预测复合材料有效性质的聚类有限元分析及相互作用矩阵性质研究  

FEM cluster-based analysis(FCA)for predicting effective properties of composite materials and study about interaction matrix

作　　者：聂英豪 程耿东[1] 李征[1] NIE Yinghao;CHENG Gengdong;LI Zheng(State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《大连理工大学学报》2020年第5期441-455,共15页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(U1906233)。

摘　　要：复合材料的非线性力学性质对其优化利用具有重要意义.基于数据聚类的思想,提出了聚类有限元分析(FCA)方法快速预测复合材料的非线性力学性质.在简要介绍FCA基本原理和方法的基础上,重点研究了FCA方法中联系施加在块上的均匀本征应变与块平均应力之间的相互作用矩阵,讨论了其自平衡性、完备性和奇异性.对于没有引入平均化误差的极限情况(采用常应变单元,每块一个单元),相互作用矩阵奇异完备,给出的块应力在有限元节点上满足平衡条件.对于一般情况,由于块内应变平均化引入的误差,相互作用矩阵非奇异且给出的块平均应力是在块最小势能意义下的平衡力系,通过补充块应变的协调条件,采用降阶模型和块最小余能原理仍可以高效近似预测复合材料的非线性有效性质.由于采用了块内应力应变的平均化,所得结果可为基于聚类分析的其他降阶模型方法面临类似的问题研究提供参考.The nonlinear mechanical properties of composite material are important for optimum use of the advanced material.Based on the data-clustering idea,the FEM cluster-based analysis(FCA)method is proposed to effectively predict the nonlinear mechanical properties of composite material.The basic concepts and methods of the FCA are briefly introduced and the interaction matrix,which relates the imposed cluster uniform eigenstrains and cluster average stresses is focused.The self-equilibrium,completeness and singularity of the interaction matrix are discussed in details.It is shown that for the limiting case in which each cluster has one constant strain element and no error of averaging process is introduced,the interaction matrix is singular,complete and provides the cluster stress in nodal equilibrium.For general case,due to the error introduced by averaging process,the interaction matrix is nonsingular,and the cluster stress obtained from the interaction matrix is in equilibrium in the sense of minimum potential energy principle.Supplemented by the compatibility condition,the reduced order model together with the cluster-based minimum structural complementary energy principle can be used to provide high efficient prediction of nonlinear effective properties with reasonable accuracy.Since strain and stress averaging process within one cluster is an essential step in all reduced order methods,the results obtained are valuable for reference.

关 键 词：降阶模型方法 聚类有限元分析 相互作用矩阵 非线性等效性质 

分 类 号：TB33[一般工业技术—材料科学与工程]