Punlished in Computers and Structures Vol. 86 (13-14), pp. 1563-1578, 2008
doi: 10.1016/j.compstruc.2007.05.010

Abstract

Evolutionary methods are a powerful and robust tool for the solution of structural shape optimization problems. Nevertheless, the use of these methods requires the structural analysis of an important number of different designs, this making the computational cost of the analysis of each design a critical issue. For this reason, each design must be analyzed at a minimum computational cost but ensuring a minimum quality of the results.

It is well known that the cheapest mesh for producing a solution with a fixed quality at minimum cost is an adapted one. Nevertheless, traditional adapted meshes are obtained from adaptive remeshing strategies, where each design has to be analyzed more than once, thereby also causing a high computational cost.

This work presents a new strategy that allows generating an adapted mesh for each design without the necessity of performing a full adaptive remeshing procedure for each of them. It is based on the use of sensitivity analysis of all magnitudes related with adaptive remeshing (location of nodes, error estimation, etc.) with respect to the design variables. This sensitivity analysis is performed only once using a geometry of reference and it is used to project the results of the corresponding analysis to all other designs to be analyzed. The projected information allows generating an appropriate adapted mesh for each new design in one shot, greatly reducing the computational cost compared with standard strategies.

J. Ródenas, G. Bugeda, J. Albelda, E. Oñate. On the need for the use of error-controlled finite element analyses in structural shape optimization processes. Int. J. Numer. Meth. Engng. 87(11) (2011) DOI 10.1002/nme.3155

D. Vučina, Ž. Lozina, I. Pehnec. Ad-hoc cluster and workflow for parallel implementation of initial-stage evolutionary optimum design. Struct Multidisc Optim 45(2) (2011) DOI 10.1007/s00158-011-0687-y

O. Marco, J. Ródenas, J. Albelda, E. Nadal, M. Tur. Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection. Struct Multidisc Optim 58(1) (2017) DOI 10.1007/s00158-017-1875-1

J. Ródenas, G. Bugeda, J. Albelda, E. Oñate, E. Nadal. Sobre la necesidad de controlar el error de discretización de elementos finitos en optimización de forma estructural con algoritmos evolutivos. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 28(1) DOI 10.1016/j.rimni.2011.11.005

G. Bugeda, J. Ródenas, J. Albelda, E. Oñate. Control of the finite element discretization error during the convergence of structural shape optimization algorithms. Int. J. Simul. Multidisci. Des. Optim. 3(3) (2009) DOI 10.1051/ijsmdo/2009012