全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
工程力学  2015 

Reddy高阶组合梁的非线性有限元分析

DOI: 10.6052/j.issn.1000-4750.2014.01.0047, PP. 87-95

Keywords: Reddy高阶梁理论,组合梁,材料非线性,有限元法,剪切效应

Full-Text   Cite this paper   Add to My Lib

Abstract:

该文基于Reddy高阶梁理论,提出了小变形双层组合梁的隐式运动学假定;应用拉格朗日乘子法,将该隐式关系引入到组合梁的最小势能原理,得到了考虑各子梁和粘结滑移层非线性材料特性的高阶组合梁非线性位移法有限单元,且该单元可以容易地转化为非线性Timoshenko和Euler-Bernoulli组合梁有限单元。随后,该研究分别应用提出的Reddy、Timoshenko和Euler-Bernoulli组合梁有限单元对双跨连续钢-混凝土组合梁进行了准静力分析,考察剪切效应对组合梁构件的挠度、粘结层滑移和截面应力的影响,且参数分析了组合梁的跨高比对剪切效应的影响。参数分析表明:短粗组合梁结构往往表现出显著的剪切效应,Newmark假定不再适用。

References

[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. Zeng Xinggui, Zhou Donghua, Li Longqi, et al. Calculation and analysis of interface slip of composite beams [J]. Engineering Mechanics, 2013, 30(6): 162―174. (in Chinese)
[5]  Dall’Asta A, Zona A. Non-linear analysis of composite beams by a displacement approach [J]. Computers and Structures, 2002, 80(27/28/29/30): 2217―2228.
[6]  Dall'Asta A, Zona A. Comparison and validation of displacement and mixed elements for the non-linear analysis of continuous composite beams [J]. Computers and Structures, 2004, 82(23/24/25/26): 2117―2130.
[7]  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.
[8]  欧阳煜, 刘慧, 杨骁. 考虑粘结滑移效应的组合梁弯曲[J]. 工程力学, 2012, 29(9): 215―222. Ouyang Yu, Liu Hui, Yang Xiao. Bending of composite beam considering effect of adhesive layer slip [J]. Engineering Mechanics, 2012, 29(9): 215―222. (in Chinese)
[9]  申志强, 钟宏志. 界面滑移组合梁的几何非线性求积元分析[J]. 工程力学, 2013, 30(3): 270―288. Shen Zhiqiang, Zhong Hongzhi. Geometrically nonlinear quadrature element analysis of composite beams with partial interaction [J]. Engineering Mechanics, 2013, 30(3): 270―288. (in Chinese)
[10]  Ranzi G, Zona A. A steel-concrete composite beam model with partial interaction including the shear deformability of the steel component [J]. Engineering Structures, 2007, 29(11): 3026―3041.
[11]  Schnabl S, Saje M, Turk G, et al. Locking-free two-layer Timoshenko beam element with interlayer slip [J]. Finite Elements in Analysis and Design, 2007, 43(9): 705―714.
[12]  Nguyen Q H, 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.
[13]  Nguyen Q H, Hjiaj M, Guezouli S. Exact finite element model for shear-deformable two-layer beams with discrete shear connection [J]. Finite Elements in Analysis and Design, 2011, 47(7): 718―727.
[14]  Zona A, Ranzi G. Finite element models for nonlinear analysis of steel-concrete composite beams with partial interaction in combined bending and shear [J]. Finite Elements in Analysis and Design, 2011, 47(2): 98―118.
[15]  Whitney J. Shear correction factors for orthotropic laminates under static load [J]. ASME, Transactions, Series E-Journal of Applied Mechanics, 1973, 40: 302―304.
[16]  Chakrabarti A, Sheikh AH, 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.
[17]  Chakrabarti A, Sheikh A H, Griffith M, et al. Analysis of composite beams with partial shear interactions using a higher order beam theory [J]. Engineering Structures, 2012, 36: 283―291.
[18]  Reddy J N. A simple higher-order theory for laminated composite plates [J]. Journal of Applied Mechanics, 1984, 51(4): 745―752.
[19]  聂建国, 王宇航. 基于ABAQUS的钢-混凝土组合结构纤维梁模型的开发及应用[J]. 工程力学, 2012, 29(1): 70―80. Nie Jianguo, Wang Yuhang. Development and application of steel-concrete composite fiber beam model in ABAQUS platform [J]. Engineering Mechanics, 2012, 29(1): 70―80. (in Chinese)
[20]  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.
[21]  Zienkiewicz O C, Taylor R L. The finite element method (fifth edition) volume 2: solid mechanics [M]. London: Butterworth-Heinemann, 2000: 31―34.
[22]  Batoz J L, Dhatt G. Incremental displacement algorithms for nonlinear problems [J]. International Journal for Numerical Methods in Engineering, 1979, 14(8): 1262―1267.
