Topology optimization of the plate using neural networks

At the moment, there are many methods of topological optimization that have become classic, including in the aviation industry. The main ones are the method of solid isotropic material with Penalization (SIMP), methods of unidirectional and bidirectional evolutionary optimization (Evolutionary topology optimization and Bi-directional evolutionary topology optimization – ESO/BESO) and the LevelSet method. The paper presents a mathematical formulation of the topological optimization problem as a statement of the problem at a conditional extremum. The function of the average pliability of the structure was chosen as the target function, the maximum value of the resulting volume was the limitation. The transformation of the problem statement into an unconditional extremum statement was performed, for this the method of quadratic penalties was used. The paper presents an algorithm that allows you to apply modern machine learning methods and neural networks in conjunction with classical methods of topological optimization. The algorithm is based on the reparametrization of virtual densities by neural network parameters, which are optimized. The method of adaptive moment estimation is used as an optimization algorithm directly by the parameter of the neural network. In this paper, two classical problems of topological optimization of plates in a plane-stressed state with different boundary conditions are solved, and the results are compared with the results obtained by other authors on similar problems using classical methods of topological optimization.