多工况结构拓扑优化的灰色权重折衷规划模型法

针对多工况结构拓扑优化问题中的载荷病态现象，基于RAMP (Rational Approximation of Material Properties)拓扑优化模型，提出应用灰色理论确定工况权重系数，并将应变能目标函数归一化的折衷规划模型法．通过专家评价方法获得工况权重系数的灰色区间，结合灰色理论计算工况权重系数灰色区间的精确值，并采用导重法推导出多工况结构拓扑优化问题的求解迭代表达式．通过定义载荷比描述载荷病态的程度，对多工况结构拓扑优化典型算例在不同载荷比及不同工况权重系数下进行结构拓扑优化分析．优化结果表明，灰色权重折衷规划模型及求解方法对多工况结构拓扑优化问题具有高效、稳定的特点，能够克服载荷病态问题，并通过大跨度甲板强横梁的结构拓扑优化设计证明本文设计方法的有效性．

Compromise Programming Approach with Grey Weight Factor for Structural Topology Optimization under Multiple Load Conditions

To avoid the phenomenon of load sickness in structural topology optimization under multiple load conditions, based on RAMP (rational approximation of material properties) method, the grey theory is applied to determine the weighting factor of load cases. The problem of load sickness is solved by the compromise programing approach, in which objective function is normalized. The weight factors’ interval in compromise programming approach can be improved through the experts evaluation method, and the exact values of weight factors’ interval are calculated by the grey theory. The Guide-Weight method is introduced to conduct the topology optimization, and the iterative formula of the Guide-Weight method for solving topology optimization is derived. The degree of load sickness is described by defining load case ratio. In this way, classical numerical examples of multiple load cases topology optimization are calculated, which optimal topological structures of numerical examples are analyzed through a serious of load ratios and weight factors. The optimization results demonstrate that combining the Guide-Weight method and compromise programming approach with grey weight factors can be used for structural topology optimization under multi load conditions with significant steady and efficiency, and can be able to overcome the problem of load sickness. Through the structural topology optimization design of large span web frame, the accuracy of the proposed method is validated.