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研究了正交各向异性功能梯度板的三维弯曲问题。假设材料参数沿板厚方向按同一函数规律变化,基于状态空间法,在板的上下表面作用机械载荷的情况下,获得了简支功能梯度平板弯曲问题的Peano-Baker级数解。通过算例,验证了Peano-Baker级数解的正确性,同时也分析了材料参数沿板厚方向为余弦函数分布时,不同梯度参数对平板响应的影响。结果表明Peano-Baker级数解具有很好的收敛性。
The three-dimensional bending problem of orthotropic functionally graded plates has been studied. The material parameters are assumed to change along the same function law along the thickness direction. Based on the state space method, the Peano-Baker series solution to the simply supported functionally graded plate bending problem is obtained under the mechanical loads acting on the upper and lower surfaces of the plate. The correctness of the Peano-Baker series solution is verified by an example. The influence of different gradient parameters on the plate response is also analyzed when the material parameters are cosine functions along the thickness direction. The results show that the Peano-Baker series solution has good convergence.