7 - Numerical Solution of Finite Element Equations

Abstract

Most problems in engineering mechanics are either continuous or discrete problems. Continuous problems involve infinite number of degrees of freedom, while discrete problems involve finite number of degrees of freedom. All discrete and continuous problems are classified as equilibrium (static), eigenvalue, and propagation (transient) problems. The finite element method is applicable for the solution of all three categories of problems. It is a numerical procedure that replaces a continuous problem by an equivalent discrete one. The matrix notation is used in formulating and solving problems using the finite element procedure. When matrix notation is used in finite element analysis, the organizational properties of matrices allows systematic compilation of the required data and the finite element analysis is then defined as a sequence of matrix operations that can be programmed directly for a digital computer. This chapter introduces matrix techniques that are useful for the solution of finite element equations along with a description of the relevant Fortran computer programs.