基于三阶剪切计算连续性方法的编织复合材料板三尺度分析模型

doi:10.7527/S1000-6893.2022.26614

Abstract

Abstract: A Third-Order Shear Computational Continua (TOS-C²) method was proposed for three-scale analysis of woven composite plates, which involves the macroscale model, mesoscale Computational Unit Cell (CUC) composed of yarns and matrix, and microscale CUC composed of fiber and matrix. The eight-node isoparametric plate element based on the Third-Order Shear Deformation Theory (TSDT) was used to discretize the macroscale problem, considering the influence of shear deformation and the moment of inertia caused by nonlinear shear strain variation along the thickness. Integrating the Computational Continua (C²) method with the finite element formulations based on the TSDT, the governing equations for three-scale problems were derived. The proposed three-scale TOS-C² method was verified by numerical examples of three-dimensional cube with quasi-isotropic inclusions. The calculated displacement and stress results of TOS-C² model show good agreement with those of Direct Numerical Simulation (DNS) model. Furthermore, the TOS-C² method was used for three-scale analysis of plain-woven composite plate, demonstrating its validity in detailed and accurate description of displacement and stress fields at three scales.

Key words: woven composite plates, three-scale, Computational Continua (C²), Third-Order Shear Deformation Theory (TSDT), finite element method

CLC Number:

V215.2
O342

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.

References

[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.

Three-scale analysis of woven composite plates based on third-order shear computational continua method

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Siji WANG, Yuwei ZHANG, Kaiming HUANG, Biao LYU, Haifeng ZHAO, Hu WANG, Mingfu LIAO. An optimization method for helicopter power turbine rotor system based on improved particle swarm optimization algorithm [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 228608-228608.
[2]	Zhenyu MA, Xiaolong DENG, Xixiang YANG, Bingjie ZHU. Thermal⁃structure coupling characteristics of flexible envelopes for stratospheric airships at float conditions [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 228337-228337.
[3]	Laixiao LU, Changguan XU, Jianhua LIU, Meizhen QIN, Yingbo LYU, Yuqin YAN. Influence of initial stress state on bilateral rolling process of thin⁃walled part [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(10): 427415-427415.
[4]	WU Zhiyuan, YAN Han, WU Linchao, MA Hui, QU Yegao, ZHANG Wenming. Vibration characteristics of rotating cracked-blade-flexible-disk coupling system [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 625442-625442.
[5]	LIU Zhihui, NIU Junchuan, JIA Ruihao. Energy flow model for high-frequency vibration of beams in thermal-gradient environment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 425336-425336.
[6]	JIN Yulin, LIU Zhiwen, CHEN Yushu. Fault simulation of blade-casing rubbing for dual-rotor system of aero-engines [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(12): 425072-425072.
[7]	ZHANG Ke, YUAN Shenfang, REN Yuanqiang, XU Yuesheng. Shape reconstruction of self-adaptive morphing wings’ fishbone based on inverse finite element method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(8): 223617-223617.
[8]	SHI Wenze, CHEN Weiwei, LU Chao, CHENG Jinjie, CHEN Yao. Characteristics and factor analyses for electromagnetic ultrasonic detection echoes in high-temperature aluminum alloy [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(12): 423854-423854.
[9]	PENG Yilin, MA Yu'e, ZHAO Yang, ZHU Liang. Shear buckling performance of Al-Li alloy stiffened panels [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(11): 423729-423729.
[10]	YUAN Weidong, GAO Zhan, LIU Haokang, MIU Guofeng. Topology optimization of composite shell damping structures based on improved optimal criteria method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(1): 223162-223162.
[11]	LIU Peng, GUO Yazhou, ZHAO Zhenqiang, XING Jun, ZHANG Chao. Meso-scale finite element simulation of compressive failure behavior of two-dimensional triaxially braided composite [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(7): 222865-222865.
[12]	TIAN Shuo, SHANG Jianqin, GAI Pengtao, CHEN Fulong, ZENG Yuansong. Numerical simulation and deformation prediction of stress peen forming for integrally-stiffened panels [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(10): 422847-422847.
[13]	CHEN Zhaolin, YANG Zhichun, WANG Yongyan, ZHANG Xinping. A high-frequency shock response analysis method based on energy finite element method and virtual mode synthesis and simulation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(8): 221893-221893.
[14]	PENG Xiao, SHU Zhan, DU Tao, XU Qiang. Peel simulating and test verification of prepreg based on laying process [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 422246-422246.
[15]	HE Huan, SONG Dapeng, ZHANG Chenkai, CHEN Guoping. Finite element model of beem considering arbitrary deformation mode of cross-section [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(12): 222228-222228.