Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method
Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method
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DOI：
10.1016/j.cma.2003.10.013
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发表时间：
2004-02
影响因子：
7.2
通讯作者：
R. Kirby;Z. Yosibash
中科院分区：
文献类型：
--
作者：
R. Kirby;Z. Yosibash
矩形域上的 von-Kármán 非线性动态偏微分系统通过空间上的切比雪夫配置方法和时间上的隐式 Newmark-β 时间推进方案来求解。在Newmark-β方案中，采用了非线性定点迭代算法。我们根据导出的解析解监控时间和空间离散化误差，展示高度准确的近似值。我们还量化了一个常见建模假设的影响，该假设忽略了完整冯卡门系统中的面内惯性项，证明了它是合理的。将我们的稳态冯卡门解与文献中先前的结果以及三维高阶有限元分析进行比较，结果显示出极好的一致性。还解决了其他建模假设，例如忽略应变表达式中的面内二次项。
The von-Kármán non-linear, dynamic, partial differential system over rectangular domains is solved by the Chebyshev-collocation method in space and the implicit Newmark-β time marching scheme in time. In the Newmark-β scheme, a non-linear fixed point iteration algorithm is employed. We monitor both temporal and spatial discretization errors based on derived analytical solutions, demonstrating highly accurate approximations. We also quantify the influence of a common modeling assumption which neglects the in-plane inertia terms in the full von-Kármán system, demonstrating that it is justified. A comparison of our steady-state von-Kármán solutions to previous results in the literature and to a three-dimensional high-order finite element analysis is performed, showing an excellent agreement. Other modeling assumptions such as neglecting in-plane quadratic terms in the strain expressions are also addressed.