Finite Element Methods in Continuum Mechanics

Abstract

Publisher Summary The chapter presents a brief introduction to the different finite element formulations for linear elastic solids and discusses similar formulations for several other field problems. The chapter presents detailed illustrations for several typical finite element formulations. In the finite element formulation, displacement and stress fields are assumed to be continuous within each discrete element. This formulation calls for modified variational principles for which the continuity or equilibrium conditions along the interelement boundaries are introduced as conditions of constraint and appropriate boundary variables are used as the corresponding Lagrangian multipliers. The chapter presents the several variational principles and the corresponding models used in the finite element formulation. The large majority of the existing finite element formulations are based on the assumed displacement approach. The chapter discusses equilibrium problems of linear elastic solids. There are several other problems in solid mechanics, which can be formulated by means of variational principles and hence can be solved by finite element methods. The finite element methods have also been extended to nonlinear problems resulting from elastic-plastic material properties or from large deflections or finite strains.