Finite Element Analysis of a Double Beam connected with Elastic Springs
Received: 8 October 2023 | Revised: 16 November 2023 | Accepted: 19 November 2023 | Online: 6 December 2023
Corresponding author: Nguyen Ngoc Lam
Abstract
This paper develops a finite element method for double beams subjected to static loading. The double beam consists of two Euler–Bernoulli beams connected continuously by an elastic spring connection. The finite element for a double beam is formulated with eight degrees of freedom based on the Euler-Bernoulli beam theory. The finite element method is implemented in MATLAB software to analyze the behavior of the double beams. The MATLAB code calculates the displacements of both the upper and lower beams. Numerical examples are compared with the analytical solution to demonstrate the high accuracy of the proposed method.
Keywords:
FEM, double beam, elastic springsDownloads
References
D. Wu, Y. Lei, Z. Wang, B. Yu, and D. Zhang, "Free Vibration Analysis of Carbon-Nanotube-Reinforced Beams Resting on a Viscoelastic Pasternak Foundation by the Nonlocal Eshelby–Mori–Tanaka Method," Mechanics of Composite Materials, vol. 59, no. 3, pp. 479–494, Jul. 2023.
H. Vinh Ha, N. Ngoc Long, and N. Van Minh, "Theoretical calculation of bending capacity of a steel beam - ultra high performance concrete slab composite girder," Transport and Communications Science Journal, vol. 74, no. 4, pp. 497–506, May 2023.
T. D. Hien, N. D. Hung, N. T. Hiep, G. V. Tan, and N. V. Thuan, "Finite Element Analysis of a Continuous Sandwich Beam resting on Elastic Support and Subjected to Two Degree of Freedom Sprung Vehicles," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10310–10315, Apr. 2023.
M. Rezaiee-Pajand, A. R. Masoodi, and A. Alepaighambar, "Lateral-Torsional Buckling of a Bidirectional Exponentially Graded Thin-Walled C-Shaped Beam," Mechanics of Composite Materials, vol. 58, no. 1, pp. 53–68, Mar. 2022.
H. D. Ta, K. T. Nguyen, T. D. Ngoc, H. T. Do, T. X. Nguyen, and D. D. Nguyen, "Approximation solution for steel concrete beam accounting high-order shear deformation using trigonometric-series," Journal of Materials and Engineering Structures, vol. 9, no. 4, pp. 599–605, Dec. 2022.
M. Usarov, G. Mamatisaev, and G. Ayubov, "Forced vibrations of a box element of a multi-story building under dynamic impact," Magazine of Civil Engineering, vol. 114, no. 6, pp. 11406–11406, 2022.
P. C. Nguyen, B. Le-Van, and S. D. T. V. Thanh, "Nonlinear Inelastic Analysis of 2D Steel Frames : An Improvement of the Plastic Hinge Method," Engineering, Technology & Applied Science Research, vol. 10, no. 4, pp. 5974–5978, Aug. 2020.
D. H. Duc, D. V. Thom, and P. M. Phuc, "Buckling analysis of variable thickness cracked nanoplates considerting the flexoelectric effect," Transport and Communications Science Journal, vol. 73, no. 5, pp. 470–485, 2022.
Yu. I. Vinogradov, "Deformation Mechanics of a Shallow Shell," Mechanics of Solids, vol. 57, no. 3, pp. 570–579, Jun. 2022.
A. V. Alekseytsev and S. A. Sazonova, "Numerical analysis of the buried fiber concrete slabs dynamics under blast loads," Magazine of Civil Engineering, vol. 117, no. 1, 2023, Art. no. 11703.
D. T. Thuy, L. N. Ngoc, D. N. Tien, and H. V. Thanh, "An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation," Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9926–9931, Feb. 2023.
A. W. de Q. R. Reis, R. B. Burgos, and M. F. F. de Oliveira, "Nonlinear Dynamic Analysis of Plates Subjected to Explosive Loads," Latin American Journal of Solids and Structures, vol. 19, Jan. 2022, Art. no. e422.
