一种新型整体与局部高阶层合梁模型

doi:10.7527/S1000-6893.2025.31719

Abstract

Abstract:

To accurately calculate displacements and stresses of laminated composite beams under static loading， this paper develops a new model for laminated beams. The initial displacement field of the model includes two parts which are global and local displacements. Each layer of laminated beams can be depicted by local displacement unknown variables and shape functions. By applying the interlayer displacement and shear stress continuous conditions， as well as the free conditions for transverse shear stress on up-down surfaces of the laminated beam， the final displacement field of the model is obtained， expressed by six unknown displacement variables. Finally， through a classical example， numerical results of the model show that this theory can accurately calculate the in-plane displacements and stresses of laminated beams under static loading conditions. Notably， the transverse shear stress can be directly obtained from constitutive equations without any additional processing， making the model convenient for engineering applications.

Key words: laminated beams, shear stresses continuous condition, global-local higher order model, constitutive equations, shape function

CLC Number:

V214

Junling SI, Shengqi YANG, Ying ZHANG. A new global-local higher order model for laminated composite beams[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(18): 231719.

Figures/Tables 11

Fig.1

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Table 2

Table 3

References 21

[1]	赵天，李营，张超，等. 高性能航空复合材料结构的关键力学问题研究进展［J］. 航空学报， 2022， 43（6）： 526851.
	ZHAO T， LI Y， ZHANG C， et al. Fundamental mechanical problems in high-performance aerospace composite structures： State-of-art review［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（6）： 526851 （in Chinese）.
[2]	CHAI G B， YAP C W. Coupling effects in bending， buckling and free vibration of generally laminated composite beams［J］. Composites Science and Technology， 2008， 68（7-8）： 1664-1670.
[3]	COWPER G R. The shear coefficient in Timoshenko’s beam theory［J］. Journal of Applied Mechanics， 1966， 33（2）： 335-340.
[4]	REDDY J N. A simple higher-order theory for laminated composite plates［J］. Journal of Applied Mechanics， 1984， 51（4）： 745-752.
[5]	MATSUNAGA H. A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings［J］. Composite Structures， 2004， 64（2）： 161-177.
[6]	SAYYAD A S， GHUGAL Y M， NAIK N S. Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory［J］. Curved and Layered Structures， 2015， 2（1）： 279-289.
[7]	MEICHE N E， TOUNSI A， ZIANE N， et al. A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate［J］. International Journal of Mechanical Sciences， 2011， 53（4）： 237-247.
[8]	REDDY J N. A generalization of two-dimensional theories of laminated composite plates［J］. Communications in Applied Numerical Methods， 1987， 3（3）： 173-180.
[9]	LEKHNITSKII S G. Strength calculation of composite beams［J］. Vestnik inzhen i tekhnikov， 1935， 9： 137-148.
[10]	CARRERA E. Historical review of Zig-Zag theories for multilayered plates and shells［J］. Applied Mechanics Reviews， 2003， 56（3）： 287.
[11]	DI SCIUVA M. An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates［J］. Journal of Applied Mechanics， 1987， 54（3）： 589.
[12]	DI SCIUVA M. Multilayered anisotropic plate models with continuous interlaminar stresses［J］. Composite Structures， 1992， 22（3）： 149-167.
[13]	MURAKAMI H. Laminated composite plate theory with improved in-plane responses［J］. Journal of Applied Mechanics， 1986， 53（3）： 661-666.
[14]	CHO M， PARMERTER R R. Efficient higher order composite plate theory for general lamination configurations［J］. AIAA Journal， 1993， 31（7）： 1299-1306.
[15]	ICARDI U. Applications of zig-zag theories to sandwich beams［J］. Mechanics of Advanced Materials and Structures， 2003， 10（1）： 77-97.
[16]	TESSLER A， DISCIUVA M， GHERLONE M. Refined zigzag theory for laminated composite and sandwich plates： NASA/TP-2009-215561［R］. Washington， D.C.： NASA， 2009.
[17]	TESSLER A， DI SCIUVA M， GHERLONE M. A refined zigzag beam theory for composite and sandwich beams［J］. Journal of Composite Materials， 2009， 43（9）： 1051-1081.
[18]	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.
	YANG S Q， ZHANG Y C， LIU S T. A new zig-zag theory for accurately predicting interlaminar shear stress of laminated beam structures［J］. Acta Aeronautica et Astronautica Sinica， 2019， 40（11）： 223028 （in Chinese）.
[19]	SI J L， CHEN W J， YI S J， et al. A new and efficient zigzag theory for laminated composite plates［J］. Composite Structures， 2023， 322： 117356.
[20]	GROH R M J， WEAVER P M. On displacement-based and mixed-variational equivalent single layer theories for modelling highly heterogeneous laminated beams［J］. International Journal of Solids and Structures， 2015， 59： 147-170.
[21]	PAGANO N J. Exact solutions for composite laminates in cylindrical bending［J］. Journal of Composite Materials， 1969， 3（3）： 398-411.

