Finite Element Methods of Structural Analysis

This chapter presents an overview of two widely used numerical methods for structural analysis. The Rayleigh–Ritz method employs a global perspective of approximation, while the finite element method (of Galerkin form), employs a local approximation basis. Both methods are introduced via a simple truss example. For the finite element method, the construction of element stiffness matrices and loading vectors are shown starting from the general differential equations for truss response, through developing a weak form of the equations, to the Galerkin approximation method and then to specific choices of assumed solutions. Finite element generation, element assembly and global solution techniques are articulated. The generality of the finite element approach is demonstrated by application to beam bending theory.

Keywords: finite element method; Rayleigh–Ritz method; structural analysis; approximation methods