Multiparameter structural optimization using FEM and multipoint explicit approximations

Abstract

A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (muttipoi~*t approximations) in order to better fit constraints and/or objective functions and to reduce the total number of FE analyses needed to solve the optimization problem. In each iteration, the subregion of the initial region in the space of design variables, defined by move limits, is chosen. In this subregion, several points (designs) are selected, for which response analyses and design sensitivity analyses are carried out using FEM. The explicit expressions are formulated using the weighted least-squares method. The explicit expressions obtained then replace initial problem functions. They are used as functions of a particular mathematical programming problem. Several particular forms of the explicit expressions are considered. The basic features of the presented approximations are shown by means of classical test examples, and the met]~Lod is compared with other optimization techniques.

Extended Multipoint Approximation Method

“…Where the coefficients refer to the weights that reflect the inequality of data obtained in different sampling points [7] and is the tuning parameters with respect to the specific surrogate.…”

Adaptive and Parallel Capabilities in the Multipoint Approximation Method

“…This technique (Toropov et al, 1993) replaces the original optimization problem by a succession of simpler mathematical programming problems. The functions in each iteration present mid-range approximations to the corresponding original functions.…”

“…could be positive or negative. The parameters w pj refer to the weights that reflect the inequality of data obtained in different sampling points P, see Toropov et al (1993).…”

“…Figure 1 demonstrates the quality of design of experiments using a proposed technique. As an example, two patterns (20 and 100 points) were generated for the two-bar truss optimization test problem; see Toropov et al (1993). Analytical tests have shown that the above technique may improve the quality of the approximate functions and therefore reduce number of MAM optimization steps.…”

Optimizing the dynamic behavior of structures using substructuring and surrogate modeling

“…These methods are effective especially when the derivatives can not be computed accurately. The multi-point-path method proposed by Toropov et al [131] uses linear combinations of predefined basis functions to approximate the objective and the constraint functions of the subproblems. Another multi-point-path method has been presented by Etman which is utilized for optimizing multi-body systems [42].…”