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.
参考文献
| [1] | 钟杰;郑勇;张一欣.功能梯度Ti（C,N）基金属陶瓷制备技术[J].复合材料学报,2009(3):111-115. |
| [2] | 梁连杰;陈少平;刘泽锋;薛鹏飞;孟庆森.电场辅助原位合成TiB2-TiC-Ni/TiAl/Ti功能梯度材料及界面结构[J].复合材料学报,2011(5):139-144. |
| [3] | B.V. Sankar.An elasticity solution for functionally graded beams[J].Composites science and technology,20015(5):689-696. |
| [4] | Zheng Zhong;Tao Yu.Analytical solution of a cantilever functionally graded beam[J].Composites science and technology,20073/4(3/4):481-488. |
| [5] | 仲政;于涛.功能梯度悬臂梁弯曲问题的解析解[J].同济大学学报（自然科学版）,2006(4):443-447. |
| [6] | Ding HJ;Huang DJ;Chen WQ.Elasticity solutions for plane anisotropic functionally graded beams[J].International Journal of Solids and Structures,200726(26):176-196. |
| [7] | H. Zhu;B.V. Sankar.Analysis of sandwich TPS panel with functionally graded foam core by Galerkin method[J].Composite structures,20073(3):280-287. |
| [8] | Analytical solution for bi-material beam with graded intermediate layer[J].Composite structures,201010(10):P.2358. |
| [9] | Qing Yang;Bailin Zheng;Kai Zhang;Jianxin Zhu.Analytical solution of a bilayer functionally graded cantilever beam with concentrated loads[J].Archive of Applied Mechanics,20133(3):455-466. |
| [10] | 杨青;郑百林;张锴;朱建新.功能梯度双材料复合悬臂梁受集中剪力作用的弹性力学解[J].兰州交通大学学报,2013(1):20-24. |
| [11] | Juan Li;Bailin Zheng;Qing Yang;Xingjian Hu.Analysis on time-dependent behavior of laminated functionally graded beams with viscoelastic interlayer[J].Composite structures,2014Jan.(Jan.):30-35. |
| [12] | M. Rahaeifard;M.H. Kahrobaiyan;MX Ahmadian;K. Firoozbakhsh.Strain gradient formulation of functionally graded nonlinearbeams[J].International journal of engineering science,2013Apr.(Apr.):49-63. |
| [13] | M. Simsek;T. Kocatuerk;S.D. Akbas.Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load[J].Composite structures,20128(8):2358-2364. |
| [14] | Ahmad Shahba;Sundaramoorthy Rajasekaran.Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials[J].Applied mathematical modelling,20127(7):3094-3111. |
| [15] | Lu CF;Chen WQ;Xu RQ;Lim CW.Semi-analytical elasticity solutions for bi-directional functionally graded beams[J].International Journal of Solids and Structures,20081(1):258-275. |
| [16] | 郑重;张海鸥;王桂兰;钱应平.三维功能梯度材料复杂形状零件的制造技术及发展趋势[J].新技术新工艺,2011(5):88-92. |
| [17] | 钱婷婷;刘栋;田象军;刘长猛;王华明.激光增材制造TA2/TA15梯度结构材料的显微组织[J].中国有色金属学报（英文版）,2014(9):2729-2736. |
| [18] | 王强;孙跃.增材制造技术在航空发动机中的应用[J].航空科学技术,2014(9):6-10. |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%