دانلود رایگان مقاله بهینه سازی توپولوژی برای ریزساختار مواد کامپوزیت ویسکوالاستیک

Abstract

The viscoelastic response of materials is often utilized for wide applications such as vibration reduction devices. This paper extends the bi-directional evolutionary structural optimization (BESO) method to the design of composite microstructure with optimal viscoelastic characteristics. Both storage and loss moduli of composite materials are calculated through the homogenization theory using complex variables. Then, the BESO method is established based on the sensitivity analysis. Through iteratively redistributing the base material phases within the unit cell, optimized microstructures of composites with the desirable viscoelastic properties will be achieved. Numerical examples demonstrate the effectiveness of the proposed optimization method for the design of viscoelastic composite materials. Various microstructures of optimized composites are presented and discussed. Meanwhile, the storage and loss moduli of the optimized viscoelastic composites are compared with available theoretical bounds.

5. Conclusions

In this paper, viscoelastic composites are supposed to be composed of a stiff and elastic material phase and a soft and viscoelastic material. The BESO method is extended to designing microstructures of composites with desirable viscoelastic properties. The given examples demonstrate the effectiveness of the proposed optimization algorithm to obtain the clear microstructures of composites with maximum damping and/or stiffness. The numerical results indicate that the damping property of composites can be greatly enhanced by properly mixing a small amount of a viscoelastic material with an elastic material, but stiffness of composites has no significant improvement. When the optimization objective changes to maximize the stiffness of composites, the damping property of viscoelastic material phase cannot be fully utilized. Comparison with theoretical bounds reveal that maximizing damping results in designs at the upper bound of loss modulus and the lower bound of storage modulus, but maximizing stiffness results in designs at the lower bound of loss modulus and the upper bound of storage modulus. Therefore, the design of viscoelastic composites is inherently a multi-objective optimization problem which is solved by maximizing damping subject to a stiffness constraint in this paper. A set of Pareto optimal solutions is obtained in the presence of trade-offs between conflicting damping and stiffness objectives for the design of viscoelastic composites.