基于分层法的功能梯度材料有限元分析

复合材料科学与工程 ›› 2013, Vol. 0 ›› Issue (2): 43-48.

基于分层法的功能梯度材料有限元分析

黄立新^1,2*, 姚祺³, 张晓磊⁴, 阳明¹

1.广西大学土木建筑工程学院,广西南宁530004;
2.广西大学工程防灾与结构安全教育部重点实验室,广西南宁530004;
3.沙洲职业工学院建筑工程系,江苏张家港215600

收稿日期:2012-07-25 发布日期:2022-03-17
作者简介:黄立新(1964-),男,教授,博士,主要研究方向为先进复合材料与力学,gxuhuanglixin@163.com。
基金资助:
国家自然科学基金(11262002)

FINITE ELEMENT ANALYSIS OF FUNCTIONALLY GRADED MATERIALS BASED ON LAYERING METHOD

HUANG Li-xin^1,2*, YAO Qi³, ZHANG Xiao-lei¹, YANG Ming¹

1. School of Civil Engineering,Guangxi University,Nanning 530004,China;
2. The Key Laboratory of Disaster Prevention and Structural Safety of the Education Ministry, Guangxi University,Nanning 530004,China;
3. Civil Engineering Department,Shazhou Professicnal Institute of Technology,Zhangjiagang 215600,China

Received:2012-07-25 Published:2022-03-17

摘要/Abstract

摘要： 基于分层法,本文采用有限元模型进行功能梯度材料平面结构的力学分析。将功能梯度材料平面结构划分成若干层,每层的材料参数按函数形式变化。在此分层模型基础上得到同一层的材料参数为常数,然后各层按照常规的有限元方法进行网格划分,建立有限元模型进行功能梯度材料平面结构的力学分析。数值算例表明,功能梯度材料平面结构应力和位移的有限元计算结果与解析解吻合得很好。通过设计组分材料Y-TZP 弹性模量的三种工况,讨论了弹性模量梯度系数对有限元计算结果的影响。数值结果显示,弹性模量梯度系数变大对应力和位移的有限元计算结果有影响,对应力的影响较大而对位移的影响较小。

关键词: 功能梯度材料, 有限元法, 分层法, 梯度系数

Abstract: Based on layering method,finite element model is used to analyze a plane structure of functionally graded materials (FGMs). The FGMs plane structure is divided into a certain number of homogeneous layers with the material property between adjacent layer varying in a functional manner and the conventional homogeneous element can be employed to mesh the plane structure for its analysis. Numerical example shows that the stress and displacement results by finite element method (FEM) are satisfactorily agreed with the analytical solutions. By designing Young's Modulus nonhomogeneity parameters of material component Y-TZP in three cases,the influence on the FEM solutions is discussed. Numerical results demonstrate that the increase of nonhomogeneity parameters has effects on the FEM solutions of stress and displacement and the effects on stress are more than those on displacement.

Key words: functionally graded materials, finite element method, layering method, nonhomogeneity parameters

中图分类号:

TB332
TP311

黄立新, 姚祺, 张晓磊, 阳明. 基于分层法的功能梯度材料有限元分析[J]. 复合材料科学与工程, 2013, 0(2): 43-48.

HUANG Li-xin, YAO Qi, ZHANG Xiao-lei, YANG Ming. FINITE ELEMENT ANALYSIS OF FUNCTIONALLY GRADED MATERIALS BASED ON LAYERING METHOD[J]. COMPOSITES SCIENCE AND ENGINEERING, 2013, 0(2): 43-48.

参考文献

[1] Reddy JN. Analysis of functionally graded plates[J]. International Journal for Numerical Methods in Engineering,2000,47(1-3): 663-684.
[2] 曹志远. 功能梯度复合材料圆柱壳基本理论及长壳固有振动解[J]. 玻璃钢/复合材料,2006,189(4): 3-6.
[3] 曹志远. 功能梯度壳体力学的一般理论[J]. 玻璃钢/复合材料, 2008,199(2): 7-11.
[4] Sankar BV. An elasticity solution for functionally graded beams[J]. Composites Science and Technology,2001,61(5): 689-696.
[5] Zhong Z,Shang ET. Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate[J]. International Journal of Solids and Structures,2003,40(2): 5335-5352.
[6] Ding HJ,Huang DJ,Chen WQ. Elasticity solutions for plane anisotropic functionally graded beams[J]. International Journal of Solids and Structures,2007,44(1): 176-196.
[7] 程红梅,曹志远. 由材料组分直接计算功能梯度复合材料开孔板宏观响应的跨尺度分析[J]. 复合材料学报,2006,23(5): 161-167.
[8] 程红梅,曹志远. 功能梯度材料单参数反演分析[J]. 玻璃钢/复合材料,2009,206(3): 16-22.
[9] Zhong Z,Cheng ZQ. Fracture analysis of a functionally graded strip with arbitrary distributed material properties[J]. International Journal of Solids and Structures,2008,45(13): 3711-3725.
[10] 王明禄,马文蕾,魏高峰. 热载荷下功能梯度材料梁的热弹性弯曲[J]. 玻璃钢/复合材料,2009,204(1): 7-9.
[11] 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): 528-540.
[12] 杨洁,李成,贾红雨,苏玉珍. 复合材料层合板孔边应力场的有限元计算[J]. 玻璃钢/复合材料,2009,206(3): 8-12.
[13] 段成红,吴祥,罗翔鹏. 碳纤维缠绕复合气瓶爆破压力的有限元分析[J]. 玻璃钢/复合材料,2012,223(2): 17-19.
[14] Wang YS,Gross D. Analysis of a crack in a functionally gradient interface layer under static and dynamic loading[J]. Key Engineering Materials,2000,183-187: 331-336.
[15] Wang YS,Huang GY,Gross D. On the mechanical modeling of functionally graded interracial zone with a griffith crack: anti-plane deformation[J]. ASME Journal of Applied Mechanics,2003,70: 676-680.
[16] 黄干云,汪越胜,余寿文. 功能梯度材料的平面断裂力学分析[J]. 力学学报,2005,37(1): 1-8.
[17] Kim JH,Paulino GH. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials[J]. ASME Journal of Applied Mechanics,2002,69(4): 502-514.
[18] Suresh S,Giannakopoulos AE and Alcala J. Spherical indentation of compositionally graded materials: theory and experiments[J]. Acta Materials,1997,45(4): 1307-1321.