线性-非线性混合的约束模态综合法及实践
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摘要
为提高大型复杂结构体系非线性动力问题的计算效率,根据结构存在局部塑性区域的特点,提出了线性-非线性混合的约束模态综合法.对于荷载作用下整体体系中不易进入非线性阶段的部件,将其划分为线性子结构,而将进入塑性变形阶段的局部部件独立划分为非线性子结构,通过坐标变换来缩减线性子结构的自由度,并最终与非线性子结构进行综合求解.使得在降低计算成本的同时,又能够合理地对结构的材料非线性特征加以考虑,是求解大型复杂结构非线性动力问题的有效方法.同时,针对约束模态综合法还提出了基于势能判据的截断准则,利用势能判据的收敛性得出了子结构主模态最佳截断阶数.最后,将该方法及势能判据截断准则应用到高层建筑-地基土非线性地震响应分析问题中,与有限元直接法的对比结果表明,所提出的方法具有更高的计算效率和求解精度,而基于势能判据的截断准则对于混合的约束模态综合法也十分有效.
In order to improve the computational efficiency of nonlinear dynamics of large complicated structures,synthesis method of linear-nonlinear mixed constrained mode has been presented based on the existence of local plastic regions in the structure.Components in the system that could not get into nonlinear stage easily under loading were defined as linear substructures while the local components that were in the plastic deformation stage were defined as nonlinear substructures.Degree of freedom of linear substructures was reduced through coordinate transformation and linear substructures were finally synthesized with nonlinear substructures,so that the computational cost was lowered and the nonliear characteristics of the structures were taken into consideration reasonably,which is an effective solution to the nonliear dynamic problem of large and complicated structures.In addition,the mode cut-off criterion for constrained mode synthesis method has been presented on the basis of potential energy criterion,in which the optimum mode cut-off number of the substructure is drawn from the convergence of potential energy criterion.The linearnonlinear mixed constrained mode synthesis method proposed and the mode cut-off criterion have been applied to nonlinear seismic response analysis of soil and multi-story building interactions.In comparison with the direct-finite-element-method,the proposed method performs better in computational efficiency and precision and the mode cut-off criterion on the basis of potential energy criterion is effective for the mixed constrained mode synthesis method.
In order to improve the computational efficiency of nonlinear dynamics of large complicated structures,synthesis method of linear-nonlinear mixed constrained mode has been presented based on the existence of local plastic regions in the structure.Components in the system that could not get into nonlinear stage easily under loading were defined as linear substructures while the local components that were in the plastic deformation stage were defined as nonlinear substructures.Degree of freedom of linear substructures was reduced through coordinate transformation and linear substructures were finally synthesized with nonlinear substructures,so that the computational cost was lowered and the nonliear characteristics of the structures were taken into consideration reasonably,which is an effective solution to the nonliear dynamic problem of large and complicated structures.In addition,the mode cut-off criterion for constrained mode synthesis method has been presented on the basis of potential energy criterion,in which the optimum mode cut-off number of the substructure is drawn from the convergence of potential energy criterion.The linearnonlinear mixed constrained mode synthesis method proposed and the mode cut-off criterion have been applied to nonlinear seismic response analysis of soil and multi-story building interactions.In comparison with the direct-finite-element-method,the proposed method performs better in computational efficiency and precision and the mode cut-off criterion on the basis of potential energy criterion is effective for the mixed constrained mode synthesis method.
引文
[1]楼梦麟.结构动力分析的子结构方法[M].上海:同济大学出版社,1997.Lou Menglin.Substructure Methods of Structural Dy-namic Analysis[M].Shanghai:Tongji University Press,1997(in Chinese).
[2]Tran D M.Dynamic analysis of structural systems using component mode[J].Computers and Structures,2001,79:209-222.
[3]Craig R R J.A review of time-domain and frequency-domain component mode synthesis method[J]..Int J Analytical Exp Modal Analysis,1987,2(2):59-72.
[4]Bucher C U A.A modal synthesis method employing physical coordinates,free component modes and resid-ual flexibilities[J].Computers and Structures,1986,22(4):559-564.
[5]白建方.复杂场地土层地震反应分析的并行有限元方法[D].上海:同济大学土木工程学院,2007.Bai Jianfang.Parallel Finite Element Method for Seismic Response Analysis of Irregular Site[D].Shanghai:College of Civil Engineering,Tongji University,2007(in Chinese).
[6]Craig R R Jr,Chang C J.A review of substructure cou-pling methods for dynamic analysis[J].Advances in En-gineering Science,1976,2(2):393-408.
[7]Wamsler M.On the selection of the mode cut-off number in component mode reduction[J].Engineering with Computers,2009,25:139-146.
[8]Craig R R Jr.Substructure method in vibration[J].Jour-nal of Mechanical Design,1995,117(B):207-213.
[9]熊洪允,曾绍标,毛云英.应用数学基础[M].天津:天津大学出版社,2004.Xiong Hongyun,Zeng Shaobiao,Mao Yunying.Ap-plied Mathematics[M].Tianjin:Tianjin University Press,2004(in Chinese).
[10]白建方,楼梦麟.基于动力子结构方法的场地地震反应分析方法[J].震灾防御技术,2008,3(2):145-154.Bai Jianfang,Lou Menglin.The dynamic substructure method for seismic response of irregular topography[J].Technology for Earthquake Disaster Prevention,2008,3(2):145-154(in Chinese).
[2]Tran D M.Dynamic analysis of structural systems using component mode[J].Computers and Structures,2001,79:209-222.
[3]Craig R R J.A review of time-domain and frequency-domain component mode synthesis method[J]..Int J Analytical Exp Modal Analysis,1987,2(2):59-72.
[4]Bucher C U A.A modal synthesis method employing physical coordinates,free component modes and resid-ual flexibilities[J].Computers and Structures,1986,22(4):559-564.
[5]白建方.复杂场地土层地震反应分析的并行有限元方法[D].上海:同济大学土木工程学院,2007.Bai Jianfang.Parallel Finite Element Method for Seismic Response Analysis of Irregular Site[D].Shanghai:College of Civil Engineering,Tongji University,2007(in Chinese).
[6]Craig R R Jr,Chang C J.A review of substructure cou-pling methods for dynamic analysis[J].Advances in En-gineering Science,1976,2(2):393-408.
[7]Wamsler M.On the selection of the mode cut-off number in component mode reduction[J].Engineering with Computers,2009,25:139-146.
[8]Craig R R Jr.Substructure method in vibration[J].Jour-nal of Mechanical Design,1995,117(B):207-213.
[9]熊洪允,曾绍标,毛云英.应用数学基础[M].天津:天津大学出版社,2004.Xiong Hongyun,Zeng Shaobiao,Mao Yunying.Ap-plied Mathematics[M].Tianjin:Tianjin University Press,2004(in Chinese).
[10]白建方,楼梦麟.基于动力子结构方法的场地地震反应分析方法[J].震灾防御技术,2008,3(2):145-154.Bai Jianfang,Lou Menglin.The dynamic substructure method for seismic response of irregular topography[J].Technology for Earthquake Disaster Prevention,2008,3(2):145-154(in Chinese).
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