WAN Aoshuang , WANG Zhenming , LI Dinghe . Three-scale analysis of woven composite plates based on third-order shear computational continua method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(12) : 226614 -226614 . DOI: 10.7527/S1000-6893.2022.26614

[1] HUANG T, WANG Y L, WANG G. Review of the mechanical properties of a 3D woven composite and its applications[J]. Polymer-Plastics Technology and Engineering, 2018, 57(8):740-756.
[2] GONZÁLEZ C, VILATELA J J, MOLINA-ALDAREG-UÍA J M, et al. Structural composites for multifunctional applications:current challenges and future trends[J]. Progress in Materials Science, 2017, 89:194-251.
[3] 郑锡涛, 杨胜春, 叶天麒. 美国纺织复合材料在航空结构上的应用研究(一)[J]. 航空工程与维修, 2001(5):13-14. ZHENG X T, YANG S C, YE T Q. Research on the application of American textile composites in aviation structure (I)[J]. Aviation Engineerging & Mainienance, 2001(5):13-14(in Chinese).
[4] 郑锡涛, 杨胜春, 叶天麒. 美国纺织复合材料在航空结构上的应用研究(二)[J]. 航空工程与维修, 2001(6):40-42. ZHENG X T, YANG S C, YE T Q. Research on the application of American textile composites in aviation structure (Ⅱ)[J]. Aviation Engineerging & Mainienance, 2001(6):40-42(in Chinese).
[5] 詹世革, 孟庆国, 方岱宁. 航空航天纺织结构复合材料力学性能研究进展与展望[J]. 中国基础科学, 2008, 10(2):5-10. ZHAN S G, MENG Q G, FANG D N. Advances on investigations of mechanical properties of textile structural composites in aeronautics and astronautics[J]. China Basic Science, 2008, 10(2):5-10(in Chinese).
[6] TERADA K, KIKUCHI N. A class of general algorithms for multi-scale analyses of heterogeneous media[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(40-41):5427-5464.
[7] MATSUI K, TERADA K, YUGE K. Two-scale finite element analysis of heterogeneous solids with periodic microstructures[J]. Computers & Structures, 2004, 82(7-8):593-606.
[8] SMIT R J M, BREKELMANS W A M, MEIJER H E H. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 155(1-2):181-192.
[9] FEYEL F, CHABOCHE J L. FE² multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 183(3-4):309-330.
[10] WATSON A, MASON J, BENSOUSSAN A. Asymptotic analysis for periodic structures[J]. Encyclopedia of Mathematics and Its Applications, 1991, 20(2):307-309.
[11] YU X G, CUI J Z. The prediction on mechanical properties of 4-step braided composites via two-scale method[J]. Composites Science and Technology, 2007, 67(3-4):471-480.
[12] GHOSH S, LEE K, MOORTHY S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 132(1-2):63-116.
[13] MIEHE C. Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation[J]. International Journal for Numerical Methods in Engineering, 2002, 55(11):1285-1322.
[14] CAO L Q. Iterated two-scale asymptotic method and numerical algorithm for the elastic structures of composite materials[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(27-29):2899-2926.
[15] ZHANG H W, WU J K, FU Z D. Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials[J]. Computational Mechanics, 2010, 45(6):623-635.
[16] 袁欣, 孙慧玉. 黏弹性树脂基三维编织复合材料的变温松弛模量[J]. 航空学报, 2012, 33(6):1036-1043. YUAN X, SUN H Y. Relaxation modulus of viscoelastic resin-based 3D braided composites under variable temperatures[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(6):1036-1043(in Chinese).
[17] 杨强, 解维华, 孟松鹤, 等. 复合材料多尺度分析方法与典型元件拉伸损伤模拟[J]. 复合材料学报, 2015, 32(3):617-624. YANG Q, XIE W H, MENG S H, et al. Multi-scale analysis method of composites and damage simulation of typical component under tensile load[J]. Acta Materiae Compositae Sinica, 2015, 32(3):617-624(in Chinese).
[18] 胡殿印, 杨尧, 郭小军, 等. 一种平纹编织复合材料的三维通用单胞模型[J]. 航空动力学报, 2019, 34(3):608-615. HU D Y, YANG Y, GUO X J, et al. A 3D general method of cells model for plain weave composites[J]. Journal of Aerospace Power, 2019, 34(3):608-615(in Chinese).
