In the automated design of mechanical systems by means of structural synthesis techniques, two cathegories of procedures, namely shape and sizing optimization, play different but equally important roles: the former is usually applied to the synthesis of solid modelled (in the finite element method sense) structures, by finding optimum positions for the model's nodes, and the later is often used to optimize direct finite element properties (shell thicknesses and bar areas, for instance).
Besides the nature of the finite element model (plane or solid) is mainly a consequence of the system's inherent features, not so seldom, the engineer can be faced with structures that allow both types of approaches and, for optimization purposes, the two aforementioned alternatives arise. Thus, in such situations, the choice for the type of finite element model to be built is also driven by which kind of structural synthesis (shape or sizing) would lead to better results.
This work describes a comparison of these two paradigms, tracing and establishing the advantages and drawbacks of each one, following some fundamental criteria: efficacy (expressed by means of the final optimization achievements: the resulting value for the objective function and the behaviour regarding all kinds of related constraints) ease of preparation for input data (concerning the time and work required for building the finite element model itself and the assembly of the optimization related subroutines), flexibility (regarding possible later changes in the model itself and/or the optimization strategy) and CPU times.
For clarification purposes, the application of both techniques is illustrated by a case study conducted over a real automotive component: the “Z - spring” of a heavy truck suspension. This interesting part is a component of the rear air suspension of the vehicle and is subjected to several different loads depending upon the operating conditions. In this study, the evaluated one simulates the case in which the vehicle is forward accelerated. Further investigation could be developed using a procedure very similar to the one shown in this paper, just changing the boundary conditions specified in the finite element model).
This task is carried out using a leading commercial structural optimization software: VMA/GENESIS version 3.0. Basically, it is an implementation of a finite element code and a non linear numerical optimizer. For the sake of computational feasibility, these main modules are not directly linked. Instead, a generator of approximate finite element models (that is, a set of algorythms specially designed for this purpose) is introduced, with the aim of reducing, by significant amounts, the calculations needed over the iterative optimization process.
By showing the details and pitfalls of the studied optimization approaches, the authors are willing to add some practical engineering insight over the deployements of their substantially different conceptual basis. In the end, there is a very reasonable degree of confidence on the fact that the knowledge of these differences and their full comprehension not only explains the results achieved but also, and most important, supplies the logical elements needed to better formulate the structural synthesis problem and answer the core question: for a given structure (possessing several known key characteristics) should the engineer choose sizing or shape optimization?