A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled by a user-specified value of the spectral radius $\rho_\infty$ in the high frequency limit. Using this user-specified parameter as a weight factor, a Pad\'e expansion of the matrix exponential solution of the equation of motion is constructed by mixing the diagonal and sub-diagonal expansions. An efficient timestepping scheme is designed where systems of equations, similar in complexity to the standard Newmark method, are solved recursively. It is shown that the proposed high-order scheme achieves high-frequency dissipation, while minimizing low-frequency dissipation and period errors. The effectiveness of the provided dissipation control and the efficiency of the scheme are demonstrated by numerical examples. A simple guideline for the choice of the controlling parameter and time step size is provided. The source codes written in MATLAB and FORTRAN are available for download at: https://github.com/ChongminSong/HighOrderTimeIntegration.
翻译:一个单步高阶隐含时间整合计划,在高频中可控制数字消散,用于对结构动态问题进行瞬时分析。数字消散的数量由高频限中光谱半径$\rho ⁇ ⁇ infty$的用户指定值控制。使用这个用户指定参数作为权重系数,通过混合二进制和亚对角扩展来构建运动方程式矩阵指数化溶液。一个高效的时间步制计划的设计,在其中,对复杂程度类似于标准新马克方法的方程式系统进行递归解决。显示,拟议的高序方案实现了高频消散,同时将低频消散和周期错误最小化。所提供的消散控制效果和系统效率通过数字示例来证明。提供了用于选择控制参数和时间步骤大小的简单指南。MATLAB和FORTRAN中写入的源代码可在以下下载: https://github.chongSongstratriat./ChongSTRAN。