This paper reviews the basic approximation concepts used in structural optimization. It also discusses some of the most recent developments in that area since the introduction of approximation concepts in the mid-seventies. The paper distinguishes between local, medium-range and global approximations; it covers function approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It appears also that some new methodologies emerge which could greatly benefit from the introduction of new computer architectures.

Approximation concepts for optimum structural design — a review

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool f...

The harmony search heuristic algorithm for discrete structural optimization

An investigation was conducted from October 1, 1990 to May 31, 1994 on the development of methodologies to improve the designs (more specifically, the shape) of aerodynamic surfaces of coupling optimization algorithms (OA) with Computational Fluid Dynamics (CFD) algorithms via sensitivity analyses (SA). The study produced several promising methodologies and their proof-of-concept cases, which have been reported in the open literature.

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Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new approximation method for dealing with stress constraints in structural synthesis is presented. The finite element nodal forces are approximated and these are used to create an explicit, but often nonlinear, approximation to the original problem. The principal motivation is to create the best approximation possible, in order to reduce the number of detailed finite element analyses needed to reach the optimum. Examples are offered and compared with published results, to demonstrate the efficiency and reliability of the proposed method.

New Approximation Method for Stress Constraints in Structural Synthesis

In the context of transmission tower optimization, the energy method and the force method are combined in order to form a holistic design and optimization approach, eliminating the need for time-intensive matrix inversion. A migration genetic algorithm is employed in the optimization process. Although this algorithm is suitable for towers with a limited number of elements, it is inefficient in the case of many towers encountered in practice. The addition of a neural network as an analysis tool reduces the overall computational load. Four examples are presented to demonstrate the important role of neural networks in reducing the computational overhead.

Optimal Design of Transmission Towers Using Genetic Algorithm and Neural Networks

Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.

An approximation method for configuration optimization of trusses

Approximation method for configuration optimization of trusses

Most research and applications in structural optimization has dealt with member sizing, where the cross-sectional area or member thickness is the design variable. Shape optimization, due to its inherent non-linearities, has lagged behind in its development. The state of the art in shape optimization at the end of the 1970’s is reviewed in reference 1. Reference 2 provides a good overview of this field by the mid-1980’s and demonstrates a dramatic increase in interest and research in this subject.

Scott R. Hansen

Papers

An approximation method for configuration optimization of trusses

Approximation method for configuration optimization of trusses

Recent Developments in Structural Shape Optimization