Machine Learning-Enhanced Topology Optimization for Beam-Stiffened Hybrid-Element Structures

Abstract This article develops an explicit topology optimization scheme enhanced by machine learning for beam-stiffened structures. The scheme specifically targets computational issues in solving multipoint constraint equations during optimization iterations. In the scheme, the stiffeners are modeled as moving morphable beams and are discretized independently from the base structure. During the optimization, these beams change their shapes and positions. Therefore, to tie the beams to the base structure, multipoint constraint equations need to be solved for finite element analysis. In the present approach, for the elements of the base structure that are crossed by a portion of a beam element, a deep neural network is employed to predict the coupled stiffness matrices through offline training, significantly reducing computation time. Stiffener overlaps are resolved via the Heaviside projection, while fixed Eulerian meshes prevent mesh distortion. The explicit parametric formulation enables the extraction of direct manufacturable designs. Numerical examples are provided to demonstrate the effectiveness of the present scheme.