An eigenelement method and two homogenization conditions

Acta Mechanica Sinica/Lixue Xuebao

Volumn 25, Issue 3, 2009, Pages 345-351

  Xing, Yufeng ^a   Wang, Xingming ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

Composites; Deformation similarity; Eigenelement method; Homogenization; The equivalence of strain energy

Indexed keywords

AVERAGE METHOD; COMPOSITES; DIFFERENCE SCHEMES; EIGENELEMENT METHOD; FREQUENCY COMPARISON; HAMILTONIAN SYSTEMS; HOMOGENIZATION; STRUCTURE-PRESERVING; SYMPLECTIC; THE EQUIVALENCE OF STRAIN ENERGY; UNIT CELLS;

CELL MEMBRANES; DEFORMATION; HAMILTONIANS; STRAIN ENERGY;

HOMOGENIZATION METHOD;

EID: 67651011687     PISSN: 05677718     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10409-008-0215-5     Document Type: Article

References (19)

1. S.R. Kalidinli E. Franco 1997 Numerical evaluation of isostrain and weighted-average models for elastic moduli of three-dimensional composites Composites Sci. Technol. 57 293 305
2. I. Babuska 1976 Solution of interface problems by homogenization. Parts I, II SIAM J. Math. Anal. 7 603 645
3. Oleinik O.A., Shamaev A.V., Yosifian G.A. (1992) Mathematical Problems in Elasticity and Homogenization. North-Holland, Amsterdam
4. P.W. Chung K.K. Tamma R.R. Namburu 2001 Asymptotic expansion homogenization for heterogeneous media: computational issues and applications Composites 32 9 1291 1301
5. L.Q. Cao J.Z. Cui 2004 Asymptotic expansion and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for the second order elliptic equations in perforated domains Numer. Math. 96 525 581
6. A.L. Kalamkarov A.V. Georgiades 2004 Asymptotic homogenization models for smart composite plates with rapidly varying thickness: Part I-theory Int. J. Multiscale Comput. Eng. 2 1 133 148
7. A.V. Georgiades A.L. Kalamkarov 2004 Asymptotic homogenization models for smart composite plates with rapidly varying thickness: Part II-applications Int. J. Multiscale Comput. Eng. 2 1 149 172
8. J. Fish W. Chen G. Nagai 2000 Nonlocal dispersive model for wave propagation in heterogeneous media: multidimensional case Int. J. Multiscale Comput. Eng. 54 347 363
9. J. Fish W. Chen 2004 Space-time multiscale model for wave propagation in heterogeneous media Comp. Methods Appl. Mech. Eng. 93 4837 4856 (Pubitemid 39408004)
10. W. Chen J. Fish 2006 A generalized space-time mathematical homogenization theory for bridging atomistic and continuum scales Int. J. Numer. Methods Eng. 67 253 271 (Pubitemid 44044325)
11. J. Fish W. Chen R. Li 2007 Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions Comput. Methods Appl. Mech. Eng. 196 908 922 (Pubitemid 44644868)
12. B. Hassani E. Hinton 1998 A review of homogenization and topology optimization I-homogenization theory for media with periodic structure Comp. Struct. 69 707 717 (Pubitemid 128409876)
13. W.X. Wang D.M. Luo Y. Takao K. Kakimoto 2006 New solution method for homogenization analysis and its application to the prediction of macroscopic elastic constants of materials with periodic microstructures Comp. Struct. 84 991 1001 (Pubitemid 43668741)
14. T.Y. Hou X.H. Wu 1997 A multiscale finite element method for elliptic problems in composite materials and porous media J. Comput. Phys. 134 169 189 (Pubitemid 127175548)
15. E. Weinan B. Engquist 2002 The heterogeneous multi-scale methods Commun. Math. Sci. 1 87 132
16. Y.F. Xing J.M. Tian 2006 The homogenization method based on eigenvector expansions for woven fabric composites Int. J. Multiscale Comput. Eng. 4 1 197 206
17. Y.F. Xing J.M. Tian 2007 Unit cell eigenelement of 3-D orthogonal woven composites and its applications (in Chinese) Acta Aeronautica Astron. Sin. 28 4 881 885
18. Y.F. Xing Y. Yang 2008 A bending moment beam eigenelement with piecewise shape functions (in Chinese) Chin. J. Theor. Appl. Mech. 40 2 222 228
19. K. Feng 1986 Difference schemes for Hamiltonian formalism and symplectic geometry JCM 4 3 279 289