New composite finite element for static, dynamic and buckling analysis of sandwich composite beams

doi:10.3785/j.issn.1008-973X.2024.03.009

Journal of ZheJiang University (Engineering Science)

2024, Vol. 58

Issue (3): 518-528 DOI: 10.3785/j.issn.1008-973X.2024.03.009

New composite finite element for static, dynamic and buckling analysis of sandwich composite beams

Jianping LIN1,2(

),Kun CHEN1,Jianchao PAN3,4,Guannan WANG3,4,Qian FENG3,*(

)

1. College of Civil Engineering, Huaqiao University, Xiamen 361021, China
2. Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, Huaqiao University, Xiamen 361021, China
3. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
4. Zhejiang Provincial Engineering Research Center for Digital and Smart Maintenance of Highway, Hangzhou 310058, China

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Abstract

A new composite finite element of a three-layer partial-interaction sandwich composite beam with interlayer interfacial slip was derived for static, dynamic and buckling analysis. The partial-interaction effects of the sandwich beam were considered by deriving the energy principle based on the Timoshenko beam theory. Then a high-order interpolation function with internal degrees of freedom was used for determining the nodal displacement, section rotary angle and interfacial slips of the sandwich beam, which could solve the frequent "slip locking" phenomenon in numerical analysis. The explicit stiffness matrix, mass matrix and geometric stiffness matrix of the sandwich beam were obtained through variational principle. The accuracy of the proposed composite finite element for the corresponding sandwich structure was verified through the numerical program which was developed based on the MATLAB software. The static, dynamic and buckling analysis of the three-layer sandwich beam with different cross-sections were then carried out, under the circumstances of various loads and different boundary conditions. The variation laws of the calculation results and their errors of sandwich composite beams with different span-depth ratios and different interfacial shear stiffnesses were also analyzed. The proposed composite finite element with explicit expressions has high calculation efficiency and is easy to be applied into other finite element programs or commercial software subroutines.

Key words： sandwich composite beam partial-interaction static and dynamic analysis stiffness matrix mass matrix Timoshenko beam theory

Received: 08 February 2023 Published: 05 March 2024

CLC:

TU 398.9

Fund: 国家自然科学基金资助项目(52378158, 12322206, 12002303)；浙江省‘尖兵’‘领雁’研发攻关计划资助项目（2022C01143）；福建省自然科学基金资助项目(2023J01106)；浙江大学-浙江交工协同创新联合研究中心资助项目（ZDJG2021002）；厦门市自然科学基金资助项目(3502Z20227200).

Corresponding Authors: Qian FENG E-mail: linjianping@hqu.edu.cn;fengqian@zju.edu.cn

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Cite this article:

Jianping LIN,Kun CHEN,Jianchao PAN,Guannan WANG,Qian FENG. New composite finite element for static, dynamic and buckling analysis of sandwich composite beams. Journal of ZheJiang University (Engineering Science), 2024, 58(3): 518-528.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.03.009 OR https://www.zjujournals.com/eng/Y2024/V58/I3/518

用于夹层梁静动力及屈曲分析的新型组合结构单元

推导出新型组合结构单元，用于考虑界面滑移的3层部分作用夹层组合梁的静动力及屈曲特性分析. 基于铁木辛柯梁理论，建立考虑夹层梁部分作用效应的能量原理. 针对其受力特性，在节点位移、横截面转角和界面滑移插值时均采用含内部自由度的高阶插值函数，以解决含界面有限元数值分析中常遇到的“滑移锁定”现象. 通过变分原理得到夹层梁的刚度矩阵、质量矩阵以及几何刚度矩阵的显示表达式. 基于MATLAB编译相应夹层结构的有限元程序并验证其准确性. 对不同截面3层夹层组合梁进行不同荷载条件和边界条件下的静动力及屈曲特性分析，并探讨不同夹层组合梁跨高比和不同界面抗剪连接刚度下的计算结果及其误差的变化规律. 所推导的显示表达式新型组合结构单元计算效率高，并便于推广应用于其他有限元程序或商业软件子程序中.

关键词： 夹层组合梁, 部分作用, 静动力分析, 刚度矩阵, 质量矩阵, 铁木辛柯梁理论

Fig.1 Three-layer sandwich composite beam and coordinate system

Fig.2 Geometrical relationship of interlayer slips, rotation angles and longitudinal displacements

Fig.3 Infinitesimal element of three-layer composite beam

Fig.4 Coordinate of e-th element

Fig.5 Simply supported and continuous three-layer steel-concrete composite beams

Tab.1 Comparison of interlayer slip and maximum deflection under simply supported condition

Tab.2 Comparison of interlayer slip and maximum bending moment under continuous boundary condition

Fig.6 Variations of relative errors of maximum deflections, maximum rotation angles and interlayer slips with different element numbers under simply supported condition

Fig.7 Variations of deformation with shear stiffness

Fig.8 Variations of relative errors of maximum deflection with shear stiffness

Fig.9 Relative errors of maximum mid span deflection obtained by two different beam theories

Tab.3 Comparison of calculation results of natural frequency and buckling load

Fig.10 Relative errors of natural frequency and buckling load

Fig.11 Two-span continuous sandwich composite beam

Fig.12 Maximum deflections and its errors of two-span continuous sandwich composite beam


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