曲线桥分析的精细传递矩阵法
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摘要
将精细积分与传递矩阵法相结合,提出一种新的精细传递矩阵格式,应用于曲线桥的分析中。与传统的传递矩阵法相比,无需对微分方程组进行求解,只需迭代即可得到所需要的传递矩阵。根据边界条件,得到结构的内力及变形。算例表明,该方法正确有效。
By combining the high-precision precise integration and the transfer matrix method, a new precise transfer matrix form is derived and applied to solve the structure analysis of the curved bridge. Compared with the traditional transfer matrix method, there is no need to solve the differential equations, and just by following the iterative formulae one can get the corresponding transfer matrix. According to the boundary conditions, the deformation and the internal force of the structure can be obtained. Example shows that the method is effective.
By combining the high-precision precise integration and the transfer matrix method, a new precise transfer matrix form is derived and applied to solve the structure analysis of the curved bridge. Compared with the traditional transfer matrix method, there is no need to solve the differential equations, and just by following the iterative formulae one can get the corresponding transfer matrix. According to the boundary conditions, the deformation and the internal force of the structure can be obtained. Example shows that the method is effective.
引文
[1]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.
[2]李青宁.几种常见变截面杆元的传递矩阵和传递常数[J].工程力学,1999(增刊):254-259.
[3]李青宁.抛物线连拱精确计算的传递矩阵法[J].西安建筑科技大学学报,1998,30(3):269-272.
[4]钟万勰,欧阳华江,邓子辰.计算结构力学与最优控制[M].大连:大连理工大学出版社,1993.
[5]钟万勰.暂态历程的精细计算方法[J].计算结构力学及其应用,1995,1(1):1-6.
[6]王梦甫,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191-195.
[7]魏双科.曲线梁桥的固有振动特性及地震反应分析[D].南京:南京工业大学,2006.
[8]邵容光,夏淦.混凝土弯梁桥[M].北京:人民交通出版社,1997.
[9]Fung T C.Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms-part2[J].International Journal for Numerical Methods in Engineering,1999,45(8):971-1006.
[10]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增刊):554-566.
[11]Zhong W X,Williams F W.A precise time step integration method[J].Journal of Mechanical Engineering Science,1994,208:427-430.
[12]张洪武.关于动力分析精细积分算法精度论[J].力学学报,2001,33(6):847-852.
[13]瞿尔仁,刘孝武,易云焜,等.传递矩阵法在曲线桥结构中的应用[J].合肥工业大学学报,1999,22(6):73-79.
[2]李青宁.几种常见变截面杆元的传递矩阵和传递常数[J].工程力学,1999(增刊):254-259.
[3]李青宁.抛物线连拱精确计算的传递矩阵法[J].西安建筑科技大学学报,1998,30(3):269-272.
[4]钟万勰,欧阳华江,邓子辰.计算结构力学与最优控制[M].大连:大连理工大学出版社,1993.
[5]钟万勰.暂态历程的精细计算方法[J].计算结构力学及其应用,1995,1(1):1-6.
[6]王梦甫,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191-195.
[7]魏双科.曲线梁桥的固有振动特性及地震反应分析[D].南京:南京工业大学,2006.
[8]邵容光,夏淦.混凝土弯梁桥[M].北京:人民交通出版社,1997.
[9]Fung T C.Weighting parameters for unconditionally stable higher-order accurate time step integration algorithms-part2[J].International Journal for Numerical Methods in Engineering,1999,45(8):971-1006.
[10]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增刊):554-566.
[11]Zhong W X,Williams F W.A precise time step integration method[J].Journal of Mechanical Engineering Science,1994,208:427-430.
[12]张洪武.关于动力分析精细积分算法精度论[J].力学学报,2001,33(6):847-852.
[13]瞿尔仁,刘孝武,易云焜,等.传递矩阵法在曲线桥结构中的应用[J].合肥工业大学学报,1999,22(6):73-79.
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