Nonlinear buckling analysis of clamped-free porous FG sandwich beams with temperature dependent materials
محورهای موضوعی : Analytical and Numerical Methods in Mechanical Design
1 - Department of Mechanics,
Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran
کلید واژه: Functionally graded material, Boundary condition, Porosity, Smart material,
چکیده مقاله :
Analysing the buckling behaviour of the two kinds of sandwich beams, the first one with functionally graded material faces and homogeneous core and the second one with functionally graded material core and homogeneous faces are presented in this paper based on a high order sandwich beam theory. Properties of the constituent materials are assumed temperature dependent and functionally graded materials are modelled by a power law rule. Even and uneven porosity distributions are considered to improve the accuracy of the model. Minimum potential energy principle is used to obtain the govern equations and Galerkin method is applied used to solve the equations in a clamped free boundary conditions. Lateral displacement, and thermal stresses of the core and Lagrange strains are considered. To verify the procedure, the results of the present study are compared with the literature. Thickness, length, porosity, wave number and temperature effect on the critical load are investigated too.
Analysing the buckling behaviour of the two kinds of sandwich beams, the first one with functionally graded material faces and homogeneous core and the second one with functionally graded material core and homogeneous faces are presented in this paper based on a high order sandwich beam theory. Properties of the constituent materials are assumed temperature dependent and functionally graded materials are modelled by a power law rule. Even and uneven porosity distributions are considered to improve the accuracy of the model. Minimum potential energy principle is used to obtain the govern equations and Galerkin method is applied used to solve the equations in a clamped free boundary conditions. Lateral displacement, and thermal stresses of the core and Lagrange strains are considered. To verify the procedure, the results of the present study are compared with the literature. Thickness, length, porosity, wave number and temperature effect on the critical load are investigated too.
Akbaş, Ş.D., (2015). On post-buckling behavior of edge cracked functionally graded beams under axial loads. International Journal of Structural Stability and Dynamics 15, 1450065.
[2] Alijani, A., Darvizeh, M., Darvizeh, A., Ansari, R., (2015). Elasto-plastic pre-and post-buckling analysis of functionally graded beams under mechanical loading. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 229, 146-165.
[3] Almitani, K.H., (2018). Buckling behaviors of symmetric and antisymmetric functionally graded beams. Journal of Applied and Computational Mechanics 4, 115-124.
[4] Basaglia, C., Camotim, D., (2015). Buckling analysis of thin-walled steel structural systems using generalized beam theory (GBT). International Journal of Structural Stability and Dynamics 15, 1540004.
[5] Bhangale, R.K., Ganesan, N., (2006). Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core. Journal of Sound and Vibration 295, 294-316.
[6] Chai, G., Yap, C., Lim, T., (2010). Bending and buckling of a generally laminated composite beam-column. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 224, 1-7.
[7] Challamel, N., Girhammar, U.A., (2011). Variationally-based theories for buckling of partial composite beam–columns including shear and axial effects. Engineering structures 33, 2297-2319.
[8] CW, Y., Chai, G., Parlapalli, M.S.R., (2008). Effect of flexural stiffness estimates on the buckling load of delaminated composite beams. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 222, 91-102.
[9] Dinzart, F., Molinari, A., Herbach, R., (2008). Thermomechanical response of a viscoelastic beam under cyclic bending; self-heating and thermal failure. Archives of Mechanics 60, 59-85.
[10] Fouda, N., El-Midany, T., Sadoun, A., (2017). Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of applied and computational mechanics 3, 274-282.
[11] Frostig, Y., Baruch, M., Vilnay, O., Sheinman, I., (1992). High-order theory for sandwich-beam behavior with transversely flexible core. Journal of Engineering Mechanics 118, 1026-1043.
[12] Gao, C.-F., Pan, Y.-H., Zhang, W., Rao, J.-X., Huang, Y., (2021). Buckling of two-directional functionally graded cylindrical beams based on a high-order cylindrical beam model. International Journal of Structural Stability and Dynamics, 2150099.
[13] Hamed, M.A., Mohamed, S.A., Eltaher, M.A., (2020). Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads. Steel and Composite Structures 34, 75-89.