[19] LIU S T, ZHANG Y C. Multi-scale analysis method for thermal conductivity of porous material with radiation[J]. Multidiscipline Modeling in Materials and Structures, 2006, 2(3):327-344.
[20] CAO L Q, CUI J Z. Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains[J]. Numerische Mathematik, 2004, 96(3):525-581.
[21] YANG Z Q, CUI J Z, NIE Y F, et al. The second-order two-scale method for heat transfer performances of periodic porous materials with interior surface radiation[J]. CMES:Computer Modeling in Engineering & Sciences, 2012, 88(5):419-442.
[22] YANG Z Q, CUI J Z, SUN Y. Transient heat conduction problem with radiation boundary condition of statistically inhomogeneous materials by second-order two-scale method[J]. International Journal of Heat and Mass Transfer, 2016, 100:362-377.
[23] MA Q, CUI J Z. Second-order two-scale analysis method for the heat conductive problem with radiation boundary condition in periodical porous domain[J]. Communications in Computational Physics, 2013, 14(4):1027-1057.
[24] TRUCU D, CHAPLAIN M A J, MARCINIAK-CZOCHRA A. Three-scale convergence for processes in heterogeneous media[J]. Applicable Analysis, 2012, 91(7):1351-1373.
[25] ABDULLE A, BAI Y. Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales[J]. IMA Journal of Numerical Analysis, 2014, 35(1):133-160.
[26] MA Q, YE S Y, CUI J Z, et al. Two-scale and three-scale asymptotic computations of the Neumann-type eigenvalue problems for hierarchically perforated materials[J]. Applied Mathematical Modelling, 2021, 92:565-593.
[27] YANG Z Q, SUN Y, CUI J Z, et al. A three-scale homogenization algorithm for coupled conduction-radiation problems in porous materials with multiple configurations[J]. International Journal of Heat and Mass Transfer, 2018, 125:1196-1211.
[28] YANG Z Q, SUN Y, CUI J Z, et al. A three-scale asymptotic expansion for predicting viscoelastic properties of composites with multiple configuration[J]. European Journal of Mechanics-A/Solids, 2019, 76:235-246.
[29] YANG Z Q, SUN Y, GUAN T Y, et al. A high-order three-scale approach for predicting thermo-mechanical properties of porous materials with interior surface radiation[J]. Computers & Mathematics with Applications, 2020, 79(9):2742-2770.
[30] YANG Z Q, LONG C Z, SUN Y. A high-order three-scale reduced asymptotic approach for thermo-mechanical problems of nonlinear heterogeneous materials with multiple spatial scales[J]. European Journal of Mechanics-A/Solids, 2020, 80:103905.
[31] YANG Z Q, SUN Y, CUI J Z, et al. A high-order three-scale reduced homogenization for nonlinear heterogeneous materials with multiple configurations[J]. Journal of Computational Physics, 2021, 425:109900.
[32] FISH J, KUZNETSOV S. Computational continua[J]. International Journal for Numerical Methods in Engineering, 2010, 84(7):774-802.
[33] FISH J, FILONOVA V, YUAN Z. Reduced order computational continua[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 221-222:104-116.
[34] FILONOVA V, FAFALIS D, FISH J. Dispersive computational continua[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 298:58-79.
[35] FISH J, FILONOVA V, FAFALIS D. Computational continua revisited[J]. International Journal for Numerical Methods in Engineering, 2015, 102(3-4):332-378.
[36] FILONOVA V, FISH J. Computational continua for thick elastic layered structures[J]. International Journal for Multiscale Computational Engineering, 2016, 14(5):439-454.
[37] LI D H, WANG Z M, ZHANG C. Computational continua method and multilevel-multisite mesh refinement method for multiscale analysis of woven composites laminates[J]. Composite Structures, 2021, 259:113441.
[38] MOYEDA A, FISH J. Towards practical multiscale approach for analysis of reinforced concrete structures[J]. Computational Mechanics, 2018, 62(4):685-700.
[39] MOYEDA A, FISH J. Multiscale analysis of prestressed concrete structures[J]. International Journal for Multiscale Computational Engineering, 2018, 16(3):285-301.
[40] LI D H, FISH J, YUAN Z F. Two-scale and three-scale computational continua models of composite curved beams[J]. International Journal for Multiscale Computational Engineering, 2018, 16(6):527-554.