computeNorms()

RMNorms ReissnerMindlin::computeNorms ( const Eigen::VectorXd & v ) const

Compute the discrete norms: rotation, displacement, Kirchoff term, and complete energy.

Parameters

v	The vector

◆ contractPara()

template<typename outValue , typename Fct >

std::function< outValue(const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::contractPara ( const Fct & F ) const

inline

Takes a function dependent on RMParameter and a position x, and returns a function depending only on x (using the parameters of this class)

◆ dimensionSpace()

size_t HArDCore2D::ReissnerMindlin::dimensionSpace ( ) const

inline

Returns the dimension of the rotation + displacement space (with BC)

◆ exCurl()

const EXCurl & HArDCore2D::ReissnerMindlin::exCurl ( ) const

inline

Returns the space EXCurl.

◆ globalDOFIndices()

std::vector< size_t > HArDCore2D::ReissnerMindlin::globalDOFIndices ( const Cell & T ) const

inline

Create the vector of DOF indices for cell T, which combines the DOFs for the spaces EXcurl and Xgrad.

◆ locUKN()

const std::vector< std::pair< size_t, size_t > > & HArDCore2D::ReissnerMindlin::locUKN ( ) const

inline

Returns the location of the unknowns among the DOFs.

◆ nb_bdryDOFs()

size_t HArDCore2D::ReissnerMindlin::nb_bdryDOFs ( ) const

inline

Returns the nb of DOFs for BC.

◆ para()

const RMParameters & HArDCore2D::ReissnerMindlin::para ( ) const

inline

Returns the parameters.

◆ ReissnerMindlin()

ReissnerMindlin::ReissnerMindlin	(	const DDRCore &	ddrcore,
		const RMParameters &	para,
		const BoundaryConditions &	BC_theta,
		const BoundaryConditions &	BC_u,
		bool	use_threads,
		std::ostream &	output = `std::cout`
	)

Constructor.

Parameters

ddrcore	Core for the DDR space sequence
para	Physical parameters
BC_theta	Boundary conditions for rotation
BC_u	Boundary conditions for displacement
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

◆ RMNorms()

HArDCore2D::RMNorms::RMNorms	(	double	norm_rotation,
		double	norm_displacement,
		double	norm_kirchoff
	)

inline

Constructor.

◆ RMParameters()

HArDCore2D::RMParameters::RMParameters	(	const double	thickness,
		const double	young_modulus,
		const double	poisson_ratio
	)

inline

Constructor.

◆ sizeSystem()

size_t HArDCore2D::ReissnerMindlin::sizeSystem ( ) const

inline

Returns the size of the system without BC.

◆ stabilizationParameter() [1/2]

double & HArDCore2D::ReissnerMindlin::stabilizationParameter ( )

inline

Returns the stabilization parameter.

◆ stabilizationParameter() [2/2]

const double & HArDCore2D::ReissnerMindlin::stabilizationParameter ( ) const

inline

Returns the stabilization parameter.

◆ systemMatrix() [1/2]

SystemMatrixType & HArDCore2D::ReissnerMindlin::systemMatrix ( )

inline

Returns the linear system matrix.

◆ systemMatrix() [2/2]

const SystemMatrixType & HArDCore2D::ReissnerMindlin::systemMatrix ( ) const

inline

Returns the linear system matrix.

◆ systemVector() [1/2]

Eigen::VectorXd & HArDCore2D::ReissnerMindlin::systemVector ( )

inline

Returns the linear system right-hand side vector.

◆ systemVector() [2/2]

const Eigen::VectorXd & HArDCore2D::ReissnerMindlin::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

◆ xGrad()

const XGrad & HArDCore2D::ReissnerMindlin::xGrad ( ) const

inline

Returns the space XGrad.

