Solving a simple 2D elasticity problem using the finite element method by means of constant strain triangular elements

This manuscript aims to show how a simple elasticity problem can be solved using the finite element method by means of constant strain triangular elements. This paper does not intends to explain the finite element method formulation, only its practical application. It shows how the element's geometric moment matrix is constructed, and corresponding shape functions and partial derivatives. It is also presented the construction of the stiffness matrix at the element level and its global assemblage. Afterwards, a swift construction of the global force vector is presented, and then how the displacement constraints can be imposed using a direct technique. Finally, the global system of equations is established and solved, and the variable fields are obtained: displacement, strain and stress fields. Afterwards, in order to show the FEM's dependency on the mesh, the convergence test is shown. In the end, a pedagogic FEM routine is delivered, and the final conclusions and remarks are presented.