框剪结构基于能量概念的抗侧刚度优化研究
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摘要
基于势能驻值原理推导框剪结构的层刚度矩阵,用有限单元法的思想,形成总体刚度矩阵,用于结构的振型分解和周期计算。选取结构滞回耗能需求值与滞回耗能能力值之比与结构所受水平地震作用的乘积作为目标函数,应用振型分解法求解多自由度体系的滞回耗能需求值和能力值,建立框剪结构基于能量概念的抗侧刚度优化数学模型。采用罚函数法的思想,将非线性约束优化问题转化为非线性无约束优化问题,采用MATLAB编制优化程序。最后给出算例,算例表明本文方法和程序是正确可行的。
In this paper,based on the principle of resident potential energy,inter-story stiffness matrix for frame-shear wall structure was deduced. The thought of finite element method was used to form the global stiffness matrix,which is helpful to conduct the modal decomposition and calculation of structural natural period of vibration. It is the product of horizontal seismic action,the ration of hysteretic energy demand and hysteretic energy capacity that was selected as the target function. Modal decomposition method was used to calculate the hysteretic energy demand and hysteretic energy capacity of multi-degree freedom system. A mathematical model with respect to lateral stiffness optimization of frame-shear wall structure was founded. In this paper,the nonlinear constrained optimization problem was transformed into nonlinear unconstrained one by adopting the idea of penalty function method. A frame-shear wall structure optimum MATLAB software was developed. Subsequently,combined with a numerical example,the results demonstrate that the method proposed in the paper is accurate and feasible.
In this paper,based on the principle of resident potential energy,inter-story stiffness matrix for frame-shear wall structure was deduced. The thought of finite element method was used to form the global stiffness matrix,which is helpful to conduct the modal decomposition and calculation of structural natural period of vibration. It is the product of horizontal seismic action,the ration of hysteretic energy demand and hysteretic energy capacity that was selected as the target function. Modal decomposition method was used to calculate the hysteretic energy demand and hysteretic energy capacity of multi-degree freedom system. A mathematical model with respect to lateral stiffness optimization of frame-shear wall structure was founded. In this paper,the nonlinear constrained optimization problem was transformed into nonlinear unconstrained one by adopting the idea of penalty function method. A frame-shear wall structure optimum MATLAB software was developed. Subsequently,combined with a numerical example,the results demonstrate that the method proposed in the paper is accurate and feasible.
引文
[1]秦力,贾小刚,杨延波.剪力墙平面布置对异形柱框剪结构地震响应的影响分析[J].建筑结构学报,2010,40(1):54-56.QIN Li,JIA Xiaogang,YANG Yanbo.Study on the influence of different layouts of shear-walls on seismic responses of a RC frame-shear wall structure with specially shaped columns[J].Journal of Building Structures,2010,40(1):54-56.
[2]李伟松.钢筋混凝土异形柱框架-剪力墙结构基础隔震性能研究[D].西安:西安建筑科技大学,2012.LI Weisong.The base isolation research of reinforced concrete frame-shear wall structure with specially-shaped columns[D].Xi’an:Xi’an University of Technology,2012.
[3]刘敏.中高层异形柱框剪结构抗侧刚度优化[D].武汉:武汉理工大学,2006.LIU Ming.Optimal analysis for lateral stiffness in midhigh rise RC frame shear wall structure with specialshaped columns[D].Wuhan:Wuhan University of Technology,2006.
[4]冯宏团.框—剪结构的剪力墙优化研究[D].西安:西安理工大学,2005.FENG Hongtuan.Study on the optimization problem of shear wall in frame-shear structure[D].Xi’an:Xi’an University of Technology,2005.
[5]秦力,宋玉普,张秀文.中高层异形柱框—剪结构的剪力墙抗侧刚度优化[J].哈尔滨工业大学学报,2004,36(8):1103-1110.QIN Li,SONG Yupu,ZHANG Xiuwen.Optimal analysis for lateral stiffness of shear wall in mid-highirise RC frame-shear wall structure with special-shaped columns[J].Journal of Harbin Institute of Technology,2004,36(8):1103-1110.
[6]盛明强.基于滞回耗能的结构抗震性能评价方法研究[D].上海:同济大学,2008.SHENG Mingqiang.The research on hysteretic energybased evaluating method of structures’seismic performance[D].Shanghai:Tongji University,2008.