E. I. Starovoitov and D. V. Leonenko, "Deformation of an Elastic Circular Sandwich Plate in a Neutron Flow," Mechanics of Composite Materials, vol. 57, no. 6, pp. 813–824, Jan. 2022.
P. Pham Minh and A. Vinh, "Stability of multi-cracked FG plate on elastic foundations," Transport and Communications Science Journal, vol. 74, pp. 544–556, May 2023.
S. V. Sheshenin and R. R. Muradkhanov, "Asymptotic Study of Plate Bending for a Strongly Orthotropic Material," Mechanics of Solids, vol. 58, no. 3, pp. 697–715, Jun. 2023.
P.-C. Nguyen, T. N. Van, and H. T. Duy, "Stochastic Free Vibration Analysis of Beam on Elastic Foundation with the Random Field of Young’s Modulus Using Finite Element Method and Monte Carlo Simulation," in 6th International Conference on Geotechnics, Civil Engineering and Structures, Ha Long, Vietnam, Oct. 2021, pp. 499–506.
N. Wu, Y. Zhao, Q. Guo, and Y. Liu, "The effect of two-parameter of Pasternak foundations on the dynamics and stability of multi-span pipe conveying fluids," Advances in Mechanical Engineering, vol. 12, no. 11, Nov. 2020, Art. no. 1687814020974530.
S. B. Akhazhanov, N. I. Vatin, S. Akhmediyev, T. B. Akhazhanov, O. Khabidolda, and A. Z. Nurgoziyeva, "Beam on a two-parameter elastic foundation: simplified finite element model," Magazine of Civil Engineering, vol. 121, no. 5, 2023, Art. no. 12107.
V. N. Paimushin, M. V. Makarov, and N. V. Levshonkova, "Mixed Bending-Shear Buckling Modes of a Sandwich Beam under the Axial Compression of its Outer Layers," Mechanics of Composite Materials, vol. 59, no. 3, pp. 521–538, Jul. 2023.
F. Han, D. Dan, and W. Cheng, "An exact solution for dynamic analysis of a complex double-beam system," Composite Structures, vol. 193, pp. 295–305, Jun. 2018.
F. Han, D. Dan, and W. Cheng, "Exact dynamic characteristic analysis of a double-beam system interconnected by a viscoelastic layer," Composites Part B: Engineering, vol. 163, pp. 272–281, Apr. 2019.
N. Yu. Tsybin, R. A. Turusov, A. Yu. Sergeev, and V. I. Andreev, "Solving the Stress Singularity Problem in Boundary-Value Problems of the Mechanics of Adhesive Joints and Layered Structures by Introducing a Contact Layer Model. Part 1. Resolving Equations for Multilayered Beams," Mechanics of Composite Materials, vol. 59, no. 4, pp. 677–692, Sep. 2023.
Y. Wu and Y. Gao, "Dynamic response of a simply supported viscously damped double-beam system under the moving oscillator," Journal of Sound and Vibration, vol. 384, pp. 194–209, Dec. 2016.
X. Zhao, "Free and forced vibration analysis of double-beam systems with concentrated masses," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 43, no. 10, Sep. 2021, Art. no. 467.
M. Abu-Hilal, "Dynamic response of a double Euler–Bernoulli beam due to a moving constant load," Journal of Sound and Vibration, vol. 297, no. 3, pp. 477–491, Nov. 2006.
J. Yang, X. He, H. Jing, H. Wang, and S. Tinmitonde, "Dynamics of Double-Beam System with Various Symmetric Boundary Conditions Traversed by a Moving Force: Analytical Analyses," Applied Sciences, vol. 9, no. 6, Jan. 2019, Art. no. 1218.
E. V. Popov et al., "Numerical buckling calculation method for composite rods with semi-rigid ties," Magazine of Civil Engineering, vol. 119, no. 3, 2023, Art. no. 11904.
D. T. Hang. "Analytical solutions for simply supported double-Beam connected by elastic spring", Journal of Transportation. vol. no. 729, pp. 105-107, 2023.
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Copyright (c) 2023 Do Thi Hang, Nguyen Xuan Tung, Nguyen Ngoc Lam
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