A Taylor Expansion Approach for Computing Structural Performance Variation Over a Shape Population

In this paper, we present a formal and efficient method for computing structural performance variation over its shape population. Each shape in the population is represented as discrete points. These shapes are then aligned together and principal component analysis is conducted to obtain the shape variation, which is represented as a sum of variations in multiple principal modes. Finite element analysis is conducted on the mean shape. For each shape specified by the shape parameters, we then invoke a thin-plate deformation based scheme to automatically deform the mesh nodes. The performance of the shapes is approximated via Taylor series expansion of the FE solution of the mean shape. Numerical study illustrates the accuracy and efficiency of this method.