[7]马千里.钢筋混凝土框架基于能量抗震设计方法研究[D].北京:清华大学,2009.MA Qianli.Study on energy-based seismic design methodology and application for RC frame[D].Beijing:Tsinghua University,2009.
[8]瞿岳前.基于能量分析法的地震损失性能控制设计及其智能优化控制设计[D].西安:西安建筑科技大学,2003.QU Yueqian.Seismic damage performance control design and intelligent optimal design based on energy analysis[D].Xi’an:Xi’an University of Architecture and Technology,2003.
[9]郭继武.建筑抗震设计[M].3版.北京:中国建筑工业出版社,2011.GUO Jiwu.Seismic design of building[M].3rd Edition.Beijing:China Construction Industry Press,2011.
[10]常磊,叶献国.结构能量反应的振型分解法研究[J].合肥工业大学学报(自然科学版),2010,33(7):1035-1052.CHANG Lei,YE Xianguo.Research on modal decomposition method for structure’s energy response equation[J].Journal of Hefei University of Technology(Natural Science Edition),2010,33(7):1035-1052.
[11]常磊,叶献国.结构能量振型分解反应谱法[J].合肥工业大学学报(自然科学版),2010,33(8):1202-1207.CHANG Lei,YE Xianguo.Modal decomposition spectrum method for structure’s energy response[J].Journal of Hefei University of Technology(Natural Science Edition),2010,33(8):1202-1207.
[2]李伟松.钢筋混凝土异形柱框架-剪力墙结构基础隔震性能研究[D].西安:西安建筑科技大学,2012.LI Weisong.The base isolation research of reinforced concrete frame-shear wall structure with specially-shaped columns[D].Xi’an:Xi’an University of Technology,2012.
[3]刘敏.中高层异形柱框剪结构抗侧刚度优化[D].武汉:武汉理工大学,2006.LIU Ming.Optimal analysis for lateral stiffness in midhigh rise RC frame shear wall structure with specialshaped columns[D].Wuhan:Wuhan University of Technology,2006.
[4]冯宏团.框—剪结构的剪力墙优化研究[D].西安:西安理工大学,2005.FENG Hongtuan.Study on the optimization problem of shear wall in frame-shear structure[D].Xi’an:Xi’an University of Technology,2005.
[5]秦力,宋玉普,张秀文.中高层异形柱框—剪结构的剪力墙抗侧刚度优化[J].哈尔滨工业大学学报,2004,36(8):1103-1110.QIN Li,SONG Yupu,ZHANG Xiuwen.Optimal analysis for lateral stiffness of shear wall in mid-highirise RC frame-shear wall structure with special-shaped columns[J].Journal of Harbin Institute of Technology,2004,36(8):1103-1110.
[6]盛明强.基于滞回耗能的结构抗震性能评价方法研究[D].上海:同济大学,2008.SHENG Mingqiang.The research on hysteretic energybased evaluating method of structures’seismic performance[D].Shanghai:Tongji University,2008.
[7]马千里.钢筋混凝土框架基于能量抗震设计方法研究[D].北京:清华大学,2009.MA Qianli.Study on energy-based seismic design methodology and application for RC frame[D].Beijing:Tsinghua University,2009.
[8]瞿岳前.基于能量分析法的地震损失性能控制设计及其智能优化控制设计[D].西安:西安建筑科技大学,2003.QU Yueqian.Seismic damage performance control design and intelligent optimal design based on energy analysis[D].Xi’an:Xi’an University of Architecture and Technology,2003.
[9]郭继武.建筑抗震设计[M].3版.北京:中国建筑工业出版社,2011.GUO Jiwu.Seismic design of building[M].3rd Edition.Beijing:China Construction Industry Press,2011.
[10]常磊,叶献国.结构能量反应的振型分解法研究[J].合肥工业大学学报(自然科学版),2010,33(7):1035-1052.CHANG Lei,YE Xianguo.Research on modal decomposition method for structure’s energy response equation[J].Journal of Hefei University of Technology(Natural Science Edition),2010,33(7):1035-1052.
[11]常磊,叶献国.结构能量振型分解反应谱法[J].合肥工业大学学报(自然科学版),2010,33(8):1202-1207.CHANG Lei,YE Xianguo.Modal decomposition spectrum method for structure’s energy response[J].Journal of Hefei University of Technology(Natural Science Edition),2010,33(8):1202-1207.
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