Computer-Aided Analysis of Mechanical Systems

Book Preface

This book is designed to introduce fondamental theories and numerical methods for use in computational mechanics. These theories and methods can be used to develop com­puter programs for analyzing the response of simple and complex mechanical systems. In such programs the equations of motion are formulated systematically, and then solved numerically. Because they are relatively easy to use, the book focuses on Cartesian co­ordinates for formulating the equations of motion. After the reader has become familiar with this method of formulation, it can serve as a stepping stone to formulating the equations of motion in other sets of coordinates. The numerical algorithms that are dis­cussed in this book can be applied to the equations of motion when formulated in any coordinate system.

Organization of the Book

The text is organized in such a way that it can be used for teaching or for self­study. The concepts and numerical methods used in kinematics are systematically treated before the concepts and numerical methods used in dynamics are introduced. Separate chapters on each of these topics allow the text to be used for the study of each topic separately or for some desired combination of topics. Furthermore, the text first treats the less complex problems of planar kinematic and dynamic analysis before it discusses spatial kinematic and dynamic analysis.  With the exception of the first two chapters and the last chapter, the text can be divided into two subjects kinematics and dynamics. Chapter 1 gives an introduction to the subject of computational methods in kinematics and dynamics. Simple examples illustrate how a problem can be formulated using different coordinate systems. Chapter 1 also explains why Cartesian coordinates provide a simple tool, if not necessarily the most computationally efficient one. Chapter 2 presents a review of vector and matrix algebra, with an emphasis on the kind of formulation that lends itself to implementation in computer programs.