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浙江大学学报(工学版)
交通工程、土木工程     
考虑界面不可压的高阶组合梁静力弯曲——位移法与混合型的有限元分析
何光辉,汪德江,杨骁
上海大学 土木工程系,上海200072
Static bending of higher order composite beams considering interfacial incompressibility:displacement and hybrid based finite element analysis
HE Guang hui, WANG De jiang, YANG Xiao
Department of Civil Engineering, Shanghai University, Shanghai 200072,China
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摘要:

为了真实地描述组合梁的界面相互作用和各子梁的力学行为,提出一种考虑界面不可压缩性与各子梁高阶位移的双层组合梁模型.根据最小势能原理和广义最小势能原理,得到高阶组合梁静力分析的位移法和混合型有限元方程.讨论变分原理类型和基本未知量的插值阶次对组合梁位移和内力收敛性能的影响.对比基于所提出的高阶组合梁模型、Reddy高阶组合梁模型、Newmark模型和平面应力模型的简支组合梁的静力分析结果,验证所建立的高阶模型的合理性.分析组合梁界面横向不可压缩性对其挠度的影响.结果表明:与Reddy模型相比,所提出的高阶模型更精细地刻画了组合梁结构;混合型单元具有抗滑移锁死性能;组合梁的界面不可压缩性对其挠度分析的影响不可忽略.

Abstract:

A two layer composite beam model was proposed to formulate the interfacial interaction and the mechanical behavior of each sub layer  realistically. The model incorporated the higher order displacement of each sub layer and the incompressibility of each sub layers interface. Displacement and hybrid based finite element (FE) equations for static analysis were respectively obtained according to the principle of minimum potential energy (PMPE) and the generalized PMPE. The convergence performances of the proposed FE on  the displacement and the internal force were discussed, resulting from the variational principle type and the interpolation order of the basic unknowns. A comparison was made among the static analysis results of simply supported composite beams generated by the proposed higher order beam model (HOBM), Reddy HOBM, Newmarks model and plane stress model to verify the reliability of the proposed model. The influence of interfacial incompressibility on the composite beam deflection was analyzed. The results show that the proposed HOBM may depict the composite beam structure more finely than the Reddys mode. The hybrid element is free of slip locking, and the interfacial incompressibility has unnegligible influence on  the deflection analysis.

出版日期: 2015-10-15
:  TU 323.3  
基金资助:

 国家“863”高技术研究发展计划资助项目(2009AA0323032).

通讯作者: 汪德江,男,讲师,博士.ORCID:0000 0003 1989 9426.     E-mail: djwang@shu.edu.cn
作者简介: 何光辉(1984-),男,博士,从事结构数值分析方法研究. ORCID:0000 0002 6461 631X. E-mail: flamehe@shu.edu.cn
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引用本文:

何光辉,汪德江,杨骁. 考虑界面不可压的高阶组合梁静力弯曲——位移法与混合型的有限元分析[J]. 浙江大学学报(工学版), 10.3785/j.issn.1008 973X.2015.09.014.

HE Guang hui, WANG De jiang, YANG Xiao. Static bending of higher order composite beams considering interfacial incompressibility:displacement and hybrid based finite element analysis. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 10.3785/j.issn.1008 973X.2015.09.014.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008 973X.2015.09.014        http://www.zjujournals.com/eng/CN/Y2015/V49/I9/1716

[1] NEWMARK N M, SIESS C P, VIEST I M. Test and analysis of composite beams with incomplete interaction [J]. Proceeding Society for Experimental Stress Analysis, 1951, 19(1): 75-92.
[2] ASTA A D, ZONA A. Slip locking in finite elements for composite beams with deformable shear connection [J]. Finite Elements in Analysis and Design, 2004, 40(13/14): 1907-1930.
[3] RANZI G, BRADFORD M A. Direct stiffness analysis of a composite beam column element with partial interaction [J]. Computers and Structures, 2007, 85(15/16): 1206-1214.
[4] 曾兴贵, 周东华, 李龙起, 等. 组合梁界面滑移的计算分析 [J]. 工程力学, 2013, 30(6): 162-174.
ZHENG Xing gui, ZHOU Dong hua, LI Long qi, et al. Calculation and analysis of interface slip of composite beams [J]. Engineering Mechanics, 2013, 30(6): 162-174.
[5] ERKMEN R E, ATTARD M M. Displacement based finite element formulations for material nonlinear analysis of composite beams and treatment of locking behaviour [J]. Finite Elements in Analysis and Design, 2011, 47(12): 1293-1305.
[6] SANTOS H, SILBERSCHMIDT V V. Hybrid equilibrium finite element formulation for composite beams with partial interaction [J]. Composite Structures, 2014, 108: 646-656.
[7] NGUYEN Q, MARTINELLI E, HJIAJ M. Derivation of the exact stiffness matrix for a two layer Timoshenko beam element with partial interaction [J]. Engineering Structures, 2011, 33(2): 298-307.
[8] SUN F, BURSI O S. Displacement based and two field mixed variational formulations for composite beams with shear lag [J]. Journal of Engineering Mechanics, ASCE, 2005, 131(2): 199-210.
[9] GARA F, RANZI G, LEONI G. Displacement based formulations for composite beams with longitudinal slip and vertical uplift [J]. International Journal for Numerical Methods in Engineering, 2006, 65(8): 1197-1220.
[10] KROFLIC A, PLANINC I, SAJE M, et al. Non linear analysis of two layer timber beams considering interlayer slip and uplift [J]. Engineering Structures, 2010, 32(6): 1617-1630.
[11] KROFLIC A, SAJE M, PLANINC I. Non linear analysis of two layer beams with interlayer slip and uplift [J]. Computers and Structures, 2011, 89(23/24): 2414-2424.
[12] WHITNEY J M. Shear correction factors for orthotropic laminates under static load [J]. Journal of Applied Mechanics, 1973, 40(1): 302-304.
[13] HE G, YANG X. Finite element analysis for buckling of two layer composite beams using Reddys higher order beam theory [J]. Finite Elements in Analysis and Design, 2014, 83: 49-57.
[14] CHAKRABARTI A, SHEIKH A H, GRIFFITH M, et al. Dynamic response of composite beams with partial shear interaction using a higher order beam theory [J]. Journal of Structural Engineering, 2012, 139(1): 47-56.
[15] REDDY J N. A simple higher order theory for laminated composite plates [J]. Journal of Applied Mechanics, 1984, 51(4): 745-752.
[16] 老大中. 变分法基础 [M]. 2版.北京: 国防工业出版社, 2011.
[17] ZIENKIEWICZ O C, TAYLOR R L. The Finite Element Method Volume 2: Solid Mechanics [M]. 5th ed. London: Butterworth Heinemann, 2000.
[18] XU R, WU Y. Two dimensional analytical solutions of simply supported composite beams with interlayer slips [J]. International Journal of Solids and Structures, 2007, 44(1): 165-175.
[19] GIRHAMMAR U A, GOPU V K. Composite beam columns with interlayer slip exact analysis [J]. Journal of Structural Engineering, ASCE, 1993, 119(4): 1265-1282.
[20] SILVA A R, SOUSA. J B M. A family of interface elements for the analysis of composite beams with interlayer slip [J]. Finite Elements in Analysis and Design, 2009, 45(5): 305-314.
[21] CHAKRABARTI A, SHEIKH A H, GRIFFITH M, et al. Analysis of composite beams with longitudinal and transverse partial interactions using higher order beam theory [J]. International Journal of Mechanical Sciences, 2012, 59(1): 115-125.

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