Topological design of sandwich structures with graded cellular cores by multiscale optimization

Abstract

Exploring ultralight sandwich structures with superior load-bearing performance is one of the important topics in structural optimization. This paper proposes a novel multiscale topology optimization method to achieve the design of high-performance sandwich structures with graded cellular cores (SSGCCs). In this method, the thicknesses of two solid face-sheets, the graded distribution of cellular sandwich cores at a single layer and their configurations are optimized to well suit for loading conditions, where the single layer is arrayed periodically at its height direction to obtain sandwich layers. Specifically, at macroscale, the variable thickness sheet (VTS) method with the capacity of generating an overall free material distribution pattern, is applied to optimize the thicknesses of two solid face-sheets and achieve the graded distribution of cellular sandwich cores at a single layer. At microscale, a progressive optimization scheme is employed to topologically optimize multiple representative cellular cores (RCCs) at a single layer, so as to achieve their similar topological configurations. With a shape interpolation method, the configurations of graded cellular cores (GCCs) with essential interconnections can be obtained by interpolating the shapes of these RCCs with similar topological features. In order to reduce the computational burden on evaluating effective properties of GCCs by the homogenization method, a Kriging metamodel is constructed based on some key cellular cores as sample points, and adopted to predict the effective properties of all the GCCs. Both 2D and 3D numerical examples are provided to test the validity and advantages of the proposed method for designing SSGCCs.