非均质复合材料力学性能的确定性多尺度计算方法

裴世源 1; 徐华 1; 2

doi:10.7652/xjtuxb201510002

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非均质复合材料力学性能的确定性多尺度计算方法

更新时间：2025-07-09

- 非均质复合材料力学性能的确定性多尺度计算方法
- Deterministic Multiscale Method for Heterogeneous Composite Material
- 西安交通大学学报 2015年49卷第10期页码：8-13+28
- 作者机构：
  
  西安交通大学现代设计与转子轴承系统教育部重点实验室,西安,710049
- 作者简介：
- 基金信息：
  
  : 2015-01-13。作者简介: 裴世源(1983—),男,讲师。基金项目: 国家重点基础研究发展计划资助项目(2011 CB706602);陕西省科技攻关资助项目(2015GY022)
- DOI：10.7652/xjtuxb201510002
  中图分类号： TP301.6
- 网络首发：2015-10-10，
  
  纸质出版：2015
- 稿件说明：
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裴世源 1, 徐华 1, 2. 非均质复合材料力学性能的确定性多尺度计算方法[J]. 西安交通大学学报, 2015,49(10):8-13+28.

Deterministic Multiscale Method for Heterogeneous Composite Material[J]. 2015, 49(10): 8-13+28.
裴世源 1, 徐华 1, 2. 非均质复合材料力学性能的确定性多尺度计算方法[J]. 西安交通大学学报, 2015,49(10):8-13+28. DOI： 10.7652/xjtuxb201510002.

Deterministic Multiscale Method for Heterogeneous Composite Material[J]. 2015, 49(10): 8-13+28. DOI： 10.7652/xjtuxb201510002.

摘要

针对具有多尺度特性的非均质复合材料进行结构强度分析

提出了一种确定性多尺度计算方法——有限细胞法(FCM)。该方法通过矩阵凝聚和插值近似得到粗网格的刚度矩阵

在计算得到粗网格解后

通过回代技术可获得全域细网格解。为验证FCM的计算精度和计算效率

构造了多个数值算例

并与理论和有限元(FEM)结果进行了对比

结果发现:相对于FEM

FCM可显著扩大计算规模

提高计算速度

且易于并行; 相对于其他多尺度计算方法

FCM在构造粗网格刚度矩阵过程中无需引入微观边界条件

计算精度高

易于降尺度计算。因此

FCM是分析复合材料结构强度的一种有效的多尺度算法

同时该方法易于推广至多尺度的非线性结构分析、热分析、地下水渗流分析等领域。

Abstract

For the strength analysis of heterogeneous materials in elasticity

a deterministic multiscale calculation method

finite cell method(FCM)

is presented. The condensation and interpolation technique are adopted to obtain the coarse element stiffness matrix

then the original problem can be solved in coarse-scale

and the fine-scale solution can be sought out by back substitution. The comparison with analytic method and finite element method(FEM)on several numerical examples indicates that FCM enables to significantly expand computational scale and greatly improve computing rate. In FCM

the artificial boundary conditions are unnecessary for constructing macroscopic meshes

and the downscaled computing can be easily performed. FCM is also feasible for non-linear multiscale structure analysis

thermal analysis and porous flow analysis.

关键词

Keywords

references

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