Abstract
This paper proposes a new multiscale topology optimization method for the design of porous composites composed of the multi-domain material microstructures considering three design elements: the topology of the macrostructure, the topologies of multiple material microstructures and their overall distribution in the macrostructure. The multiscale design involves two optimization stages: the free material distribution optimization and the concurrent topology optimization. Firstly, the variable thickness sheet (VTS) method with the regularization mechanism is used to generate multiple element density distributions in the macro design domain. Hence, different groups of elements with the identical densities can be uniformly arranged in their corresponding domains, and each domain in the space will be periodically configured by a unique representative microstructure. Secondly, with the discrete material distributions achieved in the macro domain, the topology of the macrostructure and topologies of multiple representative microstructures are concurrently optimized by a parametric level set method combined with the numerical homogenization method. Finally. Several 2D and 3D numerical examples are provided to demonstrate the effectiveness of the proposed multiscale topology optimization method.
Highlights
Porous composites, comprising solids and voids, are artificially engineered to have the superior structural performances but lightweight, such as the higher specific stiffness and strength, better fatigue strength and improved corrosion-resistance [1,2]
A wide range of methods have been developed in recent years, such as the homogenization method [7], the solid isotropic material with penalization (SIMP) [8,9], the evolutionary structural optimization (ESO) [10] and the level set method (LSM) [11,12,13], as well as the point wise-density interpolation (PDI) method [14,15]
The main motivation of this paper is to develop a new multiscale topology optimization method for the design of porous composites considering three design pillars, in order to meet both ends for the structural performance and computational efficiency
Summary
Porous composites, comprising solids and voids, are artificially engineered to have the superior structural performances but lightweight, such as the higher specific stiffness and strength, better fatigue strength and improved corrosion-resistance [1,2]. The macrostructure was topologically optimized, aligning with the optimization of the representative microstructure [37,38] This kind of multiscale designs for porous composites can save computational time, and no connectivity issue raised because all the material microstructures are identical in size, shape and topology. This assumption limits the design freedom for the further improvement of the performance. The main motivation of this paper is to develop a new multiscale topology optimization method for the design of porous composites considering three design pillars, in order to meet both ends for the structural performance and computational efficiency. Several numerical examples are presented to show its effectiveness of the proposed method
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