Variable Documentation

◆ an_g

std::function<double(const VectorRd &)> HArDCore2D::an_g = [](const VectorRd &x)->double { return sin(PI*x(0))*sin(PI*x(1)); }

static

◆ an_GRAD_g

std::function<VectorRd(const VectorRd &)> HArDCore2D::an_GRAD_g

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
                 return VectorRd( PI*cos(PI*x(0))*sin(PI*x(1)), PI*sin(PI*x(0))*cos(PI*x(1)) ); 
               }

◆ an_GRAD_V

std::function<VectorRd(const VectorRd &)> HArDCore2D::an_GRAD_V

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
                 return VectorRd((1.-x(0))*exp(-x(0))*cos(x(1)), -x(0)*exp(-x(0))*sin(x(1))); 
               }

◆ an_GRAD_v

ReissnerMindlin::SolutionRotationType HArDCore2D::an_GRAD_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return pow(para.t, 2) * an_GRAD_V(x/para.t) + an_GRAD_g(x);
               }

◆ an_HESS_g

std::function<MatrixRd(const VectorRd &)> HArDCore2D::an_HESS_g

static

Initial value:

= [](const VectorRd & x) -> MatrixRd {
                MatrixRd H = MatrixRd::Zero();
                H.row(0) << -PI*PI*sin(PI*x(0))*sin(PI*x(1)), PI*PI*cos(PI*x(0))*cos(PI*x(1));
                H.row(1) << PI*PI*cos(PI*x(0))*cos(PI*x(1)), -PI*PI*sin(PI*x(0))*sin(PI*x(1));
                return H;
              }

◆ an_HESS_V

std::function<MatrixRd(const VectorRd &)> HArDCore2D::an_HESS_V

static

Initial value:

= [](const VectorRd & x) -> MatrixRd {
                MatrixRd H = MatrixRd::Zero();
                H.row(0) << (x(0)-2.)*exp(-x(0))*cos(x(1)), -(1.-x(0))*exp(-x(0))*sin(x(1));
                H.row(1) << -(1.-x(0))*exp(-x(0))*sin(x(1)), -x(0)*exp(-x(0))*cos(x(1));
                return H;
              }

◆ an_HESS_v

ReissnerMindlin::GradientRotationType HArDCore2D::an_HESS_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> MatrixRd {
                  return para.t * an_HESS_V(x/para.t) + an_HESS_g(x);
              }

◆ an_LAPL_g

std::function<double(const VectorRd &)> HArDCore2D::an_LAPL_g = [](const VectorRd &x)->double { return -2*pow(PI,2)*sin(PI*x(0))*sin(PI*x(1)); }

static

◆ an_LAPL_V

std::function<double(const VectorRd &)> HArDCore2D::an_LAPL_V = [](const VectorRd &x)->double { return -2.* exp(-x(0))*cos(x(1)); }

static

◆ an_LAPL_v

ReissnerMindlin::SolutionDisplacementType HArDCore2D::an_LAPL_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return para.t * (an_LAPL_V)(x/para.t) + an_LAPL_g(x);
                   }

◆ an_V

std::function<double(const VectorRd &)> HArDCore2D::an_V = [](const VectorRd &x)->double { return x(0) * exp(-x(0))*cos(x(1)); }

static

◆ an_v

ReissnerMindlin::SolutionDisplacementType HArDCore2D::an_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return pow(para.t,3) * an_V(x/para.t) + an_g(x);
                   }

◆ analytical_f

ReissnerMindlin::ForcingTermType HArDCore2D::analytical_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                 return (para.beta0+para.beta1) * 4 * pow(PI,4)*sin(PI*x(0))*sin(PI*x(1));
               }

◆ analytical_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::analytical_grad_theta = an_HESS_v

static

◆ analytical_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::analytical_theta = an_GRAD_v

static

◆ analytical_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::analytical_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return an_v(para, x) - pow(para.t,2) * ( (para.beta0+para.beta1)/para.kappa ) * an_LAPL_v(para, x);
                   }

◆ beta0

double HArDCore2D::RMParameters::beta0

◆ beta1

double HArDCore2D::RMParameters::beta1

◆ constant_f

ReissnerMindlin::ForcingTermType HArDCore2D::constant_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                 return 0.;
               }

◆ constant_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::constant_grad_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> Eigen::Matrix2d {
                 return Eigen::Matrix2d::Zero();
               }

◆ constant_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::constant_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return VectorRd(1., 2.);
               }

◆ constant_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::constant_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return 1.;
                   }

◆ displacement

double HArDCore2D::RMNorms::displacement

Norm of displacement.