[14] Janevski, G., Despenić, N., Pavlović, I., (2020). Thermal buckling and free vibration of Euler-Bernoulli FG nanobeams based on the higher-order nonlocal strain gradient theory. Archives of Mechanics 72.
[15] Kheirikhah, M., Khalili, S., Fard, K.M., (2012). Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory. European Journal of Mechanics-A/Solids 31, 54-66.
[16] Koissin, V., Shipsha, A., Skvortsov, V., (2010). Effect of physical nonlinearity on local buckling in sandwich beams. Journal of Sandwich Structures & Materials 12, 477-494.
[17] Li, C., Shen, H.-S., Wang, H., (2019). Thermal post-buckling of sandwich beams with functionally graded negative Poisson's ratio honeycomb core. International Journal of Mechanical Sciences 152, 289-297.
[18] Liu, Y., Su, S., Huang, H., Liang, Y., (2019). Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Composites Part B: Engineering 168, 236-242.
[19] Magnucki, K., Smyczyński, M., Jasion, P., (2013). Deflection and strength of a sandwich beam with thin binding layers between faces and a core. Archives of Mechanics 65, 301-311.
[20] Majumdar, A., Das, D., (2018). A study on thermal buckling load of clamped functionally graded beams under linear and nonlinear thermal gradient across thickness. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 232, 769-784.
[21] Malikan, M., (2019). On the buckling response of axially pressurized nanotubes based on a novel nonlocal beam theory. Journal of Applied and Computational Mechanics 5, 103-112.
[22] Mayandi, K., Jeyaraj, P., (2015). Bending, buckling and free vibration characteristics of FG-CNT-reinforced polymer composite beam under non-uniform thermal load. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 229, 13-28.
[23] Osofero, A.I., Vo, T.P., Nguyen, T.-K., Lee, J., (2016). Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories. Journal of Sandwich Structures & Materials 18, 3-29.
[24] Paul, A., Das, D., (2017). A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings. The Journal of Strain Analysis for Engineering Design 52, 45-56.
[25] Rahmani, M., Dehghanpour, S., (2020). Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers. International Journal of Structural Stability and Dynamics, 2150016.
[26] Rahmani, M., Mohammadi, Y., (2021). Vibration of two types of porous FG sandwich conical shell with different boundary conditions. Structural Engineering and Mechanics 79, 401-413.
[27] Rahmani, M., Mohammadi, Y., Kakavand, F., (2019)-a. Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings. Steel and Composite Structures 32, 239-252.
[28] Rahmani, M., Mohammadi, Y., Kakavand, F., (2020)-a. Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings. Journal of the Brazilian Society of Mechanical Sciences and Engineering 42, 1-16.
[29] Rahmani, M., Mohammadi, Y., Kakavand, F., Raeisifard, H., (2019)-b. Buckling behavior analysis of truncated conical sandwich panel with porous FG core in different thermal conditions. Amirkabir Journal of Mechanical Engineering 52, 141-150.
[30] Rahmani, M., Mohammadi, Y., Kakavand, F., Raeisifard, H., (2020)-b. Vibration analysis of different types of porous FG conical sandwich shells in various thermal surroundings. Journal of Applied and Computational Mechanics 6, 416-432.
[31] Reddy, J.N., (2003). Mechanics of laminated composite plates and shells: theory and analysis. CRC press.
[32] Scirè Mammano, G., Dragoni, E., (2017). Mechanical design of buckled beams for low-stiffness elastic suspensions: Theory and application. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 231, 140-150.
[33] Tran, T.T., Nguyen, N.H., Do, T.V., Minh, P.V., Duc, N.D., (2019). Bending and thermal buckling of unsymmetric functionally graded sandwich beams in high-temperature environment based on a new third-order shear deformation theory. Journal of Sandwich Structures & Materials, 1099636219849268.
[34] Vo, T.P., Thai, H.-T., Nguyen, T.-K., Inam, F., Lee, J., (2015). A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Composite Structures 119, 1-12.
[35] Vo, T.P., Thai, H.-T., Nguyen, T.-K., Maheri, A., Lee, J., (2014). Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Engineering structures 64, 12-22.
