Assembly of the Stiffness Elasticity Matrix by $P_1$ -Lagrange finite elements in 3D using basic version (see report). More...

Functions
function K =	StiffElasAssembling3DP1base (nq, nme, q, me, volumes, lambda, mu, Num)
	Assembly of the Stiffness Elasticity Matrix by -Lagrange finite elements in 3D using basic version (see report).

Detailed Description

Assembly of the Stiffness Elasticity Matrix by $P_1$ -Lagrange finite elements in 3D using basic version (see report).

Definition in file StiffElasAssembling3DP1base.m.

Function Documentation

function K = StiffElasAssembling3DP1base	(	nq,
		nme,
		q,
		me,
		volumes,
		lambda,
		mu,
		Num
	)

Assembly of the Stiffness Elasticity Matrix by $P_1$ -Lagrange finite elements in 3D using basic version (see report).

The Stiffness Elasticity Matrix is given by

$\StiffElas_{m,l}=\int_{\DOMH} \Odv^t(\BasisFuncTwoD_m) \Ocv(\BasisFuncTwoD_l)dT, \ \forall (m,l)\in\ENS{1}{2\,\nq}^2,$

where $\BasisFuncTwoD_m$ are $P_1$ -Lagrange vector basis functions. Here $\Ocv=(\Occ_{xx},\Occ_{yy},\Occ_{zz}, \Occ_{xy}, \Occ_{yz}, \Occ_{xz})^t$ and $\Odv=(\Odc_{xx},\Odc_{yy},\Odc_{zz},2\Odc_{xy},2\Odc_{yz},2\Odc_{xz})^t$ are the elastic stress and strain tensors respectively.

Example

    Th=CubeMesh(10);
    KK=StiffElasAssembling3DP1base(Th.nq,Th.nme,Th.q,Th.me,Th.areas,1.,0.25,0);

See Also: BuildIkFunc, BuildElemStiffElasMatFunc

Copyright: See License issues

Parameters

nq	total number of vertices, also denoted by $\nq$ .
nme	total number of elements, also denoted by $\nme$ .
q	Array of vertices coordinates, $3\times\nq$ array. ${\q}(\il,j)$ is the $\il$ -th coordinate of the -th vertex, $\il\in\{1,2,3\}$ and $j\in\ENS{1}{\nq}$
me	Connectivity array, $4\times\nme$ array. $\me(\jl,k)$ is the storage index of the $\jl$ -th vertex of the -th tetrahedron in the array $\q$ of vertices coordinates, $\jl\in\{1,2,3,4\}$ and $k\in{\ENS{1}{\nme}}$ .
volumes	Array of volumes, $1\times\nme array$ . volumes(k) is the volume of the k-th tetrahedron.
lambda	the first Lame coefficient in Hooke's law
mu	the second Lame coefficient in Hooke's law
Num	0 global alternate numbering with local alternate numbering (classical method), 1 global block numbering with local alternate numbering, 2 global alternate numbering with local block numbering, 3 global block numbering with local block numbering.

Return values

K	$3\nq\times 3\nq$ stiffness elasticity sparse matrix

Definition at line 17 of file StiffElasAssembling3DP1base.m.

Functions

Detailed Description

Function Documentation