一种新的三阶隐式直接积分法
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摘要
将位移的三阶导定义为超加速度,并基于常平均超加速度假设推导了一种新的三阶隐式直接积分法。分析了该方法的稳定性、计算精度和计算效率。证明在不增加所需存储空间和计算量情况下,该方法是稳定的且有三阶精度。最后,用三个算例验证了该方法的准确性和适用性,能够解决实际工程问题中遇到的多种结构动力学问题。
The third-order derivative of displacement is defined as super-acceleration, and a new third-order implicit direct integration method is derived based on the assumption of constant mean super-acceleration. The stability,calculation accuracy and calculation efficiency of the method are analyzed. It is proved that the method is stable and has third-order accuracy without increasing the required storage space and calculation amount. Finally, three examples are used to verify the accuracy and applicability of the proposed method, which can solve many structural dynamics problems encountered in practical engineering problems.
The third-order derivative of displacement is defined as super-acceleration, and a new third-order implicit direct integration method is derived based on the assumption of constant mean super-acceleration. The stability,calculation accuracy and calculation efficiency of the method are analyzed. It is proved that the method is stable and has third-order accuracy without increasing the required storage space and calculation amount. Finally, three examples are used to verify the accuracy and applicability of the proposed method, which can solve many structural dynamics problems encountered in practical engineering problems.
引文
[1]NEWMARK N M.A method of computation for structural dynamics[J].Journal of Engineering Mechanics Division,1959,85(3):249-260.
[2]陈玲莉.工程结构动力学分析数值方法[M].西安:西安交通大学出版社,2006.
[3]张继锋,邓子辰.结构动力方程的增维分块精细积分法[J].振动与冲击,2008,27(12):88-90.
[4]HILBLER H M,HUGHES T J R.Collocation,dissipation and'overshoot'for time integration schemes in structural dynamics[J].Ear.Eng.Sdruct.Dyn.,1978(6):99-117.
[5]SIKANDER H K.Implementation of Newmark's method for second order initial value problems[J].Journal of Applied Sciences,2005(3):402-410.
[6]BATHE K J,WILSON E L. Numerical methods in finite element analysis[M]. New Jersey:Prentice-Hall,1976.
[7]师汉民.机械振动系统-分析·测试·建模·对策[M].武汉:华中科技大学出版社,2003.
[8]张继锋,邓子辰,徐方暖,等.一种新的改进精细直接积分法[J].动力学与控制学报,2015(4):241-245.
[2]陈玲莉.工程结构动力学分析数值方法[M].西安:西安交通大学出版社,2006.
[3]张继锋,邓子辰.结构动力方程的增维分块精细积分法[J].振动与冲击,2008,27(12):88-90.
[4]HILBLER H M,HUGHES T J R.Collocation,dissipation and'overshoot'for time integration schemes in structural dynamics[J].Ear.Eng.Sdruct.Dyn.,1978(6):99-117.
[5]SIKANDER H K.Implementation of Newmark's method for second order initial value problems[J].Journal of Applied Sciences,2005(3):402-410.
[6]BATHE K J,WILSON E L. Numerical methods in finite element analysis[M]. New Jersey:Prentice-Hall,1976.
[7]师汉民.机械振动系统-分析·测试·建模·对策[M].武汉:华中科技大学出版社,2003.
[8]张继锋,邓子辰,徐方暖,等.一种新的改进精细直接积分法[J].动力学与控制学报,2015(4):241-245.