Shape exploration for structural efficiency

Structurally efficient shapes are explored in this paper by considering two alternative shape descriptions to simultaneously minimize total weight and maximum stress-thus seeking the relevant Pareto front. As a first approach, shapes are parametrized using geometrical landmarks. The design space is then explored using the Monte Carlo search. The algorithm morphs the shape randomly, by changing the coordinates of the landmarks according to their initial position. Principal Coordinate Analysis (PCA) is then used to extract the most significant components explaining the shape morphing. As a second approach, shapes are generated as a composition of several primitive shapes i.e a shape grammar. The efficiacy of various parameterization schemes for design search and optimization are compared