梯度弹性基础上正交异性薄板的屈曲分析

基于双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板的屈曲问题. 首先,基于能量法与变分原理,给出了梯度弹性基础上正交异性薄板的屈曲控制方程,并得到了梯度弹性基础刚度系数K₁ 与K₂的计算式;进而,通过将位移函数采用三角函数展开的方法,给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;在算例中,通过将该文的解退化到单纯的正交异性板,并与经典弹性解比较,证明了理论的正确性;最后,求解了弹性模量在厚度方向上呈幂律分布的梯度基础上的薄板屈曲问题,分析了基础上下表层材料弹性模量比与体积分数指数对屈曲载荷的影响.

BUCKLING ANALYSIS OF ORTHOTROPIC THIN PLATE ON GRADED ELASTIC FOUNDATION

Based on the two-parameter foundation model, the buckling of orthotropic thin plates on graded elastic foundations is studied. Firstly, the buckling governing differential equation of orthotropic thin plates on graded elastic foundations and the expressions of two elastic parameters of the elastic foundation are obtained by using the energy method and the variational principle. Then, by expanding the displacement into trigonometric functions, the calculation formula of the uniaxial compression buckling load for orthotropic thin plates on graded elastic foundations with simply supported edges is obtained. In the example, the proposed solution is validated by comparing the degenerated results for an orthotropic thin plate with the classical elasticity solution. Finally, this paper studies the buckling load of the orthotropic thin plate on a graded elastic foundation, whose Young's modulus obeys a power law against the thickness. The effects of the top-bottom surfaces' Young's modulus ratio and the volume fraction exponent are also discussed.