Kaskade::Elastomechanics::ShellKinematics< dim, Real > Class Template Reference

A lower-dimensional kinematics ansatz useful for shell models. More...

#include <shellKinematics.hh>

Detailed Description

template<int dim = 2, class Real = double>
class Kaskade::Elastomechanics::ShellKinematics< dim, Real >

A lower-dimensional kinematics ansatz useful for shell models.

This represents the deformation \( \Phi: \Omega\subset \R^{d+1} \to \R^{d+1} \) on \(\Omega = \omega \times \R \) as

\[ \Phi(x,z) = \phi(x) + z t(x) n(x) \]

with \( \phi, n: \omega\to\R^{d+1} \), \( t:\omega\to\R \), and \( n^T\phi' = 0\).

Template Parameters

dim	the dimension of the parametrization domain, usually 2 (or 1 for beams in 2D)
Real	a real field type, usually double

Definition at line 127 of file shellKinematics.hh.

Public Types
using	Vector = Dune::FieldVector< Real, dim+1 >
	The type of deformation vectors in \( \R^{d+1} \). More...

Public Member Functions
	ShellKinematics (Vector const &phi, Dune::FieldMatrix< Real, dim+1, dim > const &dphi_dx, Real t)
ShellKinematicsDerivative< dim, Real >	derivative () const
	Returns an object for evaluating \( \Phi' \) and its parametrization derivatives. More...
Vector	d0 () const
template<int row>
auto	d1 (VariationalArg< Real, dim, 1 > const &v) const
	Computes the directional parametrization derivative. More...

Member Typedef Documentation

Vector

template<int dim = 2, class Real = double>

using Kaskade::Elastomechanics::ShellKinematics< dim, Real >::Vector = Dune::FieldVector<Real,dim+1>

The type of deformation vectors in \( \R^{d+1} \).

Definition at line 133 of file shellKinematics.hh.

Constructor & Destructor Documentation

ShellKinematics()

template<int dim = 2, class Real = double>

Kaskade::Elastomechanics::ShellKinematics< dim, Real >::ShellKinematics	(	Vector const &	phi,
		Dune::FieldMatrix< Real, dim+1, dim > const &	dphi_dx,
		Real	t
	)

Member Function Documentation

d0()

template<int dim = 2, class Real = double>

Vector Kaskade::Elastomechanics::ShellKinematics< dim, Real >::d0 ( ) const

inline

Definition at line 142 of file shellKinematics.hh.

d1()

template<int dim = 2, class Real = double>

template<int row>

auto Kaskade::Elastomechanics::ShellKinematics< dim, Real >::d1

(

VariationalArg< Real, dim, 1 > const &

v

)

const

Computes the directional parametrization derivative.

\[ \frac{\partial\Phi}{\partial p} v, \quad p\in\{\phi,t\} \]

Template Parameters

row	for row=0, the derivative wrt \( \phi \) is evaluated, for row=1 wrt \( t \)

derivative()

template<int dim = 2, class Real = double>

ShellKinematicsDerivative< dim, Real > Kaskade::Elastomechanics::ShellKinematics< dim, Real >::derivative

(

)

const

Returns an object for evaluating \( \Phi' \) and its parametrization derivatives.

---

The documentation for this class was generated from the following file:

• shellKinematics.hh