在渐进均匀化理论基础上,建立了基于单胞数字化模型的复合材料宏观等效弹性性能的三维数值分析方法(DCB-FEA).该方法采用三维光栅化技术将三维单胞模型转化为三维光栅图形(数字化模型),并将光栅图形直接转化为三维有限元求解网格.产生的离散单元具有相同的几何尺寸和规则的形状,单元刚度矩阵的数量将减少为单胞材料的个数.此外,单胞数字化模型仅需记录每个离散单元的材料种类,其他参数如单元节点编号、节点坐标等均可在求解过程中自动生成,周期性边界条件也可以自动施加.随着分辨率的提高,单胞数字化模型将产生更多数量的单元,特别是对于三维单胞模型,集成整体刚度矩阵时需要大量的计算机内存.采用基于Element-by-element策略的预处理共轭梯度法(EBE-PCG),有限元方程的求解在单元级上进行,避免了整体刚度矩阵的集成.通过对单向纤维增强复合材料的线弹性本构关系的数值模拟,表明该方法可得到较为准确的复合材料等效模量.
参考文献
| [1] | Hill R A.Self-consistent mechanics of composite materials[J].J Mech Physics and Solids,1965,12:213-222. |
| [2] | Budiansky.On the elastic moduli of some heterogeneous mater-ials[J].J Mech Physics and Solids,1965,13:223-227. |
| [3] | Mori T,Tanaka K.Average stress in matrix and average elastic energy of material with misfitting inclusions[J].Acta Metal,1973,21:571-574. |
| [4] | 方岱宁,周储伟.有限元计算细观力学对复合材料力学行为的数值分析[J].力学进展,1998,28(2):173-188.Fang Daining,Zhou Chuwei.Numerical analysis of the mechanics behavior of composites by finite element micromechanic method[J].Advances in Mechanics,1998,28(2):173-188. |
| [5] | Hassani B,Hnton E A.A review of homogenization and topology optimization I:Homogenization theory for media with periodic structure[J].Comput & Struct,1998,69:707-717. |
| [6] | Bendsor M P,Kikuchi N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1989,71:197-224. |
| [7] | 刘书田,程耿东.复合材料应力分析的均匀化方法[J].力学学报,1997,29(3):76-82.Liu Shutian,Cheng Gengdong.Homogenization method of stress analysis of composite structures[J].Chinese Journal of Theoretical and Applied Mechanics,1997,29(3):76-82. |
| [8] | 马宁,刘书田.复合材料粘弹性本构关系与热应力松弛规律研究Ⅱ:数值分析[J].复合材料学报,2005,22(1):158-163.Ma Ning,Liu Shutian.Study on the thermal stress relaxation and constitutive equations of viscoelastic composite materials Ⅱ:Numerical simulation[J].Acta Materiae Compositae Sinica,2005,22(1):158-163. |
| [9] | Terada K,Miura T,Kikuchi N.Digital image-based modeling applied to the homogenization analysis of composite materials[J].Computational Mechanics,1997,20:331-346. |
| [10] | Carey G F,Jiang B N.Element-by-element linear and non-linear solution schemes[J].Com Appl Num Meth,1986,2:145-153. |
| [11] | Chung P W,Tamma K K.Woven fabric composites:Developments in engineering bounds,homogenization and applications,AIAA-98-1812,A98-25102[R].New York:AIAA,1998:983-993. |
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%