膜结构的多目标形态优化  

Multi-objective optimization of membrane structures

作　　者：伞冰冰[1] 武岳[1] 卫东[2] 沈世钊[1] 

机构地区：[1]哈尔滨工业大学,黑龙江哈尔滨150090 [2]北京市建筑设计研究院,北京100045

出　　处：《土木工程学报》2008年第9期1-7,共7页China Civil Engineering Journal

基　　金：国家自然科学基金(50608022);哈尔滨工业大学优秀青年教师培养计划

摘　　要：根据膜结构的力学特点,建立膜结构的多目标形态优化模型,确定"刚度最大"、"受荷后应力分布最均匀"和"支座反力最小"为优化目标,并明确各目标的数学表达形式;重点比较用于描述刚度的三种表达形式(应变能、最大位移和平均位移)在力学概念及优化结果上的区别;通过加权系数法将多目标优化问题转化为单目标问题,并采用遗传算法进行求解;最后,给出相关算例对上述理论和方法进行验证。研究结果表明:膜结构形态优化模型是有效的、实用的;采用不同的刚度描述指标对优化结果影响很大,其中,应变能最能反映膜结构刚度的本质,优化结果也更为合理;结合加权系数法和遗传算法,可以获得各项力学性能均较为理想的优化结果。A multi-objective optimization model is proposed for membrane structures. Three objectives are established according to the characteristics of membrane structures, including maximum stiffness, most uniform stress and minimum value of reaction. Mathematical formulations are presented for these objectives. Especially, three types of functions for stiffness, respectively based on strain energy, maximum displacement and average displacement, are investigated to show their different aspects in mechanical concepts and optimization solutions. Further more, weighting method is introduced to combine the three objectives into a single objective and a genetic algorithm is applied to solve this optimization problem. Finally, several numerical examples are provided to illustrate the proposed model and method. The study shows that the proposed multi-objective optimization model is feasible and efficient for membrane structures; the differences in stiffness functions result in different optimization solutions, and comparing with the others, the strain energy is more comprehensive and apt to reveal the essence of stiffness, which in turn leads to better results; the desired optimal membrane structures can be obtained by the weighting method and genetic algorithm.

关 键 词：膜结构 多目标形态优化 加权系数法 遗传算法 

分 类 号：TU383[建筑科学—结构工程]