Shape Optimization of Skeletal Structures: A Review

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Abstract
This paper presents a state of the art review of mathematical programming methods used in the design of skeletal elastic structures in which the possibility of altering the shape, position or layout of the members is considered. Virtually every type of optimization procedure including linear, nonlinear, and dynamic programming has been applied to this design problem. These methods have been implemented using three main approaches. The first, referred to as the ground structure approach, is one in which members are removed from a highly connect structure to derive an optimum subset of bars. In the second approach the co‐ordinates of the joints of the structure are treated as design variables and moved during the optimization procedure to enable an optimum layout to be designed. The third type of method includes those which allow for topological considerations at certain points during the design process and generally keeps the design variables in two separate groups. The paper discusses the way in which each of the mathematical programming methods has been applied to these approaches.