【摘要】 本文从空间解耦有限元常微分方程组出发,探讨了结构动力学方程的高精度显式积分格式。通过被积函数的拉格朗日多项式内插和分部积分导出了波动数值模拟的一组显式时步积分公式。这组公式是时间和空间解耦的,即波场内任一离散节点在任一时刻的波动数据可以用这组公式依据该节点及其邻近节点在该时刻之前的n+1个时刻的波动数据显式地算出(n为非负整数),阐明了这组公式的如下特点:第一,其截断误差的量级不超过O(Δtn+3),Δt为时间步距。第二,它不仅可用于线性波动的数值模拟,而且可用于本构方程具有强非线性情形。第三,这组公式也可推广应用于一系列数学物理暂态问题的数值求解。针对一个简单的时不变系统初步分析了此组积分格式的稳定性。但是,对其稳定性尚需作进一步研究。更多还原

【Abstract】 Starting from the spacial decoupling finite element ordinary differential equations,this paper explores the explicit time integration method for structural dynamic equations.A group of explicit schemes for the numerical simulation of wave motion are derived via the Lagrange polynomial interpolation and integration by parts;the schemes are decoupling both in time and space,which mean that the motion of a discrete nodal point at a time can be computed explicitly by the schemes in term of the data of motion of the point and its neighboring nodal points at n+1 moments before the time.The schemes have the following features.Firsty,their truncation error is limited to O(Δtn+3),where Δt is time step and n is a non-negative integer.Seconly,they are not only suitable for the numerical simulation of linear wave motion,but also applicable for the numerical simulation of nonlinear constitutive equations.Finally,the schemes can be generalized to solve a series of transient mathematic-physical problems.The stability of the schemes are investigated preliminary by a simple time-invariant system,however,the stability should be further researched.更多还原