◆ E

double HArDCore2D::RMParameters::E

◆ energy

double HArDCore2D::RMNorms::energy

Total energy.

◆ kappa

double HArDCore2D::RMParameters::kappa

◆ kir_f

ReissnerMindlin::ForcingTermType HArDCore2D::kir_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                return sin(PI*x(0))*sin(PI*x(1));
               }

◆ kir_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::kir_grad_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> Eigen::Matrix2d {
                 double coef = 12.*(1-pow(para.nu,2))/ (para.E * 4.*pow(PI, 4));
                 Eigen::Matrix2d H = Eigen::Matrix2d::Zero();
                 H.row(0) << -PI*PI*sin(PI*x(0))*sin(PI*x(1)), PI*PI*cos(PI*x(0))*cos(PI*x(1));
                 H.row(1) <<  PI*PI*cos(PI*x(0))*cos(PI*x(1)), -PI*PI*sin(PI*x(0))*sin(PI*x(1));
                 return coef * H;
               }

◆ kir_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::kir_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                double coef = 12.*(1-pow(para.nu,2))/ (para.E * 4.*pow(PI, 4));
                return coef * PI * VectorRd(cos(PI*x(0))*sin(PI*x(1)), sin(PI*x(0))*cos(PI*x(1)));
               }

◆ kir_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::kir_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                  double coef = 12.*(1-pow(para.nu,2))/ (para.E * 4.*pow(PI, 4));
                  return coef  * sin(PI*x(0))*sin(PI*x(1));
               }

◆ kirchoff

double HArDCore2D::RMNorms::kirchoff

Norm of kirchoff term.

◆ nu

double HArDCore2D::RMParameters::nu

◆ PI

const double HArDCore2D::PI = boost::math::constants::pi<double>()

static

◆ polynomial_f

ReissnerMindlin::ForcingTermType HArDCore2D::polynomial_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                double val = 0;
                
                val += 12*x(1)*(x(1)-1)*(5*x(0)*x(0)-5*x(0)+1) * 
                        ( 2*x(1)*x(1)*(x(1)-1)*(x(1)-1) + x(0)*(x(0)-1)*(5*x(1)*x(1)-5*x(1)+1) );
                val += 12*x(0)*(x(0)-1)*(5*x(1)*x(1)-5*x(1)+1) * 
                        ( 2*x(0)*x(0)*(x(0)-1)*(x(0)-1) + x(1)*(x(1)-1)*(5*x(0)*x(0)-5*x(0)+1) );
                
                return val * para.E / (12* (1.-para.nu*para.nu) );
               }

◆ polynomial_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::polynomial_grad_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> Eigen::Matrix2d {
                 Eigen::Matrix2d G = Eigen::Matrix2d::Zero();
                 G(0,0) = 2.*pow(x(0),2)*pow(x(1),3)*pow(x(0)-1.0,2)*pow(x(1)-1.0,3)+2.*x(0)*pow(x(1),3)*(2.*x(0)-1.)*pow(x(0)-1.,2)*pow(x(1)-1.0,3)+pow(x(0),2)*pow(x(1),3)*(2.*x(0)-1.)*(2.*x(0)-2.)*pow(x(1)-1.,3);
                 G(0,1) = 3.*pow(x(0)*x(1),2)*(2.*x(0)-1.)*pow(x(0)-1.,2)*pow(x(1)-1.,3)+3.*pow(x(0),2)*pow(x(1),3)*(2.*x(0)-1.)*pow(x(0)-1.,2)*pow(x(1)-1.,2);
                 G(1,0) = 2.*pow(x(1),2)*pow(x(0),3)*pow(x(1)-1.0,2)*pow(x(0)-1.0,3)+2.*x(1)*pow(x(0),3)*(2.*x(1)-1.)*pow(x(1)-1.,2)*pow(x(0)-1.0,3)+pow(x(1),2)*pow(x(0),3)*(2.*x(1)-1.)*(2.*x(1)-2.)*pow(x(0)-1.,3);
                 G(1,1) = 3.*pow(x(1)*x(0),2)*(2.*x(1)-1.)*pow(x(1)-1.,2)*pow(x(0)-1.,3)+3.*pow(x(1),2)*pow(x(0),3)*(2.*x(1)-1.)*pow(x(1)-1.,2)*pow(x(0)-1.,2);
 
