Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods
Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods
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DOI：
10.1016/j.apm.2005.11.023
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发表时间：
2007-03
影响因子：
5
通讯作者：
Ö. Civalek
中科院分区：
文献类型：
--
作者：
Ö. Civalek
本文介绍了弹性地基上矩形薄板几何非线性静动力问题的耦合数值解法。考虑Winkler-Pasternak双参数地基模型。动力学模拟Von Karman方程。分别采用离散奇异卷积（DSC）和谐波微分求积（HDQ）方法对板的控制非线性偏微分方程进行空间和时间域离散。选择正则化香农核（RSK）和拉格朗日增量核（LD）两种不同的奇异核实现作为奇异卷积来说明本DSC算法。该分析提供了固支和简支板与不可移动的面内边界条件的边缘。各种类型的动态加载，即阶跃函数，正弦脉冲，N波脉冲，和三角形负载进行了研究，结果以图形方式呈现。研究了Winkler和Pasternak地基参数、地基质量对反应的影响。此外，还研究了阻尼对动力分析的影响。数值算例验证了所提出的DSC-HDQ耦合方法的准确性。
This article introduces a coupled methodology for the numerical solution of geometrically nonlinear static and dynamic problem of thin rectangular plates resting on elastic foundation. Winkler–Pasternak two-parameter foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the discrete singular convolution (DSC) and harmonic differential quadrature (HDQ) methods, respectively. Two different realizations of singular kernels such as the regularized Shannon’s kernel (RSK) and Lagrange delta (LD) kernel are selected as singular convolution to illustrate the present DSC algorithm. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse, an N-wave pulse, and a triangular load are investigated and the results are presented graphically. The effects of Winkler and Pasternak foundation parameters, influence of mass of foundation on the response have been investigated. In addition, the influence of damping on the dynamic analysis has been studied. The accuracy of the proposed DSC–HDQ coupled methodology is demonstrated by the numerical examples.