Victorio Úbeda Sosa: On the use of artificial neural networks in multiresolution topology optimization

Abstract.

Topology optimization is a computational methodology that seeks to determine the optimal material distribution within a predefined design domain to achieve desired performance objectives while satisfying constraints. Topology optimization is a very computationally expensive process, where the computational cost is usually dominated by the repeated assembly of stiffness matrices related to several finite element analyses that are part of an iterative optimization loop. Since the material properties depend on the design variables –which are updated each iteration of the optimization loop– a new global stiffness ma- trix needs to be assembled, and a new system needs to be solved at each optimization step. For this reason, large research efforts in topology optimization are directed towards reducing the computational cost by finding more efficient methods for the assembly and solution of the finite element analysis.

In this work, we implement a multi-scale finite element procedure similar to the extended multi-scale finite element method (EMsFEM). We construct an approximate direct mapping from the local element densities to the coarse-resolution element stiffness matrix using machine learning. The aim is to avoid the need to compute one condensation operator for each coarse-resolution element and optimization step; hence significantly reducing the computational cost of the assembly. Finally, the performance of our method is evaluated and compared to exact condensation.