一种模量双向变化的梯度复合平面梁的级数解

发布时间：2018-06-01 02:09

本文选题：复数形式傅里叶分解 + 模量双向变化　；参考：《复合材料学报》2016年12期

【摘要】：3D打印技术的发展使复杂梯度结构的制造更加容易,有必要对复杂梯度问题的求解开展研究;目前,关于梁结构模量沿轴向或厚度方向梯度变化问题的研究已经较多,但对模量沿2个方向同时变化的研究较少。因此,通过复数形式傅里叶分解的方法对模量以指数形式沿厚度方向和轴向同时变化梯度平面复合梁问题进行了求解。首先,采用弹性力学半逆解法得到了问题的四阶变系数偏微分控制方程的通解;然后,利用级数展开,求解了对称载荷作用下该梁的特解;最后,通过与有限元结果进行对比,说明了级数解的正确性。结果表明:当梯度双向变化时,梁结构的应力分布和变形情况更加复杂,模量较高的位置应力较大,而模量较低的位置应力较小。提出的级数解还可推广至其他相关的梯度双向变化非均匀平面和半平面问题的研究。
[Abstract]:With the development of 3D printing technology, the manufacture of complex gradient structures is easier, so it is necessary to study the solution of complex gradient problems. However, little research has been done on the simultaneous variation of modulus along two directions. Therefore, the complex Fourier decomposition method is used to solve the problem of composite beams whose modulus varies exponentially along the thickness direction and the axial direction at the same time. First, the general solution of the fourth order partial differential control equation with variable coefficients is obtained by using the semi-inverse method of elasticity, then, the special solution of the beam under symmetric load is solved by using series expansion; finally, the results are compared with the finite element results. The correctness of the series solution is explained. The results show that the stress distribution and deformation of the beam structure are more complex when the gradient changes in both directions. The position stress with higher modulus is larger and the position stress with lower modulus is smaller. The proposed series solution can also be extended to the study of other related gradient bidirectional variation inhomogeneous plane and half plane problems.
【作者单位】：中国商飞上海飞机制造有限公司;东华大学民用航空复合材料协同创新中心;同济大学航空航天与力学学院;
【基金】：中国博士后科学基金(2015M581681) 中国商飞中欧合作专项(SAMC14-JS-13-012)
【分类号】：TB33

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