正交异性弹性基础板的屈曲分析

摘要

T he energy method and the double‐parameter elastic foundation model of Vlazov are used to study the buckling of orthotropic plate on elastic foundation .Firstly ,based on the energy method and the variation principle ,the buckling governing equation of orthotropic plate on elastic foundation is presented .Then ,the use of the trigonometric functions to expand the displacement results in obtai‐ning the calculation formula of buckling load for the orthotropic plate on elastic foundation with simply‐supported edges ,and the effects of the elastic modulus ,Poisson′s ratio and the depth of elastic foun‐dation on the buckling load are also analyzed .Finally ,the degeneration example of the orthotropic plate buckling is discussed .And the theory is proved to be correct by the comparison with the classical elasticity solution .%采用能量法和Vlazov双参数弹性基础模型，对正交异性弹性基础板的屈曲问题进行了研究。首先，基于能量法和变分法，给出了正交异性弹性基础板的屈曲控制方程；然后，通过采用三角函数将位移函数展开的方法，得出了单向压缩载荷作用下四边简支正交异性弹性基础板屈曲载荷的计算式，并分析了弹性基础的材料弹性模量、泊松比和深度对正交异性弹性基础板屈曲载荷的影响规律；最后，在算例中通过将文中的解退化到单纯的正交异性板，并与经典弹性解进行了比较分析，证明了文中理论的正确性。