                 return G;
               }

◆ polynomial_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::polynomial_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return VectorRd(
                          pow(x(1),3)*pow(x(1)-1,3)*pow(x(0),2)*pow(x(0)-1,2)*(2*x(0)-1),
                          pow(x(0),3)*pow(x(0)-1,3)*pow(x(1),2)*pow(x(1)-1,2)*(2*x(1)-1)
                          );
               }

◆ polynomial_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::polynomial_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                 double val = 0;
                 
                 val += (1./3.)*pow(x(0),3)*pow(x(0)-1,3)*pow(x(1),3)*pow(x(1)-1,3);
                 
                 val -= ( 2*pow(para.t,2) / (5*(1.-para.nu)) ) *
                          ( pow(x(1),3)*pow(x(1)-1,3)*x(0)*(x(0)-1)*(5*x(0)*x(0)-5*x(0)+1)
                            + pow(x(0),3)*pow(x(0)-1,3)*x(1)*(x(1)-1)*(5*x(1)*x(1)-5*x(1)+1) );
                 
                 return val;
                 }

◆ rotation

double HArDCore2D::RMNorms::rotation

Norm of rotation.

◆ t

double HArDCore2D::RMParameters::t

◆ ukn_f

ReissnerMindlin::ForcingTermType HArDCore2D::ukn_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                double val = 1.;
                if (x(0)<.5){
                  val = -1.;
                }
                return val;
               }

◆ ukn_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::ukn_grad_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> Eigen::Matrix2d {
                 return Eigen::Matrix2d::Zero();
               }

◆ ukn_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::ukn_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return VectorRd(0., 0.);
               }

◆ ukn_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::ukn_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return x(0);
                   }

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ ForcingTermType

◆ GradientRotationType

◆ SolutionDisplacementType

◆ SolutionRotationType

◆ SystemMatrixType

Function Documentation

◆ assembleLinearSystem()

◆ bdryMatrix()

◆ bdryValues()

◆ computeNorms()

◆ contractPara()

◆ dimensionSpace()

◆ exCurl()

◆ globalDOFIndices()

◆ locUKN()

◆ nb_bdryDOFs()

◆ para()

◆ ReissnerMindlin()

◆ RMNorms()

◆ RMParameters()

◆ sizeSystem()

◆ stabilizationParameter() [1/2]

◆ stabilizationParameter() [2/2]

◆ systemMatrix() [1/2]

◆ systemMatrix() [2/2]

◆ systemVector() [1/2]

◆ systemVector() [2/2]

◆ xGrad()

Variable Documentation

◆ an_g

◆ an_GRAD_g

◆ an_GRAD_V

◆ an_GRAD_v

◆ an_HESS_g

◆ an_HESS_V

◆ an_HESS_v

◆ an_LAPL_g

◆ an_LAPL_V

◆ an_LAPL_v

◆ an_V

◆ an_v

◆ analytical_f

◆ analytical_grad_theta

◆ analytical_theta

◆ analytical_u

◆ beta0

◆ beta1

◆ constant_f

◆ constant_grad_theta

◆ constant_theta

◆ constant_u

◆ displacement

◆ E

◆ energy

◆ kappa

◆ kir_f

◆ kir_grad_theta

◆ kir_theta

◆ kir_u

◆ kirchoff

◆ nu

◆ PI

◆ polynomial_f

◆ polynomial_grad_theta

◆ polynomial_theta

◆ polynomial_u

◆ rotation

◆ t

◆ ukn_f

◆ ukn_grad_theta

◆ ukn_theta

◆ ukn_u