THE STABILITY OF FGM CIRCULAR PLATES SUBJECTED TO FOLLOWER FORCE

Abstract

Abstract: The stability of the functionally graded material circular plate made of ceramic and metal subjected to follower force were investigated. It is assumed that the properties of the functionally graded material vary continuously only with the thickness of the plate and their variation has a simple power law distribution with the volume fraction of the constituents. The governing equations are derived, and then the nonlinear governing equations with two kind boundary conditions are numerically solved by shooting method, respectively. The effects of power index and boundary condition on the behavior of buckling and bending were discussed. The numerical results indicated that homogenous circular plate occurred in the traditional sense of the buckling under two kinds of boundary conditions, and FGM circular plate under the follower load will be buckling when the gradient index p<1, and plate only bending when p>1. Results show that the gradient properties of the materials and the boundary conditions have important effects on the bending and buckling behavior.

Key words: functionally graded material (FGM), circular plates, follower force, stability, shooting method

CLC Number:

TB332

LI Qing-lu, LUAN Wei-di, LI Shi-rong. THE STABILITY OF FGM CIRCULAR PLATES SUBJECTED TO FOLLOWER FORCE[J]. Fiber Reinforced Plastics/Composites, 2016, 0(10): 5-10.

References

[1] Koizumi M. The concept of FGM. Ceramic transitions[J]. Functionally Gradient Materials, 1993, 34: 3-10.
[2] Vosoughi A R . Thermal Postbuckling Analysis of Functionally Graded Beams[J]. Journal of Thermal Stresses, 2014, 37: 532-544.
[3] Reddy J N. Analysis of functionally graded plates[J]. International Journal for Numerical Methods in Engineering, 2000, 47 (1-3): 663-684.
[4] Yang J, Shen H S. Non-linear analysis of functionally graded plates under transverse and in plane loads[J]. International Journal of Non-linear Mechanics, 2003,38(4): 467-482.
[5] 仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展[J]. 力学进展, 2010, 40(5): 528-541.
[6] 杨帆, 马连生. 前屈曲耦合变形对 FGM 圆板稳定性的影响[J]. 工程力学, 2010, 27(4): 68-72(89).
[7] Najafizadeh M M, Eslami M R. Buckling analysis of circular plates of functionally graded materials under uniform radial compression[J]. International Journal of Mechanical Sciences, 2002, 44: 2479-2493.
[8] Zhang D G, Zhou Y H. A theoretical analysis of FGM doubly curved shallow thin shell based on physical neutral surface[J]. International Journal of Applied Electromagnetics and Mechanics, 2011, 35: 67-78.
[9] Ma L S, WANG T J. Nonlinear bending and postbuckling of a functionally graded circular plate under mechanical and thermal loadings[J]. International Journal of Solids and Structures, 2003, 40: 3311-3330.
[10] 黄立新, 杨真真, 赵文举. 基于模态应变能变化率法的Euler-Bernoulli功能梯度梁的损伤识别[J]. 玻璃钢/复合材料, 2015(8): 14-17.
[11] Yang J, Shen H S. Non-linear analysis of functionally graded plates under transverse and in-plane loads[J]. International Journal of Non-linear Mechanics, 2003, 38(4): 467-482.
[12] 李世荣, 高颖, 张靖华. 功能梯度与均匀圆板静动态解之间的相似转换关系[J]. 固体力学学报, 2011, 32(专辑).
[13] 王铁军,马连生,石朝峰. 功能梯度中厚圆/环板轴对成弯曲问题的解析解[J].力学学报,2004, 36(3): 348-353.
[14] Shen H S, Wang Z X. Assessment of Voigt and Mori-Tanaka models for vibration analysis of functionally graded plates[J]. Composite Structures, 2012, 94: 2197-2208.
[15] 莫宵依, 师俊平, 刘协会. 复合材料层合板在非保守力作用下的动力稳定性[J]. 复合材料学报, 2002, 19(4): 76-80.
[16] 王忠民, 高敬伯, 李会侠. 非保守圆薄板的轴对称振动和稳定性[J]. 固体力学学报, 2003, 24(2): 155-162.
[17] Li S R, Zhou Y H. Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates[J]. Journal of sound and vibration, 248(2): 379-386.