基于改进离散材料插值格式的复合材料结构优化设计

 针对采用离散材料优化(DMO) 模型优化复合材料纤维分布时角度优化结果收敛率低的问题,将连续化惩罚策略与Heaviside惩罚函数引入传统DMO模型中,提出了一种改进的HPDMO (Heaviside Penalization of Discrete Material Optimization)模型,从而提高结构的收敛率。建立了复合材料单层板基于最小柔顺性设计的优化列式,给出了多种离散材料构成结构的灵敏度信息求解方法。分析比较了DMO模型、连续化惩罚模型和HPDMO模型对最终优化结果收敛率、目标函数、迭代历史的影响。数值算例表明,改进的离散材料惩罚模型不但可以显著地提高优化结果的收敛率,给出清晰的优化构型,而且可以通过较少的优化迭代步数实现这一结果,为纤维增强复合材料的优化设计在工程中的应用提供了新的技术手段。

Design Optimization of Composite Materials Based on Improved Discrete Materials Optimization Model

An improved discrete materials optimization (DMO) model, HPDMO (Heaviside Penalization of Discrete Materials Optimization) model, is established in this paper with continuous penalization and Heaviside penalization to improve the convergence rate of the optimization results of composite materials using traditional DMO. A minimum structural compliance design model is built to optimize the distribution of ply angles of composite materials. A sensitivity analysis is carried out via the direct method based on the HPDMO model. The convergence rate of optimization results, the value of objective function and the iteration history of the traditional DMO, continuous DMO and HPDMO models are compared. Numerical example shows that the HPDMO model can not only improve significantly the convergence rate of optimization of the ply angles of composite materials and provide a clear optimization result, but also do so with a relatively small number of optimization iterations. Thus the paper presents a new approach for the optimization of composite materials in engineering structures.