BUCKLING ANALYSIS OF THIN RECTANGULAR PLATES UNDER COSINE-DISTRIBUTED COMPRESSIVE LOADS
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摘要: 针对不同支承条件，两对边受半余弦非线性分布压力下弹性矩形薄板的屈曲问题，进行了分析研究。对于只产生对称变形的矩形薄板，基于辛弹性力学的平面矩形域理论，给出了精确的面内应力分布。运用Galerkin法分析计算了半余弦分布压力下矩形薄板的屈曲载荷。根据各种不同支承矩形薄板弯曲的位移边界条件，借助于符号运算软件Maple，编写了相应的用户计算程序。对九种不同支承组合下的弹性矩形薄板进行了计算，得到了不同长宽比矩形薄板的屈曲载荷系数。通过与已有文献结果的比较表明，该文求解方法是有效和精确的。基于所给出的结果，可望为解决矩形薄板在非线性分布载荷下的屈曲分析提供一种新的研究方法。Abstract: The buckling of thin rectangular plates with various combinations of boundary conditions is studied, whose cosine-distributed compressive loads are applied along two opposite plate edges. On the basis of the symplectic elasticity in plane rectangular domain under symmetrical deformation, precise in-plane stress distribution is given. The buckling loads of the thin rectangular plates are analyzed by using the Galerkin method. After applying various combinations of boundary conditions, with the help of the symbolic computational software Maple, the Maple user program for calculating buckling loads is prepared. Nine combinations of boundary conditions are considered. The buckling coefficients are gained for thin rectangular elastic plates with various aspect ratios. The efficiency and validity of the proposed method are confirmed by a comparison with the published results. It can be concluded that the proposed method could provide a new way for the buckling analysis of thin rectangular plates subjected nonlinearly distributed in-plane loadings.
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Keywords:
- buckling /
- symplectic elasticity /
- Galerkin method /
- cosine-distributed loads /
- rectangular plates
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