Example on FEM constant strain triangular element

thickness

enter the nodal coordinates

element 1: nodes: 1,2,4

element 2: nodes: 1,3,4

area of element 1

area of element 2

Create stiffness matrices

Expand stiffness matrices

Reduced Stiffness matrix

Boundary Conditions:

Forces: Two forces on nodes 3 and 4 in x and y directions respectively. Distribted force on 3-4 endge (element 2 only).

The line equation is,

A matrix is,

Multiply by the equation of the 3-4 edge

results in,

by matrix transposition, yields

yields

Force correspond to u1,u3, and u4 respectively

displacements of nodes 3 and 4 in x and y directions

Display the results:

magnification factor

Upper edge:

yields

yields

Outer edge:

yields

yields

Lower edge

yields

yields

Undeformed shape