基于B样条曲线的自由曲面索支撑空间网格结构多目标形态优化  

Multi-objective shape optimization of free-form cable-braced grid shells with B-spline method

作　　者：冯若强[1] 葛金明 胡理鹏 叶继红[1] 

机构地区：[1]东南大学混凝土与预应力混凝土结构教育部重点实验室,江苏南京210096 [2]江苏筑森建筑设计有限公司,江苏常州213000

出　　处：《土木工程学报》2015年第6期17-24,共8页China Civil Engineering Journal

基　　金：国家自然科学基金(51278117);国家杰出青年基金(51125031);教育部新世纪优秀人才资助计划(NCET-13-0120);江苏省六大人才高峰(2013-JZ-009)

摘　　要：对自由曲面索支撑空间网格结构进行多目标形态优化研究。首先根据索支撑空间网格结构的建模方法,将优化结构整个曲面转化为优化结构的准线和母线。其次为保证优化后的自由曲面光顺,引进B样条曲线建立曲面,并将B样条曲线已知点作为优化变量。出于不同结构设计需要,选用力学指标和几何指标、或力学指标和经济指标、或不同性能力学指标组合作为多优化目标进行结构优化。得到结论如下:首先,采用本优化方法,优化前后曲面形状变化不大,适用于对给定初始曲面结构进行形态优化。其次,以应变能和用钢量为优化目标,属于融合了截面优化和形态优化的多目标优化,其对于索支撑空间网格结构效果较好,具有较高的工程实用价值。最后,以应变能和杆件长度均方差为优化目标,所得优化结果对杆长均方差和应变能加权系数变化不敏感,可满足杆长均匀性和结构力学要求。The study on multi-objective morphology optimization of free-form cable-braced grid shells is carried out.First,by using the shape forming method of grid shells,shape optimization can be realized by adjusting the generatrix and directrix instead of optimizing the whole surface. Second,the multi-objective shape optimization is applied to freeform cable-braced grid shells for smooth free-form surface. To satisfy the requirements of different structural designs,the mechanical and geometric indexes,mechanical and economic indexes,or different combinations of mechanical indexes shall be chosen as multiple optimization objectives for the structural optimization. Consequently,three main conclusions can be drawn. First,with the present shape optimization method,the optimized surface does not change significantly compared to the one without optimization,so that this method is useful in the shape optimization of grid shells with the given initial surfaces. Second,with the consumption of steel tubes and strain energy as the optimization objectives,the multi-objective optimization combines the section optimization with the shape optimization,which shall be favorable to cable-braced grid shells and practical in engineering applications. Third,with the strain energy and mean-square error of tube lengths as the multiple optimization objectives,the optimized results are not sensitive to the weighting factor of strain energy and mean-square error of tube lengths,and the requirements for mechanical behavior and uniformity of tube length can be satisfied.

关 键 词：自由曲面 多目标优化 空间网格结构 形态优化 

分 类 号：TU399[建筑科学—结构工程]