TABLE OF CONTENTS S. Rajasekaran
Numerical solutions for the governing differential equilibrium equations for elastic and plastic beam-columns have been achieved in Chap. 10 by the finite difference technique in which the differential equation is approximated by discrete values of the variables at selected points. On the other hand, finite-segment method is applied in Chap. 11 for the elastic-plastic beam-column by replacing it with an assembly of finite segments. Segment stiffness matrices have been evaluated using the exact displacement field of elastic beam-column along the length of the segment. In this chapter, the beam-column is physically replaced by an assembly of discrete elements and the element stiffness will be evaluated using the approximate displacement field along the element length. Hence one can consider the finite difference scheme described in Chap. 10 as point-wise approximation, and the finite segment method described in the preceding chapter and the finite element method described here as element-wise approximations.
The basic concept underlying the finite element method is that a real structure can be modelled analytically by its subdivisions into finite number of elements. In each of the finite element regions, the behavior of the element can be studied independently of the behavior of other elements in the ensemble by a set of assumed functions approximating the stresses or displacements in that region. The process of connecting elements together to form a complete model is purely a topological one and is independent of the physical nature of the problem. The set of functions for...
