input_file_1ele.m

The Finite Element Method Usign MATLAB.pdf

% Input Data for Example 9.3 (1 element)

% material properties
E  = 30e6;     % Young's modulus 
ne = 0.3;      % Poisson ratio  
D  = E/(1-ne^2) * [1    ne     0          
                   ne    1     0  
                   0     0     (1-ne)/2];

% mesh specifications
nsd  = 2;         % number of space dimensions
nnp  = 4;         % number of nodal nodes
nel  = 1;         % number of elements
nen  = 4;         % number of element nodes 
nee  = 4;         % number of element edges

ndof = 2;         % degrees of freedom per node
neq  = nnp*ndof;  % number of equations


f = zeros(neq,1);      % initialize nodal force vector
d = zeros(neq,1);      % initialize nodal displacement matrix
K = zeros(neq);        % initialize stiffness matrix

counter    = zeros(nnp,1);  % counter of nodes for stress plots
nodestress = zeros(nnp,3);  % stresses at nodes for the stress plots [sxx syy sxy]

flags = zeros(neq,1);  % array to set B.C flags 
e_bc  = zeros(neq,1);  % essential B.C array
n_bc  = zeros(neq,1);  % natural B.C array

P     = zeros(neq,1);          % point forces applied at nodes
b     = zeros(nen*ndof,nel);   % body forces defined at nodes

ngp    = 2;             % number of gauss points in each direction
nd     = 4;             % number of essential boundary conditions (x and y)

% dof:    1x    1y    2x     2y    3x    3y    4x     4y 
flags   = [2     2     2     2     0     0      0      0]';     % 


% plots
plot_mesh      = 'yes';
plot_nod       = 'yes';
plot_disp      = 'yes';
compute_stress = 'yes';
plot_stress_xx = 'yes';
plot_mises     = 'yes';
fact           = 9.221e3;      % factor for scaled displacements plot





n_bc  = [ 1              %  node 1 
          4              %  node 2   
          0              %  traction at node 1 in x 
         -20             %  traction at node 1 in y 
          0              %  traction at node 2 in x 
         -20 ];          %  traction at node 2 in y 
            
nbe = 1;   % number of edges on the boundary


% mesh generation
% node:  1    2    3    4
x   =  [0.0  0.0  2.0  2.0];     % X coordinate
y   =  [1.0  0.0  0.5  1.0];     % Y coordinate

IEN =  [2    3    4    1  ]';     % connectivity array

% function to plot the mesh
plotmesh;