Elasticity Solutions for Functionally Graded Plates in Cylindrical Bending
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摘要: 利用推广后的Main和Spencer功能梯度板理论,研究了功能梯度矩形板在均布荷载作用下的柱面弯曲问题．采用该理论中的位移展开公式,并且材料参数沿板厚方向可以任意连续变化,但将材料由各向同性推广到正交各向异性,以及由不考虑板的横向荷载作用发展到受横向均布荷载作用．假设板在y方向无限长,从而得到了一个从弹性力学理论出发的正交各向异性功能梯度板在横向均布荷载作用下柱面弯曲问题的板理论．通过算例分析,讨论了边界条件和梯度变化程度对功能梯度板静力响应的影响．Abstract: The plate theory of functionally graded materials suggested by Mian and fencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load.The expansion formula for displacements was adopted.While keeping the assumption that the material parameters can vary along the thiclmess direction in an arbitrary fashion,it was considerect orthotropic materials rather than isotropic materials.In addition,the traction-free condition on the top surface was replaced by the condition of uniform load applied on the top surface.The plate theory for the particular case of cylindrical bending was presented by considering an infinite extent in the y-direction.The effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates were inwestigated through a numerical example.
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Key words:
- functionally graded plates /
- cylindrical bending /
- elastiaty
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