弹性支承功能梯度圆板轴对称弯曲问题精确解

Exact Solution for Axisymmetric Bending of Functionally Graded Circular Plate Under Elastically Supported Boundary Condition

摘要:

对周边为弹性支承边界条件下的功能梯度材料圆板轴对称弯曲问题进行了分析.将位移函数写成傅立叶贝塞尔级数的形式，根据各向同性功能梯度材料基本方程，并针对指数函数形式的梯度分布情况，对功能梯度圆板轴对称弯曲问题的位移和应力进行了精确分析.通过具体算例，分析了在圆板上、下表面荷载作用下，材料性质的不同梯度变化对圆板结构响应的影响.分析结果表明，材料性质的梯度变化对圆板的力学性能有显著影响.

Abstract:

The paper presents an analysis of the axisymmetric bending of a functionally graded circular plate under elastically supported boundary condition.The displacement function of the functionally graded circular plate was written as Fourier Bessel series.Based on the basic equations of axisymmetric isotropic functionally graded materials under the assumption that the material property has the exponential dependence on the thickness coordinate,an exact solution of displacements and stresses field was obtained for an elastically supported circular plate subject to axisymmetric normal and shearing loadings on its upper and lower surfaces.With the variation of material graded distributions,the response of the circular plate subjected to axisymmetric loadings on its upper and lower surfaces was studied through a numerical example.The obtained solution demonstrates that the graded material properties have significant effects on the mechanical behavior of the plate.