On An Evolutionary Developmental Methodology For Pin-joint Framework Optimization

Abstract

The formal investigation into optimal structures, called topology optimization, commenced from the 1904 paper of A.G.M. Michell. While impractical for real constructions, the criteria considered therein allow for a determination of the limit of material economy attainable for truss structures, called Michell structures. These analytical solutions are a useful tool for benchmarking, but have been solved only for a small number of simple cases. The usual computational approaches for identifying these optima rely on a presupposed ground structure, which covers the design space with an initial assemblage of members and joints. While denser ground-structures provide for more refined optima, the stipulation of an initial structure (i.e., topology) artificially restricts the allowable optima. In the present work, we are concerned with the development and application of a biologically inspired methodology for the study of layout (size, shape, and topology) optimization in pin-jointed frameworks. The methodology is based on the formalism of map L-systems, whose grammar generates purely topological information. This topology is encoded and optimized using an evolutionary algorithm coupled to a non-linear programming method for sizing and shape optimization. Three benchmark test cases are examined which show the gains attainable when a ground-structure is not presupposed.