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rGOOSEFEM/docs/examples/theory/diagonal_mass/Quad4/diagonal.cpp
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diagonal.cpp
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#include <iostream>
#include <Eigen/Eigen>
#include <GooseFEM/GooseFEM.h>
// alias relevant types for <Eigen/Eigen>
using MatD = GooseFEM::MatD;
using MatS = GooseFEM::MatS;
using ColD = GooseFEM::ColD;
using ColS = GooseFEM::ColS;
// =================================================================================================
int main()
{
// --------
// geometry
// --------
// create a mesh
GooseFEM::Mesh::Quad4::Regular mesh ( 2 , 2 );
// element type for extrapolation and quadrature
GooseFEM::Quad4 el;
// extract relevant mesh data
size_t nnode = mesh.nnode(); // number of nodes
size_t nelem = mesh.nelem(); // number of elements
size_t ndim = mesh.ndim (); // number of dimensions (== 2)
size_t nne = mesh.nne (); // number of nodes per element (== 3)
MatS conn = mesh.conn (); // connectivity (nodes of each element) : one row per element
MatD x0 = mesh.coor (); // nodal position in x- and y-direction : one row per node
size_t ndof = nnode * ndim; // total number of DOFs
// DOF-numbers for each vector component of each node (sequential)
MatS dofs = GooseFEM::Mesh::dofs(nnode,ndim);
// perturb position for testing purpose
x0(0,0) -= .5 ; x0(0,1) -= .2 ;
x0(1,0) -= .1 ; x0(1,1) -= .1 ;
x0(2,0) += .2 ; x0(2,1) -= .15;
x0(3,0) += .1 ; x0(3,1) += .2 ;
x0(4,0) += .1 ; x0(4,1) += .1 ;
x0(5,0) -= .2 ; x0(5,1) += .15;
x0(6,0) -= .5 ; x0(6,1) += .4 ;
x0(7,0) -= .1 ; x0(7,1) += .2 ;
x0(8,0) += .2 ; x0(8,1) += .3 ;
// -------------------------------------
// element & quadrature-point - allocate
// -------------------------------------
// element arrays
ColS dof_e(nne*ndim ); // array with DOF numbers of each row/column of "m_e"
MatD x0_e (nne ,ndim); // nodal positions and displacements (column of vectors)
// quadrature-point position and weight factor (this depends on the element type!)
ColD xi_k(ndim);
// ------------------------
// global system - allocate
// ------------------------
// mass matrix: diagonal only
ColD M(ndof);
// density (constant in space)
double rho = 1.0;
// ------------------------
// global system - assemble
// ------------------------
// zero-initialize global system
M.setZero();
// loop over all elements
for ( size_t e = 0 ; e < nelem ; ++e )
{
// - DOF numbers and nodal positions for element "e"
for ( size_t m = 0 ; m < nne ; ++m ) x0_e .row(m) = x0 .row(conn(e,m));
for ( size_t m = 0 ; m < nne ; ++m ) dof_e.segment(m*ndim,ndim) = dofs.row(conn(e,m));
// - loop to integrate and assemble (N.B. quadrature-points coincide with the nodes)
for ( size_t m = 0 ; m < nne ; ++m )
{
// -- define position of the quadrature-point in area coordinates (coincides with node "m")
if ( m == 0 ) { xi_k(0) = -1.; xi_k(1) = -1.; }
else if ( m == 1 ) { xi_k(0) = +1.; xi_k(1) = -1.; }
else if ( m == 2 ) { xi_k(0) = +1.; xi_k(1) = +1.; }
else if ( m == 3 ) { xi_k(0) = -1.; xi_k(1) = +1.; }
// -- evaluate the (gradient of the) shape functions
el.eval( x0_e, xi_k, 1. );
// -- assemble element mass matrix to global system
for ( size_t i = 0; i < ndim ; ++i )
M( dof_e(m*ndim+i) ) += rho * el.V; // N.B. "el.N(m) == 1", so omitted here
}
}
// ---------------
// print to screen
// ---------------
std::cout << M << std::endl;
return 0;
}
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