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首页> 外文期刊>Advances in Engineering Software >Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides
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Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides

机译：余弦分布压缩载荷在相对两侧的矩形薄板屈曲的差分正交分析

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The buckling of thin rectangular plates with non-linearly distributed compressive loading on two opposite sides received lesser attention than the one with uniformly or linearly distributed loads. The problem is considerably more complicated since it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses, and then the buckling problem is solved. Since it is difficult to obtain the analytical solutions accurately with a few series terms for the in-plane problem, very few analytical solutions have been available in the literature thus far. Therefore, the problem is analyzed by using differential quadrature (DQ) method. Detailed formulations and solution procedures are given herein. Nine combinations of boundary conditions and various aspect ratios are considered. Comparisons are made with finite element data obtained by NASTRAN with very fine meshes and existing analytical or numerical solutions. It is found that fast convergent rate can be achieved by the DQ method with non-uniform grids. And the first known accurate results are given herein.
机译：与具有均匀或线性分布载荷的矩形板相比，在两侧具有非线性分布的压缩载荷的矩形薄板的屈曲受到的关注较少。由于首先需要解决平面弹性问题以获得平面内应力的分布，然后解决屈曲问题，因此问题变得更加复杂。由于很难利用平面内问题的几个序列项来准确获得解析解，因此迄今为止，文献中很少有解析解可用。因此，通过使用差分正交（DQ）方法分析该问题。本文给出了详细的配方和解决方法。考虑了边界条件和各种纵横比的九种组合。使用NASTRAN获得的具有非常精细的网格的有限元数据和现有的解析或数值解决方案进行比较。发现采用非均匀网格的DQ方法可以实现快速收敛。并且在此给出了第一已知的准确结果。

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