Solid Mechanics

Abstract

Solid mechanics is arguably one of the most important areas of application for finite elements. Indeed, finite element analysis is used together with computer aided design (CAD) to optimize and speed up the design and manufacturing process of practically all mechanical structures, ranging from bearings to airplanes. In this chapter we derive the equations of linear elasticity and formulate finite element approximations of them. We do this in the abstract setting of elliptic partial differential equations introduced before and prove existence and uniqueness of the solution using the Lax-Milgram lemma. A priori and a posteriori error estimates are also proved. Some effort is laid on explaining the implementation of the finite element method. We also touch upon thermal stress-and modal analysis.