Shear Buckling of Thin Plates with Constant In-Plane Stresses
Shear Buckling of Thin Plates with Constant In-Plane Stresses
复制标题
具有恒定面内应力的薄板的剪切屈曲
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
M. Eisenberger
中科院分区：
文献类型：
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作者：
I. Shufrin;M. Eisenberger
这项工作提出了高精度的数值计算的屈曲载荷薄弹性矩形板与已知的恒定单轴面内加载，和面内剪切载荷，直到临界载荷的获得和板失去其稳定性增加。用多项扩展Kantorovich方法求解。该解决方案寻求作为两个一维函数的乘法之和。在这种方法中，假设在板的一个方向上有一个解，这使得能够将板平衡的偏微分方程转化为常微分方程组。用精确单元法[1]对这些方程进行精确求解，得到了近似的屈曲载荷。在第二步中，将导出的解作为一个方向上的假定解，并重复该过程以找到改进的屈曲载荷。该过程收敛于少量的解循环。对于剪切屈曲，只有在解的展开式中取两项或多项时，才能用这个过程。作为一个例子，如图1所示，在不同水平的恒定压缩载荷的简支方板的剪切屈曲载荷，给出。在图2中，显示了作为压缩水平的函数的归一化剪切屈曲载荷的变化。更多的新成果将被公布。
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This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant uni-axial in-plane loading, and in-plane shear loading that is increased until the critical load is obtained and the plate losses its stability. The solutions are obtained using the multi term extended Kantorovich method. The solution is sought as the sum of multiplications of two one dimensional functions. In this method a solution is assumed in one direction of the plate, and this enables to transform the partial differential equations of the plate equilibrium into a system of ordinary differential equations. These equations are solved exactly by the exact element method [1], and an approximate buckling load is obtained. In the second step, the derived solution is now taken as the assumed solution in one direction, and the process is repeated to find an improved buckling load. This process converges with a small number of solution cycles. For shear buckling this process can only be used if two or more terms are taken in the expansion of the solution. As an example the shear buckling load of a simply supported square plate with different levels of constant compressive load, as shown in Figure 1, is given. In Figure 2 the variation of the normalized shear buckling load as a function of the compression level is shown. Many more new results will be given.
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