Concurrent multi-material and multi-scale design optimization of fiber-reinforced composite material and structures for minimum structural compliance

Abstract

With the development of additive manufacturing technology for fiber-reinforced composite materials, topology optimization of fiber-reinforced composite laminates involving multiple materials and variable stiffness is gaining increasing attention. This study proposes an effective methodology for a Multi-scale and Multi-material Composite Anisotropic Penalization (MMCAP) model to investigate multi-scale and multi-material design optimization of a fiber-reinforced variable stiffness (VS) composite structure to minimize structural compliance. In the concurrent MMCAP model, the macroscopic multi-material structural topology and microscopic discrete fiber laying angle selection are introduced as independent design variables and optimized simultaneously. The modified Solid Isotropic Material with Penalization (SIMP) and the Discrete Material Optimization (DMO) approaches are utilized at the macro- and micro-scales, respectively, to realize a clear macroscopic multi-material structural topology and microscopic specific discrete fiber laying angle selection. Multi-material fiber-reinforced plastic (FRP) materials, such as carbon fiber–reinforced plastic (CFRP) and glass fiber–reinforced plastic (GFRP), are considered two types of solid materials in terms of structural volume cost. Sensitivity analysis of the structural compliance concerning the variables of the two geometrical scales is performed using the analytical sensitivity analysis method. The DMO approach is utilized to couple two geometrical scales: macroscopic topology and microscopic material selection. The capabilities of the proposed MMCAP are demonstrated by concurrent multi-material and multi-scale design optimization of composite panels. The influence of the number of discrete fiber laying angles on the structural compliance and optimized topology configuration is also been discussed. Numerical studies showed that the proposed MMCAP scheme can effectively realize multi-material and multi-scale design optimization of fiber-reinforced composite structure with achieving a clear macroscopic multi-material structural topology and microscopic fiber laying angle. The proposed MMCAP scheme provides a new implementation strategy for lightweight, multi-material, and multi-scale design optimization of composite materials, considering the design and manufacturing collaboration through additive manufacturing technology.