General Problems and Nonlinearity in Solid Mechanics

This chapter addresses general problems and nonlinearities in solid mechanics, providing a detailed summary of the main principles for formulating finite element equations for solid and structural mechanics problems, as well as the fundamental steps required to solve general small-strain solid mechanics problems. The equations are presented in both the strong form of partial differential equations and the weak form in integral representation. The chapter also offers a detailed introduction to variational principles and explains how certain problems become nonlinear. As this chapter provides a broad overview, beginners are advised to focus on understanding the basic concepts rather than delving deeply into the equations. After reading the subsequent chapters, revisiting this chapter will help achieve a more comprehensive understanding of its content.