Introduction to Finite Element Analysis and Design, 2nd Edition

Chapter 5Review of Solid Mechanics

5.1 INTRODUCTION

The finite element method is a powerful numerical method for solving partial differential equations. It has been applied to solve many physical problems whose governing equations are partial differential equations. The method has been implemented and is available as commercial software that can perform a variety of analysis including solids, structures, and thermal systems to mention a few. However, to use these programs effectively, one must understand the underlying physics of the problem being solved. This is important not only to be able to construct the right models for analysis but also to interpret the results and verify its accuracy. In this chapter, we review the main principles and the governing equations of solid mechanics. We explain the physical meaning behind the stress and strain tensors and the relation between them. Stress analysis is a major step, and in fact, it can be considered the most important one in the mechanical design process. There are many design considerations that influence the design of a machine element or structure. The most important design considerations are the following¹: (i) the stress at every point should be below a certain limit for the material; (ii) the deflection should not exceed the maximum allowable for proper functioning of the system; (iii) the structure should be stable; and (iv) the structure or machine element should not fail due to fatigue. The failure mode corresponding ...