一种准确预测层合梁结构层间剪应力的新锯齿理论

doi:10.7527/S1000-6893.2019.23028

固体力学与飞行器总体设计

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一种准确预测层合梁结构层间剪应力的新锯齿理论

杨胜奇, 张永存, 刘书田

大连理工大学工程力学系工业装备结构分析国家重点实验室, 大连 116024

收稿日期:2019-03-26 修回日期:2019-04-22 出版日期:2019-12-03 发布日期:2019-07-15
通讯作者: 刘书田 E-mail:stliu@dlut.edu.cn
基金资助:
国家自然科学基金（U1808215，11572071，11572073）；中央高校基本科研业务费专项资金（DUT18ZD103）；111引智计划（B14013）

A new zig-zag theory for accurately predicting interlaminar shear stress of laminated beam structures

YANG Shengqi, ZHANG Yongcun, LIU Shutian

State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China

Received:2019-03-26 Revised:2019-04-22 Online:2019-12-03 Published:2019-07-15
Supported by:
National Natural Science Foundation of China (U1808215, 11572071, 11572073); the Fundamental Research Funds for the Central Universities of China (DUT18ZD103); 111 Project (B14013)

摘要/Abstract

摘要： 层合梁是航空航天领域典型的承力构件，而过大的层间剪应力（层间处的横向剪应力）是导致其分层失效的主要原因。针对常见的层数较多的复合材料层合梁以及材料属性差异较大的三明治夹层梁，现有的理论模型仍然无法准确预测其横向剪应力。通过构造一个新的线性分段锯齿函数，提出了一种能够准确预测层合梁结构横向剪应力的新锯齿理论模型。几个典型的数值算例表明，本文提出的新锯齿理论模型在计算层数较多和材料属性差异较大的层合梁时，具有较高的计算精度，能够准确预测层合梁的分层。另外，该模型预先满足横向剪应力层间连续条件，无需三维平衡方程后处理就能够准确预测层合梁的横向剪应力。位移场中未知量个数少，不含横向位移的一阶导，便于C⁰梁单元的构造。

关键词: 锯齿理论, 层合梁, 夹层梁, 层间应力, Reissner混合变分原理

Abstract: Laminated beams are typical bearing members in the aerospace industry. Excessive interlaminar shear stress (transverse shear stress at the interlayer) is the main cause of delamination failure. The existing laminated beam models can not accurately predict the transverse shear stress for the composite laminated beams with large number of layers and sandwich beams with large differences in material properties. In this study, a new zig-zag theoretical model that can accurately predict the transverse shear stress of laminated beams is proposed by constructing a new linear piecewise zig-zag function. Several typical numerical examples show that the new zig-zag theoretical model has higher calculation accuracy for the composite laminated beams with large number of layers and sandwich beams with large differences in material properties, and can predict the delamination of laminated beams. In addition, the model fulfills a priori the interlaminar transverse shear stress continuous condition at the interfaces and can accurately predict the transverse shear stress of laminated beam without the post-processing of three-dimensional equilibrium equation. The number of unknown variables of this model in displacement field is small. Without the first derivatives of transverse displacement in the displacement field, this model is well suited for developing C⁰ elements.

Key words: zig-zag theory, laminated beam, sandwich beam, interlaminar stress, Reissner mixed variational theorem

中图分类号:

V214.8

杨胜奇, 张永存, 刘书田. 一种准确预测层合梁结构层间剪应力的新锯齿理论[J]. 航空学报, 2019, 40(11): 223028-223028.

YANG Shengqi, ZHANG Yongcun, LIU Shutian. A new zig-zag theory for accurately predicting interlaminar shear stress of laminated beam structures[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(11): 223028-223028.

