The numerical analysis of structures

Abstract

Elasticity theory, even in its simplest guise, linear with respect to geometrical deformations and with respect to material properties, has few so-called “closed form” solutions. The need for solving numerically elasticity problems and the advent of fast and powerful computing machines seem even to have partly robbed such types of solutions of their interest. It is now often easier and faster to produce numerical results of a given problem by using modern discretization methods than to have to compute the special functions involved in a closed form presentation. In the end the value of such presentations lies in the ease with which they can be manipulated to exhibit the influence of the design parameters, whereas a similar computer study of the influence of design is still a long and costly process. Structural optimization, which is the goal of such studies, receives nowadays a good deal of attention; its costeffective implementation will largely depend on the speed and accuracy with which the more classical problems can be solved, namely the determination, for a given design, of its statical and dynamical response to external loads or displacements of supports.