Basic principles of the finite element method 2nd Edition PDF

INTRODUCTION

We shall concern ourselves in this book with the application of the finite element method to the calculation of the elastic stress and strain distribution in loaded bodies. The method can be applied also to analyse problems involving electro-magnetic fields, acoustics, heat flow, soil mechanics and fluid mechanics, but we shall not address any of these areas in this book.

In this introduction we present an overview of the scope of the chapters that follow and, in the process, refer to specific terms in the finite element vocabulary which are of major importance and the explanation of which will occupy our energies in the ensuing text. These terms are dignified by capitals to give them prominence.

The basic idea infinite element elastic stress analysis is the following. The elastic body is first divided into discrete connected parts called FINITE ELEMENTS. These elements are commonly either triangles or quadrilaterals for two-dimensional models, with either straight or curved sides. For three-dimensional problems they might be tetrahedra or parallelepipeds. Examples are drawn in Fig. 1.1. The points at which the elements are connected together are called NODES, located at the corners of the elements and sometimes along the sides. The process of dividing the loaded body into elements is called (inelegantly) DISCRETEISATION. The pattern of elements is called a MESH. The selection of the mesh pattern and the element size is a matter of judgement and experience. Commercial finite element packages commonly have a programme that will form a mesh automatically.

Edited by: K. M. Entwistle