土-结构三维动力分析的线性-非线性混合子结构法
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摘要
为提高土-结构三维非线性动力分析问题的计算效率,根据结构存在局部塑性区域的特点,提出了适合于非线性子结构与多个线性子结构存在边界耦合情况的线性-非线性混合约束模态综合法。该方法将整体体系划分为线性和非线性两类子结构,对线性子结构依照势能判据截断准则进行自由度的缩减,并最终与非线性子结构进行综合,进而获得非线性体系的动态响应。进一步将该方法应用到土-高层建筑相互作用体系的三维动力分析算例中,针对两种不同的土体边界条件分别进行了多组地震动激励作用下的动力时程分析,验证了该方法的精确性与有效性。最后,针对非线性土体区域范围的多种不同取值进行了多组数值试验,结果表明:对于该文算例,当非线性土体区域的范围取为上部结构水平尺寸的3倍时即可获得满意的计算结果,进一步说明了该方法的有效性。
To improve the computational efficiency of a 3D nonlinear dynamic problem of a soil-structure interactive system,based on the characteristic that structures have local plastic regions,the mixed linear-nonlinear constrained mode synthesis method,suitable for nonlinear substructure coupled with several linear substructures at the interface boundaries,is presented.This method divides the system into linear and nonlinear substructures.The dynamic response of the whole nonlinear system can be obtained by reducing the degree of freedom of linear substructures using mode cut-off criterion based on potential energy criterion and synthesizing with the nonlinear substructure.Furthermore,the proposed method is used to solve the 3D soil and multi-story buildings interaction system dynamic problem and several dynamic analyses has been carried out according to two kinds of soil boundary conditions by different seismic excitations.The analysis results indicate that the proposed method is accurate and effective.Finally,the nonlinear soil region scale is studied by several groups of numerical experiments,the comparison results show that the satisfactory result can be obtained when the range of nonlinear substructure gets 3 times of superstructure's,the effectiveness of the proposed method has been further verified.
To improve the computational efficiency of a 3D nonlinear dynamic problem of a soil-structure interactive system,based on the characteristic that structures have local plastic regions,the mixed linear-nonlinear constrained mode synthesis method,suitable for nonlinear substructure coupled with several linear substructures at the interface boundaries,is presented.This method divides the system into linear and nonlinear substructures.The dynamic response of the whole nonlinear system can be obtained by reducing the degree of freedom of linear substructures using mode cut-off criterion based on potential energy criterion and synthesizing with the nonlinear substructure.Furthermore,the proposed method is used to solve the 3D soil and multi-story buildings interaction system dynamic problem and several dynamic analyses has been carried out according to two kinds of soil boundary conditions by different seismic excitations.The analysis results indicate that the proposed method is accurate and effective.Finally,the nonlinear soil region scale is studied by several groups of numerical experiments,the comparison results show that the satisfactory result can be obtained when the range of nonlinear substructure gets 3 times of superstructure's,the effectiveness of the proposed method has been further verified.
引文
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[11]陈国兴,庄海洋,程绍革,等.土-地铁隧道动力相互作用的大型振动台试验:试验方案设计[J].地震工程与工程振动,2006,26(6):178―183.Chen Guoxing,Zhuang Haiyang,Cheng Shaoge,et al.Alarge-scale shaking table test for dynamic soil-metrotunnel interaction:test scheme[J].EarthquakeEngineering and Engineering Vibration,2006,26(6):178―183.(in Chinese)
[2]Craig R R,Chang C J.A review of substructure couplingmethods for dynamic analysis[J].Advances inEngineering Science,1976,2:393―408.
[3]宫晓春,曹登庆.含参数多自由度非线性系统的降维方法研究[J].动力学与控制学报,2009,7(2):129―135.Gong Xiaochun,Cao Dengqing.Dimension reduction ofnonlinear multi-degree-of-freedom system with multipleparameters[J].Journal of Dynamic and Control,2009,7(2):129―135.(in Chinese)
[4]尉飞,郑钢铁.利用POD方法的固定界面模态综合技术[J].振动工程学报,2008,21(4):365―370.Wei Fei,Zheng Gangtie.Fixed-interface componentmode synthesis using proper orthogonal decomposition[J].Journal of Vibration Engineering,2008,21(4):365―370.(in Chinese)
[5]Wamsler M.On the selection of the mode cut-off numberin component mode reduction[J].Engineering withComputers,2009,25:139―146.
[6]Craig R R.Substructure method in vibration[J].TransASME,1995,117:207―213.
[7]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.Fundamentals of applied mathematics[M].Tianjin:Tianjin University Press,2004.(in Chinese)
[8]路观平,王晓泉,王雨苗.模态综合的交叉子结构方法[J].振动工程学报,2002,15(3):300―304.Lu Guanping,Wang Xiaoquan,Wang Yumiao.Crosssubstrucural method for modal synthesis[J].Journal ofVibration Engineering,2002,15(3):300―304.(inChinese)
[9]Craig R R,Chang C J.A review of substructure couplingmethods for dynamic analysis[J].Advances inEngineering Science,1976,2:393―408.
[10]Pan L J,Zhang B M.A new method for the determinationof damping in cocured composite laminates withembedded viscoelastic layer[J].Journal of Sound andVibration,2009,319:822―831.
[11]陈国兴,庄海洋,程绍革,等.土-地铁隧道动力相互作用的大型振动台试验:试验方案设计[J].地震工程与工程振动,2006,26(6):178―183.Chen Guoxing,Zhuang Haiyang,Cheng Shaoge,et al.Alarge-scale shaking table test for dynamic soil-metrotunnel interaction:test scheme[J].EarthquakeEngineering and Engineering Vibration,2006,26(6):178―183.(in Chinese)
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