| 功能梯度曲梁弯曲问题的解析解 |
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| 引用本文： | 余莲英,张亮亮,尚兰歌,孙振冬,高恩来,井文奇,高阳.功能梯度曲梁弯曲问题的解析解[J].工程力学,2014,31(12):4-10. |
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| 作者姓名： | 余莲英 张亮亮 尚兰歌 孙振冬 高恩来 井文奇 高阳 |
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| 作者单位： | 1.中国农业大学理学院, 北京 100083; |
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| 基金项目： | 国家自然科学基金项目(11172319,11172321,11072260,11472299);中央高校基本科研业务费专项资金项目(2011JS046,2013BH008);教育部新世纪优秀人才支持计划项目(NCET-13-0552);非线性力学国家重点实验室开放基金;北京市大学生科学研究与创业行动计划项目(2012bj091) |
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| 摘 要： | 该文采用弹性力学逆解法,求得了功能梯度曲梁在端部受弯矩作用的解析解。假设弹性模量E=E0rn沿径向呈幂函数的梯度分布。根据弹性力学平面问题的基本方程,在极坐标系下,引入应力函数,得到了弯曲问题的解析解。进而将功能梯度曲梁问题进行扩展,求得了整环或厚壁圆筒以及向错问题的解析解。将所得到的解退化到均匀弹性情况,与经典的理论解一致。最后对梯度函数按幂函数变化的算例进行了分析,结果显示梯度因子n对应力及位移的分布产生了巨大的影响。该文所得到的结论可以作为功能梯度曲梁构件优化设计的理论基础。
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| 关 键 词： | 功能梯度材料 曲梁 弯曲问题 幂函数 逆解法 |
| 收稿时间： | 2013-06-27 |
BENDING SOLUTIONS OF FUNCTIONALLY GRADED CURVED-BEAM |
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| Affiliation: | 1.College of Science, China Agricultural University, Beijing 100083, China;2.College of Engineering, China Agricultural University, Beijing 100083, China |
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| Abstract: | Based on the inverse method, analytical solutions are obtained for a functionally graded curved-beam which is subjected to a moment force at the free end. Elastic properties within a curved-beam is assumed to vary in the radial direction, according to a power law, i.e. E = E0rn. In virtue of the elastic theory of plane problems, the bending solution of functionally graded curved-beam is derived. Then, the analytical solutions of a circular ring and edge dislocation are presented. Degenerated results for homogeneous elastic case are coincided well with the existing analytical solutions. Finally, numerical case studies are performed, and the results show that the stress and displacement fields are greatly influenced by graded factor n. The analytical solutions can be used as benchmark results to optimally design the functionally graded curved-beams. |
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