TABLE OF CONTENTS In this chapter we will develop a method of numerical analysis referred to as the finite element method. It will provide us with a general method for analyzing bodies of complex shapes such as those commonly encountered by engineers.
Most of the remaining chapters of this book deal with various analytical techniques for analyzing problems concerning the stress and deformation of solid bodies. For the most part the goal in these chapters is to obtain an exact solution to the governing equations for a particular problem. This is possible as long as the geometry that is, the shape of the boundary is a simple shape, which can be described using a standard coordinate system. As we discussed in Chapter 6, it is the shape of the boundary that determines the coordinate system to be used. It might be preferable to solve the differential equations for each of the problems in the Cartesian coordinate system if for no other reason than for the great amount of experience we would gain working in this coordinate system. However, application of the boundary conditions can only be accomplished with a great deal of difficulty unless the body happens to be rectangular with sides parallel to the Cartesian axes. For example, to specify a constant pressure p on the surface of a cylinder of radius b, we simply write ? rr = ? p at r = b in cylindrical coordinates. The same condition is quite complicated if...