[23]  Sousa J B, Oliveira C E, Silva A R. Displacement-based nonlinear finite element analysis of composite beam-columns with partial interaction [J]. Journal of Constructional Steel Research, 2010, 66(6): 772―779.
[24]  Sousa J B, Silva A R. Nonlinear analysis of partially connected composite beams using interface elements [J]. Finite Elements in Analysis and Design, 2007, 43(11/12): 954―964.
[25]  CEB-FIP, Model code 1990, Design code [S]. London: Thomas Telford, 1998.
[26]  EN 1992-1-1, Eurocode 2: Design of concrete structures-Part 1-1: General rules and rules for buildings [S]. Brussels: European committee for standardization, 2004.
[27]  Ollgaard J G, Slutter R G, Fisher J W. Shear strength of stud connectors in lightweight and normal-weight concrete [J]. AISC Engineering Journal, 1971, 8(2): 55―64.
[28]  28 由图2所示有限单元的节点构造以及节点自由度:、、、、、、、、和( i =1,2,3; j =1,2,3,4),节点自由度向量:
[29]  29 (A.1)
[30]  30 三个节点构成的单元自由度向量:
[31]  31 (A.2)
[32]  32 基于拉格朗日插值基可构造基本未知量、、、、和的拉格朗日插值函数:
[33]  33 (A.3)
[34]  34 其中,形函数向量、、、、和定义为:
[35]  35 (A.4)
[36]  36 式(A.4)中,为13阶单位矩阵,而插值基定义如下:
[37]  37 (A.5)
[38]  38 利用式(1)和式(2)可导出:
[39]  39 (A.6)
[40]  40 其中:
[41]  44 根据式(3)可以继续导出应变插值函数:
[42]  45 (A.7)
[43]  46 其中:
[44]  48 (上接第73页)
[45]  方海. 新型复合材料夹层结构受力性能及其道面垫板应用研究[D]. 南京: 南京工业大学, 2008: 39―44. Fang Hai . Study on mechanical properties of innovative sandwich composites and its application to composite matting [D]. Nanjing: Nanjing University of Technology, 2008: 39―44. (in Chinese)
[46]  陈向前, 刘伟庆, 方海. 双向纤维腹板增强复合材料夹层板受弯性能试验研究[J]. 实验力学, 2012, 27(4): 486―491. Chen Xiangqian, Liu Weiqing, Fang Hai. Experimental study of flexural behavior of composite sandwich panel reinforced by two way webs [J]. Journal of Experimental Mechanics, 2012, 27(4): 486―491. (in Chinese)
[47]  崔德刚. 结构稳定性设计手册[M]. 北京: 航空工业出版社, 2006: 1―286. Cui Degang. Design manual for structural stability [M]. Beijing: Aviation Industry Press, 2006: 1―286. (in Chinese)
[48]  沈观林, 胡更开. 复合材料力学[M]. 北京: 清华大学出版社, 2006: 144―159. Shen Guanlin, Hu Gengkai. Mechanics of composite materials [M]. Beijing, Tsinghua University Press, 2006: 144―159. (in Chinese)
[49]  秋洪燕, 矫桂琼, 黄涛. 复合材料层压梁梯形波纹腹板刚度和稳定性等效分析方法研究[J]. 机械强度, 2012, 34(6): 899―906. Qiu HongYan, Jiao Guiqiong, Huang Tao. Investigation of the composite laminated beams with trapezoidal corrugated plate stiffness and stability equivalent analysis method [J]. Journal of Mechanical Strength, 2012, 34(6): 899―906. (in Chinese)
[50]  朱力, 蔡建军, 聂建国. 波形钢腹板的弹性剪切屈曲强度[J]. 工程力学, 2013, 30(7): 40―46. Zhu Li, Cai Jianjun, Nie Jianguo. Elastic shear buckling strength of trapezoidal corrugated steel webs [J]. Engineering Mechanics, 2013, 30(7): 40―46. (in Chinese)
[51]  Briscoe C R, Mantell S C, Davidson J H. Shear buckling of foam-filled web core sandwich panels using a Pasternak foundation model [J]. Thin-Walled Structures, 2010, 48: 460―8.
[52]  Behzad D Manshadi, Anastasios P Vassilopoulos, Julia de Castro, et al. Instability of thin-walled GFRP webs in cell-core sandwiches under combined bending and shear loads [J]. Thin-Walled Structures, 2012, 52: 200―210.
[53]  Whitney J M. Structural analysis of laminated anisotropic plates [M]. Lancaster: Technomic Publishing Company, 1987: 41―58.
[54]  Aiello M A, Ombres L. Maximum buckling loads for unsymmetric thin hybrid laminates under in-plane and shear forces [J]. Composite Structures, 1996, 36(11): 1―11.
[55]  宰金珉, 宰金璋. 高层建筑基础分析与设计: 土与结构物共同作用的理论与应用[M]. 北京: 中国建筑工业出版社, 1993: 26―56. Zai Jinmin, Zai Jinzhang. Analysis and design of high-rise building foundation: theory and application of soil-structure interaction [M]. Beijing: China Building Industry Press, 1993: 26―56. (in Chinese)

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133