A Numerical Study on the Large Displacement in Functionally Graded Beam under Thermal Effect

Abstract

The large displacement behavior of a Functionally Graded (FG) beam under uniform thermal load is investigated numerically. Six different effects are taken into consideration when examining the large displacement behavior of the beam. These are the effects of temperature, material, geometry, slenderness, force, and boundary condition. The nonlinear numerical analysis is carried out by using the Simulation mode of SolidWorks, which is a finite element-based commercial program. As a result, the displacement of the end of the beam increase with increasing temperature, slenderness ratio, and force. However, it decreases with increase in the ratio of ceramic in Functionally Graded Material (FGM) and the width of the beam. Moreover, as expected, the maximum and minimum displacements are obtained in the beams with Clamped-Free and Clamped-Clamped boundary conditions, respectively.

Keywords

• Large displacement
• Beam
• FGM
• Thermal load

A Numerical Study on the Large Displacement in Functionally Graded Beam under Thermal Effect

Öz

The large displacement behavior of a Functionally Graded (FG) beam under uniform thermal load is investigated numerically. Six different effects are taken into consideration when examining the large displacement behavior of the beam. These are the effects of temperature, material, geometry, slenderness, force, and boundary conditions. The nonlinear numerical analysis is carried out by using the Simulation mode of SolidWorks, which is a finite element-based commercial program. It is obtained from the results that the displacement of the end of the beam increases with increasing temperature, slenderness ratio, and force. It is also found that it decreases with increase in the ratio of ceramic in Functionally Graded Material (FGM). Moreover, the displacement of the end of the beam decreases with increasing the width of the beam. Furthermore, as expected, the maximum and minimum displacements are obtained in the beams with Clamped-Free and Clamped-Clamped boundary conditions, respectively.

Anahtar Kelimeler

• Large displacement
• Beam
• FGM
• Thermal load

Kaynakça

1. Chen L., An integral approach for large deflection cantilever beams. International Journal of Non-Linear Mechanics 45(3), 301-305, 2010.
2. Davoodinik A.R., Rahimi G.H., Large deflection of flexible tapered functionally graded beam. Acta Mechanica Sinica 27(5), 767-777, 2011.
3. Demir E., Sayer M., Callioglu M., An approach for predicting longitudinal free vibration of axially functionally graded bar by artificial neural network. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science DOI: 10.1177/09544062221141246, 2022.
4. Gan B.S., Kien N.D., Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation. Journal of Asian Architecture and Building Engineering 13(3), 649-656, 2014.
5. Horibe T., Mori K., Large deflections of tapered cantilever beams made of axially functionally graded material. Mechanical Engineering Journal 5(1), DOI: 10.1299/mej.17-00268, 2018.
6. Kang Y.A., Li X.F., Large Deflections of a Non-linear Cantilever Functionally Graded Beam, Journal of Reinforced Plastics and Composites, 29(12), 1761-1774, 2010.
7. Khosravi M., Jani M., Numerical resolution of large deflections in cantilever beams by Bernstein spectral method and a convolution quadrature. International Journal of Nonlinear Analysis and Applications 9(1), 117-127, 2018.
8. Kimiaeifar A., Domairry G., Mohebpour S.R., Sohouli A.R., Davodi A.G., Analytical Solution for Large Deflections of a Cantilever Beam Under Nonconservative Load Based on Homotopy Analysis Method. Numerical Methods for Partial Differential Equations 27(3), 541-553, 2011.

9. Kimiaeifar A., Lund E., Thomsen O.T., Series solution for large deflections of a cantilever beam with variable flexural rigidity. Meccanica 47(7), 1787-1796, 2012.
10. Kimiaeifar A., Tolou N., Barari A., Herder, J.L., Large deflection analysis of cantilever beam under end point and distributed loads. Journal of the Chinese Institute of Engineers 37(4), 438-445, 2014.
11. Li D.K., Li X.F., Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending. Comptes Rendus Mecanique 344(8), 556-568, 2019.
12. Li S.R., Song X., Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise. Mechanics Research Communications 33(1), 84-92, 2006.
13. Mien N.D., Gan B.S., Large deflections of tapered functionally graded beams subjected to end forces. Applied Mathematical Modelling 38(11-12), 3054-3066, 2014.
14. Mohyeddin A., Fereidoon A., An analytical solution for the large deflection problem of Timoshenko beams under three-point bending. International Journal of Mechanical Sciences 78, 135-139, 2014.
15. Rahimi G.H., Davoodinik A.R., Large Deflection of Functionally Graded Cantilever Flexible Beam with Geometric Non-Linearity: Analytical and Numerical Approaches. Scientia Iranica Transaction B-Mechanical Engineering 17(1), 25-40, 2010.
16. Shen H.S., Functionally Graded Materials Nonlinear Analysis of Plates and Shells. CRC Press Taylor & Francis Group, Boca Raton, Florida, USA, 2009.
17. Sitar M., Kosel F., Brojan M., Large deflections of nonlinearly elastic functionally graded composite beams. Archives of Civil and Mechanical Engineering 14(4), 700-709, 2014.
18. Tari H., Kinzel G.L., Mendelsohn D.A., Cartesian and piecewise parametric large deflection solutions of tip point loaded Euler-Bernoulli cantilever beams. International Journal of Mechanical Sciences 100, 216-225, 2015.
19. Ünal H., Ermiş K., Demirtaş Ş., Investigation of mechanical and microstructural properties of polyolefin rubber and glass beads filled polypropylene composites. Journal of Materials and Mechatronics: A 3(1), 91-105, 2022.
20. Yin Y.Z., Wang Y.C., A numerical study of large deflection behaviour of restrained steel beams at elevated temperatures. Journal of Constructional Steel Research 60(7), 1029-1047, 2004.
21. Zhou P., Liu Y., Liang X.Y., Analytical solutions for large deflections of functionally graded beams based on layer-graded beam model. International Journal of Applied Mechanics 10(9), DOI: 10.1142/S1758825118500989, 2018.