A First Step Towards the Use of Proper General Decomposition Method for Structural Optimization

Abstract

In structural optimization, the implicit nature of the cost function with respect to the optimization parameters, i.e. through the solution of the structural problem calculated with fixed values of these parameters, leads to prohibitive computations whatever the adopted formulation.

Consequently, it yields limitations in both the number of parameters and the size of the structural problem. Moreover, some know-how is required to define a relevant structural problem and a well-behaved cost function.

Here, we profit from the ability of the Proper Generalized Decomposition (PGD) method to handle large-dimensionality problems to transform the optimization parameters into variables of an augmented-structural problem which is solved prior to optimization. As a consequence, the cost function becomes explicit with respect to the parameters.

As the augmented-structural problem is solved a priori, it becomes independent from the a posteriori optimization. Obviously, such approach promises numerous advantages, e.g. the solution of the structural problem can be easily analyzed to provide a guide to define the cost function and advanced optimization schemes become numerically tractable because of the easy evaluation of the cost function and its gradients.