Shape optimization of structures for multiple loading conditions using a homogenization method

Abstract

A b s t r a c t A formulation for shape optimization of elastic structures subject to multiple load cases is presented. The problem is solved using a homogenization method. When compared to the single load solution strategy, it is shown that the more general formulation can produce more stable designs while it introduces little additional complexity. I n t r o d u c t i o nIn a paper by BendsCe and Kikuchi (1988) and in several papers that followed by the same authors and others (Bendsce 1989; Suzuki and Kikuchi 1991;Dfaz and Belding 1990; O1-hoff et al. 1991), a new approach to shape optimization in structural design, based on a homogenization method, was introduced. The strength of the new approach is based primarily on the versatility with which arbitrary topologies can be represented. In a typical problem the optimum shape is found without the specification of more geometric details than the amount of material used and the location of the supports and points of application of the loads, as illustrated in Fig. 1. The method does not require that the topology (e.g. the connectivity or the number of holes present in the structure) be prescribed a priori, a significant advantage over traditional methods that use parametric boundary representations of the shape.

Explicit solution of an optimal design problem with non-affine displacement boundary conditions

“…In that setting energy minimization is a traditionally accepted mechanism for explaining the shapes of precipitates. We also note that our problem is closely linked with others addressed in the recent literature on optimal design, such as [1], [3], [6], [7], [12], [16], [18], [19], [20]. These articles are concerned with designing "stiff" structures, e.g.…”

Bi-directional evolutionary method for stiffness optimisation

“…In this example, the second factor dominates and the strength of BESO is offset by a large number of iterations. This example has been studied by the homogenisation method (Diaz and Bends0e 1992). Where similar topologies have been obtained.…”

“…The simplest one uses some post-processing techniques to smooth the resulted topology. Also, some techniques are suggested to suppers the appearance of checkerboard right in the solution process, such as the patch and filter techniques introduced to the homogenisation method (Bendsee et al 1993, Diaz andBends0e 1992). In the evolutionary method, it is found that checkerboard pattern is more likely to occur to four-node elements.…”

Minmax topology optimization

“…Díaz and Bendsoe [2] generate robust designs by subjecting structures to multiple load cases. In their formulation they minimize the norm of a set of weighted compliances resulting from the individual load cases.…”