Evolutive methods are a powerful and robust tool for the resolution of structural shape optimization problems. Nevertheless, the use of these methods requires the analysis of an important number of different designs. The computational cost and the quality of the solutions are very much dependent on the quality of the finite element meshes used for the analysis. One important ingredient of the numerical analysis is the strategy for the generation of a proper mesh for each design. Here we can see two types of strategies: 1. To adapt a single existing mesh to the geometries of all different designs. Some existing strategies allow adapting an existing mesh for very big modifications of the boundary shape preventing the elements from being too much distorted. Nevertheless, despite the fact that this type of strategies provides a valid mesh for each design, there is no control of the discretization error contained in the results of each analysis. 2. To perform a classical adaptive remeshing procedure for the analysis of each different design. Of course, this procedure ensures good quality results in the numerical analysis of each design, but the total computational cost grows significantly because each design is computed more than once. 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. It is based on the use of sensitivity analysis of all magnitudes related with adaptive remeshing (location of nodes, error estimation,...) 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 usually in one shot, greatly reducing the computational cost compared with the described strategy 2. This method was developed and used in the context of the solution of shape optimization problems using deterministic methods.
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- An adaptive mesh generation strategy for the solution of structural shape optimization problems using evolutionary methods
Juan José Ródenas
- Springer Netherlands
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