ABSTRACT. The present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms (GA), in developing near-optimal topologies ofload bearing truss structures. The problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space. The development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness. The approach is an adaptation of the ground-structure method of topology optimization, and is implemented in a two-level GA based search. In this process, the kinematic stability constraints are imposed at one level, followed by the treatment of response constraints at a second level of optimization. Singular value decomposition is used to assess the kinematic stability constraint at the first level of design, and results in the creation of a finite number of increasing weight, stable topologies. Member sizing is then introduced at a second level of design, where minimal weight and response constraints are simultaneously considered. At this level, the only admissible topologies are those identified during the first stage and any stable combinations thereof. The design variable representation scheme allows for both the removal and addition of structural members during optimization.
The paper describes the use of genetic algorithms in determining the optimal layout and sizing of twodimensional (2D) and three-dimensional (3D) grillage structures for stress, displacement, and element buckling constraints. The design space for this problem is highly nonconvex and not readily amenable to traditional methods of nonlinear programming. The approach develops an optimal topology from a set of predefined structural universe so as to satisfy kinematic stability requirements and other constraints on structural response. A two-level genetic algorithm-based search is used, wherein the kinematic stability constraints are imposed at one level, followed by the treatment of stress and displacement constraints at a second level of optimization. Since genetic algorithms search for an optimal design from a discrete set of alternatives in the design space, their adaptation in the topologic design problem is natural and is governed only by issues related to computational efficiency. Strategies designed to alleviate the computational requirements of a genetic algorithm-based search are discussed in the paper.
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