An integration of a low cost adaptive remeshing strategy in the solution of structural shape optimization problems using evolutionary methods

On the need for the use of error‐controlled finite element analyses in structural shape optimization processes

“…In the cases where evolutionary algorithms are used, and in order to reduce the computational cost associated with the creation of an adapted mesh for each of the individuals to be analyzed, we propose the use of the technique described by Bugeda et al 1 that will be summarized below. The origin of this technique, and its application to deterministic optimization algorithms, can be seen in References 2, 3.…”

“…The magnitudes to be projected are the nodal coordinates ( x and y ), the error estimator in energy norm (η) and the energy norm (∥ u ∥). The following expressions are used in these projections: where sub‐indexes r and p are, respectively, related to the reference individual and the individual to which the information is projected, and v i are the design variables used to define the geometry, see 1.This projection provides, without any additional computation, an approximation to the values that would be obtained for each specific individual if it would have been computed with the same FE mesh used for the reference individual; thus, providing the necessary information to perform an adaptive remeshing over the next design, even before any new computation is performed. Generation of the h‐adapted mesh .…”

“…One hundred and fifty generations with 30 individuals per generation were considered. The results showed that in the 97% of the 4500 individuals analyzed, the use of the proposed technique 1 directly provided the appropriate mesh for the FE analysis. This implies a considerable reduction of the computational cost associated with the h ‐adaptive analyses.…”

“…The second numerical example is the optimization of the shape of a hook in order to minimize its weight. Note that this example is a modification of that presented in 1, using a different load and a different prescribed error level. Therefore, the results here obtained cannot be directly compared with those in 1.…”

“…The computational cost related to the use of these traditional adaptive analysis techniques can be critical when evolutionary algorithms are used. To solve this problem, in this paper we propose the use of the h ‐adaptive analysis technique for generations of individuals described in 1. The procedure consists of using the sensitivity analysis of the discretization error in energy norm with respect to the design variables 2–4 to project the error obtained from a representative individual of the generation into the different geometrical configurations to be analyzed.…”