The use of numerical methods enables the engineer to expand his or her ability to solve design problems of practical significance. Treated in this chapter are real shapes and loadings, as distinct from the somewhat limited variety of shapes and loadings amenable to simple analytical solution. Among the most important of the numerical approaches are the method of finite differences (Part A) and the finite element method (Part B). As illustrated in detail in this chapter, both techniques eventually require the solution of a system of linear algebraic equations. Such calculations are commonly performed with the aid of a computer employing matrix methods.
Observe that the finite difference method is simple, versatile and suitable for use with a computer or programmable calculator and results in acceptable accuracy for most technical purposes, provided that a relatively fine mesh is used. Finite element methods have proven to be extremely powerful and versatile tools for static and dynamic analysis of a wide variety of beam, plate and shell problems. They do, however, require the use of computers of considerable speed and storage capacity.