参考文献 36

[1]	欧阳小穗, 刘毅. 高速流场中变刚度复合材料层合板颤振分析[J]. 航空学报, 2018, 39(3):221539. OUYANG X S, LIU Y. Panel flutter of variable stiffness composite laminates in supersonic flow[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(3):221539(in Chinese).
[2]	卓航, 李是卓, 韩恩林, 等. 高强高模聚酰亚胺纤维增强环氧树脂复合材料力学性能与破坏机制[J]. 复合材料学报, 2019, 36(9):2101-2109. ZHUO H, LI S Z, HAN E L, et al. Mechanical properties and failure mechanism of high strength and high modulus polyimide fiber reinforced epoxy composites[J]. Acta Materiae Compositae Sinica, 2019, 36(9):2101-2109(in Chinese).
[3]	沈裕峰, 李勇, 王鑫, 等. 湿热环境下K-cor夹层复合材料的力学性能[J]. 航空学报, 2016, 37(7):2303-2311. SHEN Y F, LI Y, WANG X, et al. Mechanical properties of K-cor sandwich composite under hygrothermal environment[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(7):2303-2311(in Chinese).
[4]	李汪颖, 杨雄伟, 李跃明. 多孔材料夹层结构声辐射特性的两尺度拓扑优化设计[J]. 航空学报, 2016, 37(4):1196-1206. LI W Y, YANG X W, LI Y M. Two-scale topology optimization design of sandwich structures of a porous core with respect to sound radiation[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(4):1196-1206(in Chinese).
[5]	LIU Y, ZHANG Y C, LIU S T, et al. Effect of unbonded areas around hole on the fatigue crack growth life of diffusion bonded titanium alloy laminates[J]. Engineering Fracture Mechanics, 2016, 163:176-188.
[6]	顾轶卓, 李敏, 李艳霞, 等. 飞行器结构用复合材料制造技术与工艺理论进展[J]. 航空学报, 2015, 36(8):2773-2797. GU Y Z, LI M, LI Y X, et al. Progress on manufacturing technology and process theory of aircraft composite structure[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(8):2773-2797(in Chinese).
[7]	PHIL E, SOUTIS C. Polymer composites in the aerospace industry[M]. Armstand:Elsevier, 2014.
[8]	BOLOTIN V V. Delaminations in composite structures:Its origin, buckling, growth and stability[J]. Composites Part B:Engineering, 1996, 27(2):129-145.
[9]	赵丽滨, 龚愉, 张建宇. 纤维增强复合材料层合板分层扩展行为研究进展[J]. 航空学报, 2019, 40(1):171-199. ZHAO L B, GONG Y, ZHANG J Y. A survey on the delamination growth behavior in fiber reinforced composite laminates[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):171-199(in Chinese).
[10]	孙长玺. 基于形状等效和刚度折减的复合材料分层损伤分析方法[D]. 大连:大连理工大学, 2016:1-2. SUN C X. Analysis method for composite delamination based on shape simplification and stiffness degradation[D]. Dalian:Dalian University of Technology, 2016:1-2(in Chinese).
[11]	REISSNER E. The effect of transverse shear deformation on the bending of elastic plates[J]. Journal of Applied Mechanics, 1945, 12:69-77.
[12]	REDDY J N. A simple higher-order theory for laminated composite plates[J]. Journal of Applied Mechanics, 1984, 51(4):745-752.
[13]	REDDY J N. An evaluation of equivalent-single-layer and layerwise theories of composite laminates[J]. Composite structures, 1993, 25(1-4):21-35.
[14]	XING Y F, WU Y, LIU B, et al. Static and dynamic analyses of laminated plates using a layerwise theory and a radial basis function finite element method[J]. Composite Structures, 2017, 170:158-168.
[15]	MURAKAMI H. Laminated composite plate theory with improved in-plane responses[J]. Journal of Applied Mechanics, 1986, 53(3):661-666.
[16]	DI SCIUVA M. Multilayered anisotropic plate models with continuous interlaminar stresses[J]. Composite Structures, 1992, 22(3):149-167.
[17]	CHO M, PARMERTER R. Efficient higher order composite plate theory for general lamination configurations[J]. AIAA Journal, 1993, 31(7):1299-1306.
[18]	TESSLER A, DI SCIUVA M, GHERLONE M. A refined zigzag beam theory for composite and sandwich beams[J]. Journal of Composite Materials, 2009, 43:1051-1081.
[19]	REDDY J N. Mechanics of laminated composite plates and shells:Theory and analysis[M]. 2nd ed. Boca Raton:CRC press, 2004.
