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- 2015
基于密度分布曲线法的复合材料变刚度铺层优化
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Abstract:
基于梯度的优化方法对复合材料层合板进行了变刚度铺层优化设计.在优化过程中需确定铺层中各单元的密度以及角度.为了使优化结果具有可制造性, 优化结果需满足制造工艺约束并且铺层角度需从预定角度中选取.为了避免在优化问题中引入过多的约束并减少设计变量的数目, 提出密度分布曲线法(DDCM)对层合板中各单元的密度进行参数化.根据各单元的密度以及角度设计变量并基于Bi-value Coding Parameterization(BCP)方法中的插值公式确定各单元的弹性矩阵.优化过程中以结构柔顺度作为优化目标, 结构体积作为约束, 优化算法采用凸规划对偶算法.对碳纤维复合材料的算例结果表明: 采用DDCM可得到较理想的优化结果, 并且收敛速率较快. A gradient based optimization method for variable stiffness design of laminates was proposed. The optimal element density and orientations were determined in the optimization process. In order to attain industrial relevance, the manufacturing constraint should be satisfied and candidate orientations were limited to a finite set. For the purpose of eliminating the number of constraints and design variables in optimization model, the density distribution curve method (DDCM) was established to parameterize element density. The elastic matrix of element was determined on basis of interpolation scheme in bi-value coding parameterization(BCP) method, according to element density and design variables of orientations. Strucrure compliance and volume were treated as optimization objective and constraint respectively in optimization process. The optimization problem was solved by the convex programming dual algorithm. Numerical examples for the carbon fiber composite demonstrate that reasonable results can be got by DDCM with relatively high convergence rate.
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