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采用载荷叠加法将集中载荷下四边固支正交各向异性矩形板线性弯曲的挠度分为3个部分:集中载荷下四边简支板的挠度、上下边简支左右边受弯矩的板的挠度、左右边简支上下边受弯矩的板的挠度,3个挠度之和在满足固支边界条件的情况下即为所要求的挠度的解。采用MATLAB软件编写程序进行计算,并将相同长宽的板在4种不同的厚度和载荷情况下的挠度计算结果与有限元分析结果进行比较,验证了解析解的正确性。最后讨论了经典的Kirchhoff薄板假设对于集中载荷的适用性问题。
The deflection of the linear bending of rectangular orthotropic plates with four sides under concentrated load is divided into three parts by the load superposition method: the deflection of the simple supported plate with four sides under concentrated load, Deflection, left and right simply supported by the upper and lower bending moments of the plate deflection, the sum of the three deflection in the case of fixed boundary conditions to meet the requirements of the deflection solution. The program of MATLAB software was used to calculate. The deflection calculation results and the finite element analysis results of the same length and width plates at four different thicknesses and loads were compared to verify the correctness of the analytical solution. Finally, the applicability of classical Kirchhoff thin plate assumption to concentrated loads is discussed.