基于响应面的结构非概率可靠性优化设计
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摘要
将结构系统中的不确定参数描述为区间变量,在基于区间模型的可靠性分析基础上,考虑到复杂结构的极限状态函数表达式往往很难直接求出,提出了基于响应面模型的非概率可靠性结构优化方法。该方法用二次多项式拟合结构的极限状态函数,通过区间模型计算出结构的非概率可靠度,并将其作为约束条件来对结构进行优化设计,应用嵌套优化模型解决此类优化问题。最后用该方法对25杆桁架结构进行了优化,结果表明提出的方法是正确可行的。
A structural optimization method based on response surface model(RSM)and non-probabilistic reliability analysis is presented in this paper. By virtue of quadratic polynomial expansion the response surface model is constructed to replace approximately the limitation state function for complex structure and thus avoid the difficult for obtaining the explicit mathematical expression of this function. In structural system the uncertain parameters are described as interval variables which are used to evaluate the non-probabilistic reliability and then establish constraint conditions in structural optimization problem. This problem can be solved by using double nested optimal strategy. As a numerical example,a twenty-five-bar truss structure is optimized for its minimum volume. The results show that the method presented here is correct and feasible.
A structural optimization method based on response surface model(RSM)and non-probabilistic reliability analysis is presented in this paper. By virtue of quadratic polynomial expansion the response surface model is constructed to replace approximately the limitation state function for complex structure and thus avoid the difficult for obtaining the explicit mathematical expression of this function. In structural system the uncertain parameters are described as interval variables which are used to evaluate the non-probabilistic reliability and then establish constraint conditions in structural optimization problem. This problem can be solved by using double nested optimal strategy. As a numerical example,a twenty-five-bar truss structure is optimized for its minimum volume. The results show that the method presented here is correct and feasible.
引文
[1]祁武超,邱志平.基于区间分析的结构非概率可靠性优化设计[J].中国科学,2013,43(1):85-93.(Qi Wu-chao,Qiu Zhi-ping.Non-probabilistic reliability-based structural design optimization based on the interval analysis method[J].Science China,2013,43(1):85-93.)
[2]Doltsinis I,Kang Zhan.Robust design of structures using optimization methods[J].Computer Methods in Applied Mechanics Engineering,2004(193):2221-2237.
[3]Elishakoff I.Essay on uncertainties in elastic and viscoelastic structures:from A.M Freudenthal’s criticisms to modern convex modeling[J].Computers&Structures,1995,56(6):875-895.
[4]Ben-Haim Y.A non-probabilistic concept of reliability[J].Structural Safety,1994,14(4):227-245.
[5]Elishakoff I.Discussion on a non-probabilistic concept of reliability[J].Structures Safety,1995,17(3):195-199.
[6]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56-60.(Guo Shu-xiang,Lv Zhen-zhou,Feng Yuan-sheng.A non-probabilistic model of structural reliability based on interval analysis[J].Chinese Journal of Computer Mechanics,2001,18(1):56-60.)
[7]郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法[J].计算力学学报,2005,22(2):227-231.(Guo Shu-xiang,Zhang Ling,Li Ying.Procedures for computing the nonprobabilistic reliability index of uncertain structures[J].Chinese Journal of Computer Mechanics,2005,22(2):227-231.)
[8]Bai Y C,Han X,Jiang C.A response surface-based structural reliability analysis method by using non-probability convex model[J].Applied Mathematical Modeling,2014(38):3834-3874.
[9]郭书祥,吕震宙.结构的非概率可靠性方法和概率可靠性方法的比较[J].应用力学学报,2003,20(3):107-110.(Guo Shu-xiang,Lv Zhen-zhou.Comparison between the non-probabilistic and probabilistic reliability methods for uncertain structure design[J].Chinese Journal of Applied Mechanics,2003,20(3):107-110)
[10]亢战,罗阳军.基于凸模型的结构非概率可靠性优化[J].力学学报,2006,38(6):807-815.(Kang Zhan,Luo Yang-jun.On structural optimization for non-probabilistic reliability based on convex models[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(6):807-815.)
[11]隋允康,宇慧萍.响应面方法的改进及其对工程优化的应用[M].北京:科学出版社,2010.(Sui Yun-kang,Yu Hui-ping.The Improvement and Applications for Engineering Optimization of the Respond Surface Method[M].Beijing:Science Press,2010.)
[12]Jiang C,Bi R G,Lu G Y.Structural reliability analysis using non-probabilistic convex model[J].Computer Methods in Applied Mechanics Engineering,2013(254):83-98.
[2]Doltsinis I,Kang Zhan.Robust design of structures using optimization methods[J].Computer Methods in Applied Mechanics Engineering,2004(193):2221-2237.
[3]Elishakoff I.Essay on uncertainties in elastic and viscoelastic structures:from A.M Freudenthal’s criticisms to modern convex modeling[J].Computers&Structures,1995,56(6):875-895.
[4]Ben-Haim Y.A non-probabilistic concept of reliability[J].Structural Safety,1994,14(4):227-245.
[5]Elishakoff I.Discussion on a non-probabilistic concept of reliability[J].Structures Safety,1995,17(3):195-199.
[6]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56-60.(Guo Shu-xiang,Lv Zhen-zhou,Feng Yuan-sheng.A non-probabilistic model of structural reliability based on interval analysis[J].Chinese Journal of Computer Mechanics,2001,18(1):56-60.)
[7]郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法[J].计算力学学报,2005,22(2):227-231.(Guo Shu-xiang,Zhang Ling,Li Ying.Procedures for computing the nonprobabilistic reliability index of uncertain structures[J].Chinese Journal of Computer Mechanics,2005,22(2):227-231.)
[8]Bai Y C,Han X,Jiang C.A response surface-based structural reliability analysis method by using non-probability convex model[J].Applied Mathematical Modeling,2014(38):3834-3874.
[9]郭书祥,吕震宙.结构的非概率可靠性方法和概率可靠性方法的比较[J].应用力学学报,2003,20(3):107-110.(Guo Shu-xiang,Lv Zhen-zhou.Comparison between the non-probabilistic and probabilistic reliability methods for uncertain structure design[J].Chinese Journal of Applied Mechanics,2003,20(3):107-110)
[10]亢战,罗阳军.基于凸模型的结构非概率可靠性优化[J].力学学报,2006,38(6):807-815.(Kang Zhan,Luo Yang-jun.On structural optimization for non-probabilistic reliability based on convex models[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(6):807-815.)
[11]隋允康,宇慧萍.响应面方法的改进及其对工程优化的应用[M].北京:科学出版社,2010.(Sui Yun-kang,Yu Hui-ping.The Improvement and Applications for Engineering Optimization of the Respond Surface Method[M].Beijing:Science Press,2010.)
[12]Jiang C,Bi R G,Lu G Y.Structural reliability analysis using non-probabilistic convex model[J].Computer Methods in Applied Mechanics Engineering,2013(254):83-98.