| 功能梯度板的柱面弯曲弹性力学解 |
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| 引用本文： | 杨云芳,杨博,陈伟球,丁皓江.功能梯度板的柱面弯曲弹性力学解[J].应用数学和力学,2015,36(12):1257-1264. |
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| 作者姓名： | 杨云芳 杨博 陈伟球 丁皓江 |
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| 作者单位： | 1浙江理工大学 建筑工程学院 土木工程系, 杭州 310018;2浙江大学 航空航天学院 工程力学系, 杭州 310027;3浙江大学 建筑工程学院 土木工程系, 杭州 310027 |
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| 基金项目： | 国家自然科学基金(11202188；11172263) |
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| 摘 要： | 在推广后的England-Spencer功能梯度板理论基础上,研究了功能梯度板在不同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,并将材料由各向同性推广到正交各向异性.假设板在y方向无限长,最终建立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分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、材料梯度及板厚跨比等因素对功能梯度板静力响应的影响.
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| 关 键 词： | 功能梯度板 柱面弯曲 弹性力学解 |
| 收稿时间： | 2015-09-17 |
Elasticity Solutions for Cylindrical Bending of Functionally Graded Plates |
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| Affiliation: | 1Department of Civil Engineering, School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China;2Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, P.R.China;3Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310027, P.R.China |
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| Abstract: | The cylindrical bending of functionally graded rectangular plates under different loads was studied based on a generalization of the England-Spencer theory. The expansion formulae for displacements and the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion were adopted. The elasticity solutions were obtained for an orthotropic functionally graded plate in cylindrical bending with an infinite length in y-direction. The effects of the boundary conditions, the material gradient and the thickness-to-span ratio on the static responses of the functionally graded plates were investigated through a numerical example. The proposed solutions are useful for the validation of various numerical methods or approximate plate theories. |
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