线性分布载荷作用下功能梯度各向异性悬臂梁的解析解

对功能梯度各向异性弹性悬臂梁在线性分布载荷作用下的弯曲问题进行了研究．从平面应力问题的基本方程出发，假定应力函数为梁长度方向的多项式形式，由应力函数求导给出应力，利用协调方程和边界条件可完全确定应力函数．将解析解与有限元数值方法的结果进行了对比，两者吻合良好．

Analytical Solution for Functionally Graded Anisotropic Cantilever Beam Subjected to Linearly Distributed Load

The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis was based on the exact elasticity equations for the plane stress problem. The stress function was introduced and assumed in form of a polynomial of the longitudinal coordinate. The expressions for stress components were then educed from the stress function by simple differentiation. The stress function was determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution was compared with FEM calculation, indicating a good agreement.