内部荷载作用下圆柱形孔洞的动力响应解答
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摘要
考虑土与衬砌结构的动力相互作用,本文研究了内源荷载作用下,圆柱形孔洞的动力响应问题。将土体和衬砌结构视为弹性均匀介质,通过引入势函数将位移控制方程化为二维轴对称波动方程。采用拉普拉斯变换,得到土体及衬砌的位移应力的表达式。利用土体与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,可确定表达式的未知系数。采用逆拉普拉斯变换的数值方法,给出了问题的数值解。分析了土中圆形衬砌结构的动力响应随土体和衬砌结构参数的变化规律。
Considering the dynamic interaction between the lining and soil,the dynamic response of a cylindrical cavity under an internal load was presented.The lining structure and soil are treated as homogeneous elastic media.Two dimensional axisymmetric wave equation was derived from the governing equation of displacement by introducing potentials functions.The expressions of the displacement and stress for both the soil and lining structure were obtained by using Laplace transform.Utilizing the inner boundary condition of the lining and the continuity conditions between the soil and the lining,the unknown coefficients in the expressions were determined.With the inverse Laplace transform,the numerical solution of the problem was presented.The dynamic responses of the lining structure in soil were analyzed for the different parameters of soil and lining.
Considering the dynamic interaction between the lining and soil,the dynamic response of a cylindrical cavity under an internal load was presented.The lining structure and soil are treated as homogeneous elastic media.Two dimensional axisymmetric wave equation was derived from the governing equation of displacement by introducing potentials functions.The expressions of the displacement and stress for both the soil and lining structure were obtained by using Laplace transform.Utilizing the inner boundary condition of the lining and the continuity conditions between the soil and the lining,the unknown coefficients in the expressions were determined.With the inverse Laplace transform,the numerical solution of the problem was presented.The dynamic responses of the lining structure in soil were analyzed for the different parameters of soil and lining.
引文
[1]张庆元,战人瑞.爆轰载荷作用下球形空腔的动力响应[J].爆炸与冲击,1994,14(2):182-185.
[2]杨俊,宫全美,吴世明等.饱和土体中圆柱形孔洞的动力分析[J].上海力学,1996,17(1):37-44.
[3]Manolis G D.Elastic wave scattering around cavities in inhomogeneous continua by the BEM[J].Journal of Sound and Vibration.2003,266:281-305.
[4]Forrestal M J,Sagartz M J.Radiated pressure in an acoustic medium produced by pulsed cylindrical and spherical shells[J].AMSE Jour-nal of Applied Mechanics,1971,93:1057-1060.
[5]Duffey T A.Transient response of viscoplastic and viscoelastic shells submerged in fluid media[J].AMSE Journal of Applied Mechanics,1976,98:137-143.
[6]Karpp R R,Duffey T A,Neal T R.Response of containment vessels to explosive blast loading[R].University of California,Los AlamosNational Laboratory Report LA-8082,1980.
[7]高广运,高盟,冯世进.无限弹性介质中隧道内爆炸动力响应的解析解[J].西北地震学报,2008,30(2):124-127.
[8]Glenn L A,Kidder R E.Blast loading of a spherical container surrounded by an infinite elastic medium[J].Journal of Impact Engineer-ing,1983,50(10):723-726.
[9]Auslender F,Combescure A.Spherical elastic-plastic structures under internal explosion:Approximate analytical solutions and application[J].Engineering,structures,2000,22:984-992.
[10]Feldgun V R,Kochetkov A V,Karinski Y S.Internal blast loading in a buried lined tunnel[J].International Journal of Impact Engi-neering,2007(1):2-12.
[11]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988.
[12]Durbin F.Numerical inversion of Laplace transforms:an efficient improvement to Dubner and Abate s method[J].The Computer Jour-nal,1974,17(4):371-376.
[2]杨俊,宫全美,吴世明等.饱和土体中圆柱形孔洞的动力分析[J].上海力学,1996,17(1):37-44.
[3]Manolis G D.Elastic wave scattering around cavities in inhomogeneous continua by the BEM[J].Journal of Sound and Vibration.2003,266:281-305.
[4]Forrestal M J,Sagartz M J.Radiated pressure in an acoustic medium produced by pulsed cylindrical and spherical shells[J].AMSE Jour-nal of Applied Mechanics,1971,93:1057-1060.
[5]Duffey T A.Transient response of viscoplastic and viscoelastic shells submerged in fluid media[J].AMSE Journal of Applied Mechanics,1976,98:137-143.
[6]Karpp R R,Duffey T A,Neal T R.Response of containment vessels to explosive blast loading[R].University of California,Los AlamosNational Laboratory Report LA-8082,1980.
[7]高广运,高盟,冯世进.无限弹性介质中隧道内爆炸动力响应的解析解[J].西北地震学报,2008,30(2):124-127.
[8]Glenn L A,Kidder R E.Blast loading of a spherical container surrounded by an infinite elastic medium[J].Journal of Impact Engineer-ing,1983,50(10):723-726.
[9]Auslender F,Combescure A.Spherical elastic-plastic structures under internal explosion:Approximate analytical solutions and application[J].Engineering,structures,2000,22:984-992.
[10]Feldgun V R,Kochetkov A V,Karinski Y S.Internal blast loading in a buried lined tunnel[J].International Journal of Impact Engi-neering,2007(1):2-12.
[11]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988.
[12]Durbin F.Numerical inversion of Laplace transforms:an efficient improvement to Dubner and Abate s method[J].The Computer Jour-nal,1974,17(4):371-376.
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