基于分层设计变量的复合材料层合板优化设计及灵敏度分析

在复合材料层合板的结构优化设计中,提出分层设计变量的优化方法以满足实际工程需要。在结构位移、自振频率和屈曲临界荷载灵敏度分析中,给出了刚度矩阵对分层厚度和分层角度设计变量的灵敏度计算公式,考虑了分层厚度变化引起层合板对称中心的改变,保证了计算准确性。数值算例验证了灵敏度算法的精度,应用实例显示了分层设计变量方法的实用性。

DESIGN OPTIMIZATION AND SENSITIVITY ANALYSIS OF LAMINATED COMPOSITE PLATES WITH SUB-LAYER VARIABLES

In this paper, a sub-layer design variable method is proposed for optimization design of laminated composite plate structures. With this method, the laminated plate is divided into several sub-layers and each sub-layer is composed of some plies, which have the same thickness and orientation angles. The direct design variables of optimization are the thickness and angle of the sub-layers. This sub-layer variable method meets the requirement of practical design. The objectives and/or constraints include structural weight, displacements, free-vibration frequencies, and critical load of buckling. The accurate sensitivity analysis is performed in detail, and the optimization of asymmetric laminate plate is also available. It should be noticed that the centerline of the laminated plate changes with the variation of the thickness of sub-layers. This aspect has been considered to maintain the accuracy of sensitivity analysis and process the optimization design of asymmetric laminated plates. The Sequential Linear Programming (SLP) or the Sequential Quadratic Programming (SQP) algorithms are employed in the optimization solution. The methods proposed in this paper have been implemented in the software JIFEX of the finite element analysis and optimization design of general purposed structures and applied to the problems of static, buckling, and vibration optimization of laminated composite structures. Numerical examples are given to demonstrate the validation of the algorithms and program.