L/h	铺层3层：0°/90°/0°			铺层4层：0°/90°/0°/90°
L/h	Pagano	NGLHT计算	误差/%	Pagano	NGLHT计算	误差/%
2	8.588 0	8.769 7	2.09	11.435 8	11.530 1	0.82
4	2.893 4	2.906 3	0.45	4.191 1	4.192 3	0.03
10	0.932 5	0.931 0	0.16	1.658 7	1.650 0	0.52
20	0.617 9	0.615 4	0.40	1.259 7	1.250 9	0.70
50	0.527 6	0.524 8	0.53	1.145 8	1.137 2	0.75
100	0.514 6	0.511 8	0.54	1.129 5	1.120 8	0.77
1 000	0.510 3	0.507 5	0.55	1.124 1	1.1154	0.77

理论模型	W（L/2，0）		U（0，-h/2）		S_x （L/2，h/2）		S（C）_xz （0，0）		S（E）_xz （0，0）
理论模型	计算值	误差/%	计算值	误差/%	计算值	误差/%	计算值	误差/%	计算值	误差/%
Pagano	3.269 2		1.072 9		21.500 4		1.649 7		1.649 7
NGLHT	3.274 8	0.17	1.075 9	0.28	21.266 2	1.09	1.661 8	0.73	1.646 0	0.22
RZT	3.074 2	5.96	0.871 0	18.81	17.145 1	20.27	1.351 8	18.06	1.808 2	9.61
RHSDT	2.792 5	14.58	1.093 9	1.96	21.533 2	0.15	1.028 1	37.68	1.608 3	2.51

理论模型	W（L/2，0）		U（0，h/2）		S_x （L/2，-h/2）		S（C）_xz （0，0）		S（E）_xz （0，0）
理论模型	计算值	误差/%	计算值	误差/%	计算值	误差/%	计算值	误差/%	计算值	误差/%
Pagano	3.581 2		-1.603 7		-23.192 4		1.765 2		1.765 2
NGLHT	3.574 8	0.18	-1.550 0	3.34	-23.391 3	0.86	1.803 9	2.19	1.744 6	1.17
RZT	3.160 7	11.74	-0.953 0	40.57	-18.895 0	18.55	1.263 7	28.41	1.922 3	8.90
RHSDT	3.076 4	14.09	-1.393 9	13.08	-24.459 9	5.47	1.064 7	39.68	1.757 9	0.41

A new global-local higher order model for laminated composite beams

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 11

References 21

Related Articles 7

Recommended Articles

Metrics

Comments

[1]	Yifeng HUANG, Shuhua ZENG, Zhongzheng JIANG, Weifang CHEN. Numerical study on high-altitude lateral jet based on nonlinear coupled constitutive relation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 8-22.
[2]	LUO Junting, ZHAO Jingqi, YANG Zheyi, LIU Weipeng, ZHANG Chunxiang. Microstructure prediction of multi-directional forging of TA15 alloy based on secondary development of Deform and BP neural network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(12): 424693-424693.
[3]	LI Tuo, BAI Hongbai, CAO Fengli. A quasi-static compression constitutive model for knitted-dapped metal rubber considering temperature effect [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(10): 422062-422062.
[4]	YANG Wu, LIU Li, ZHOU Sida, MA Zhisai. Modal parameter identification of linear time-varying structures using Kriging shape function [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(4): 1169-1176.
[5]	WANG Linpeng, WANG Hanping, YANG Ming, BI Shihua, WANG Shaozhu. Multi-body Dynamics Analysis Method for Vibration of Flexible Guide Activated by Moving Missile [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(3): 756-763.
[6]	ZHANG Zhenming, DING Yunliang, LIU Yi, ZHANG Tieliang. Shape Optimization Design Method for the Conceptual Design of Reentry Vehicles [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(11): 1971-1979.
[7]	HUANG Zai-xing. INFLUENCE OF THE CONSTITUTIVE EQUATIONS ON THE WELL-POSEDNESS OF FUNDAMENTAL EQUATIONS IN CONTINUUM DAMAGE MECHANICS ——THE CASE OF ONE DIMENSION ELASTIC DAMAGE [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2000, 21(2): 124-127.