Finite-Element Methods in Structural Mechanics

Abstract

The investigation of deformations and stresses in solids belongs to the most frequent tasks in engineering applications. In practice nowadays the numerical study of such problems involves almost exclusively finite-element methods. Due to the great importance of these methods, in this chapter we will address in more detail the particularities and the practical treatment of corresponding problems. In particular, the important concept of isoparametric finite elements will be considered. We will do this exemplarily by means of linear two-dimensional problems for a 4-node quadrilateral element. However, the formulations employed allow in a very simple way an understanding of the necessary modifications if other material laws, other strain-stress relations, and/or other types of elements are used.