assembly.h File Reference

Go to the source code of this file.

Classes
struct	ElasticityAssembly
struct	ThetaA0
struct	AssemblyA0
struct	ThetaA1
struct	AssemblyA1
struct	ThetaA2
struct	AssemblyA2
struct	ThetaF0
struct	AssemblyF0
struct	ThetaF1
struct	AssemblyF1
struct	ThetaF2
struct	AssemblyF2
struct	ThetaPointLoadX
struct	AssemblyPointLoadX
struct	ThetaPointLoadY
struct	AssemblyPointLoadY
struct	ThetaPointLoadZ
struct	AssemblyPointLoadZ
struct	InnerProductAssembly
struct	ElasticityThetaExpansion
struct	ElasticityAssemblyExpansion

Functions
Real	kronecker_delta (unsigned int i, unsigned int j)
Real	elasticity_tensor (unsigned int i, unsigned int j, unsigned int k, unsigned int l)

Function Documentation

elasticity_tensor()

Real elasticity_tensor	(	unsigned int	i,
		unsigned int	j,
		unsigned int	k,
		unsigned int	l
	)

Definition at line 43 of file assembly.C.

References kronecker_delta(), and libMesh::Real.

Referenced by LinearElasticity::assemble(), compute_stresses(), LinearElasticity::compute_stresses(), LargeDeformationElasticity::compute_stresses(), ElasticitySystem::element_time_derivative(), AssemblyA0::interior_assembly(), AssemblyA1::interior_assembly(), AssemblyA2::interior_assembly(), LargeDeformationElasticity::jacobian(), and LargeDeformationElasticity::residual().

{
  // Define the Poisson ratio and Young's modulus
  const Real nu = 0.3;
  const Real E  = 1.;

  // Define the Lame constants (lambda_1 and lambda_2) based on nu and E
  const Real lambda_1 = E * nu / ((1. + nu) * (1. - 2.*nu));
  const Real lambda_2 = 0.5 * E / (1. + nu);

  return lambda_1 * kronecker_delta(i, j) * kronecker_delta(k, l)
    + lambda_2 * (kronecker_delta(i, k) * kronecker_delta(j, l) + kronecker_delta(i, l) * kronecker_delta(j, k));
}

kronecker_delta()

Real kronecker_delta ( unsigned int  i, unsigned int  j  )

inline

Definition at line 37 of file assembly.C.

Referenced by elasticity_tensor(), ElasticitySystem::elasticity_tensor(), LargeDeformationElasticity::elasticity_tensor(), and LinearElasticity::elasticity_tensor().

{
  return i == j ? 1. : 0.;
}