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工程力学  2014 

功能梯度曲梁弯曲问题的解析解

DOI: 10.6052/j.issn.1000-4750.2013.06.0585, PP. 4-10

Keywords: 功能梯度材料,曲梁,弯曲问题,幂函数,逆解法

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Abstract:

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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