[20]	CARRERA E. Cz0 requirements-models for the two dimensional analysis of multilayered structures[J]. Composite Structures, 1997, 37(3-4):373-383.
[21]	LEKHNITSKII S G. Strength calculation of composite beams[J]. Vestnik inzhen itekhnikov 1935. No. 9.
[22]	DI SCIUVA M. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates:An evaluation of a new displacement model[J]. Journal of Sound and Vibration, 1986, 105(3):425-442.
[23]	CHO M, OH J. Higher order zig-zag plate theory under thermo-electric-mechanical loads combined[J]. Composites Part B:Engineering, 2003, 34(1):67-82.
[24]	TESSLER A. Refined zigzag theory for homogeneous, laminated composite, and sandwich beams derived from Reissner's mixed variational principle[J]. Meccanica, 2015, 50(10):2621-2648.
[25]	IURLARO L, GHERLONE M, DI SCIUVA M, et al. Refined Zigzag Theory for laminated composite and sandwich plates derived from Reissner's Mixed Variational Theorem[J]. Composite Structures, 2015, 133:809-817.
[26]	贺丹, 杨万里. 基于广义变分原理和锯齿理论的高精度层合梁模型[J]. 宇航总体技术, 2017, 1(2):26-32. HE D, YANG W L. A high-accuracy composite laminated beam model based on generalized variational principle and zigzag theory[J]. Astronautical Systems Engineering Technology, 2017, 1(2):26-32(in Chinese).
[27]	郭绍伟, 张永存, 宋恩鹏, 等. 开孔碳纤维层合板层间应力分析[J]. 复合材料学报, 2011, 28(5):228-233. GUO S W, ZHANG Y C, SONG E P, et al. Interlaminar stress analysis of carbon fiber reinforced laminated plate with a hole[J]. Acta Materiae Compositae Sinica, 2011, 28(5):228-233(in Chinese).
[28]	刘颖卓, 张永存, 刘书田, 等. 考虑复合材料蒙皮稳定性的飞机翼面结构布局优化设计[J]. 航空学报, 2010, 31(10):1985-1992. LIU Y Z, ZHANG Y C, LIU S T, et al. Layout optimization design of wing structures with consideration of stability of composite skin[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31(10):1985-1992(in Chinese).
[29]	CARRERA E. On the use of the Murakami's zig-zag function in the modeling of layered plates and shells[J]. Computers & Structures, 2004, 82(7-8):541-554.
[30]	WU Z, CHEN W J. A global higher-order zig-zag model in terms of the HW variational theorem for multilayered composite beams[J]. Composite Structures, 2016, 158:128-136.
[31]	REN X H, CHEN W J, WU Z. A new zig-zag theory and C0 plate bending element for composite and sandwich plates[J]. Archive of Applied Mechanics, 2011, 81(2):185-197.
[32]	REN X H, CHEN W J, WU Z. A C0-type zig-zag theory and finite element for laminated composite and sandwich plates with general configurations[J]. Archive of Applied Mechanics, 2012, 82(3):391-406.
[33]	WU Z, SH L O, REN X H. A C0 zig-zag model for the analysis of angle-ply composite thick plates[J]. Composite Structures, 2015, 127:211-223.
[34]	HAN J W, KIM J S, CHO M. Generalization of the C0-type zig-zag theory for accurate thermomechanical analysis of laminated composites[J]. Composites Part B:Engineering, 2017, 122:173-191.
[35]	PANDEY S, PRADYUMMA S. A new C0 higher-order layerwise finite element formulation for the analysis of laminated and sandwich plates[J]. Composite Structures, 2015, 131:1-16.
[36]	DI SCIUVA M, GHERLONE M, IURLARO L, et al. A class of higher-order C0 composite and sandwich beam elements based on the refined zigzag theory[J]. Composite Structures, 2015, 132:784-803.

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一种准确预测层合梁结构层间剪应力的新锯齿理论

A new zig-zag theory for accurately predicting interlaminar shear stress of laminated beam structures

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[2]	李顺林;肖军. 有限宽层合板边界效应影响拉伸强度的修正方法[J]. 航空学报, 1989, 10(8): 403-408.
[3]	杨秉宪. 考虑层间应力的复合材料层板优化设计[J]. 航空学报, 1988, 9(8): 324-329.
[4]	徐明;徐桂祺. 层合梁在大挠度下弯扭耦合变形的有限元分析[J]. 航空学报, 1988, 9(4): 132-139.
[5]	刘夏石. 复合材料、蜂窝夹层和/或金属结构有限元分析[J]. 航空学报, 1987, 8(4): 147-156.
[6]	熊跃熙;王俊奎. 纤维铺设角对Beck型层合梁柱临界值的影响[J]. 航空学报, 1987, 8(11): 628-631.
[7]	叶林;杨秉宪. 受弯曲对称复合材料层板的层间应力分析[J]. 航空学报, 1986, 7(3): 234-240.