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

万傲霜; 王振名; 李顶河

doi:10.7527/S1000-6893.2022.26614

航空学报 >

2022 , Vol. 43 >Issue 12: 226614 - 226614

DOI: https://doi.org/10.7527/S1000-6893.2022.26614

固体力学与飞行器总体设计

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

万傲霜 ,
王振名 ,
李顶河

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中国民航大学航空工程学院, 天津 300300

收稿日期: 2021-11-03

修回日期: 2021-12-08

网络出版日期: 2022-01-26

基金资助

国家自然科学基金（12072364）

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

WAN Aoshuang ,
WANG Zhenming ,
LI Dinghe

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College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China

Received date: 2021-11-03

Revised date: 2021-12-08

Online published: 2022-01-26

Supported by

National Natural Science Foundation of China (12072364)

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摘要

提出了基于三阶剪切计算连续性（TOS-C²）方法的编织复合材料板三尺度分析模型，包括宏观尺度模型、由纤维束和基体构成的介观尺度计算胞元（CUC）、由单丝纤维和基体构成的微观尺度CUC。采用基于三阶剪切变形理论（TSDT）的八节点四边形板单元对宏观问题进行离散，考虑了剪切变形和沿厚度方向非线性剪切应变变化引起的转动惯量。将计算连续性（C²）方法与基于TSDT的有限元方程相结合，推导了三尺度问题的控制方程。利用含夹杂三维立方体的数值算例，验证了提出的三尺度TOS-C²方法的有效性，TOS-C²模型的位移和应力计算结果与直接数值模拟（DNS）模型吻合良好。采用TOS-C²方法对平面编织复合材料板进行三尺度分析，获得了详细准确的三尺度位移场和应力场。

关键词： 编织复合材料板; 三尺度; 计算连续性(C²); 三阶剪切变形理论(TSDT); 有限元方法

本文引用格式

万傲霜 , 王振名 , 李顶河 . 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[J]. 航空学报, 2022 , 43(12) : 226614 -226614 . DOI: 10.7527/S1000-6893.2022.26614

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

参考文献

[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.

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