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首页> 外文期刊>Journal of Mathematical Sciences >SOLUTION OF THE PROBLEMS OF STABILITY OF LAMINATED PLATES WITH HOLES BY THE METHOD OF R -FUNCTIONS
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SOLUTION OF THE PROBLEMS OF STABILITY OF LAMINATED PLATES WITH HOLES BY THE METHOD OF R -FUNCTIONS

机译：通过R函数方法解决孔隙孔稳定性问题的解决方案

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摘要

We propose a method for the evaluation of the critical loads for laminated plates with holes. Plates and holes made in these plates may have different geometric shapes and conditions of their fastening. It is assumed that the plate is compressed by static forces in its middle plane. The mathematical statement of the problem is formulated within the framework of the refined first-order theory based on the hypothesis of straight line (Timoshenko-type theory). To solve the problem, we use the Ritz method and the R-functions theory. The solution of the problem of elasticity theory takes into account the inhomo-geneous subcritical state of the laminated plate. The reliability of the proposed approach is confirmed by good agreement of the obtained numerical results with the available data. Its efficiency is illustrated by an example of investigation of the problem of stability of laminated plates with one and two quadrangular holes. We analyze the influence of the arrangement of holes, their sizes, and the method of fastening on the critical load and natural frequencies.
机译：我们提出了一种利用孔评估用于层压板的关键载荷的方法。在这些板中制造的板和孔可能具有不同的几何形状和紧固条件。假设板通过其中间平面中的静力被压缩。基于直线的假设（TimosheNKO型理论），在精制的一阶理论的框架内配制了问题的数学陈述。为了解决问题，我们使用RITZ方法和R函数理论。弹性理论问题的解决方案考虑了层压板的非族族亚临界状态。通过可用数据获得的数值结果的良好协议，确认了所提出的方法的可靠性。其效率通过调查层压板稳定性与一个和两个四边形孔的问题进行了说明的示例。我们分析了孔，它们的尺寸和固定方法对临界负荷和自然频率的影响。

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