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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。
Based on the gradient optimization method, the variable stiffness laminate design of composite laminates was optimized. In the process of optimization, the density and angle of each unit in the ply should be determined. In order to make the optimization result manufacturable, the optimization results must meet the manufacturing process constraints and the ply angle should be selected from a predetermined angle. In order to avoid introducing too many constraints and reduce the number of design variables in the optimization problem, density distribution curve method (DDCM) is proposed to parameterize the density of each unit in the laminate. The variables are designed according to the density and angle of each cell and the elasticity matrix of each cell is determined based on the interpolation formula in the Bi-value Coding Parameterization (BCP) method. In the optimization process, the structural compliance is taken as the optimization goal and the structure volume is used as the constraint. The optimization algorithm uses convex programming duality algorithm. The numerical results of carbon fiber composites show that using DDCM can achieve better optimization results and faster convergence rate.