Thermal Buckling Analysis of Temperature Dependent Porous FGM Mindlin Nano Circular Plate on Elastic Foundation
محورهای موضوعی : Computational Mechanics
1 - Department of Mechanical Engineering,Faculty of Mechatronics,Karaj Branch,Islamic Azad University,Karaj,Iran
کلید واژه: DQM, circular nano/micro plate, Porous material, Thermal buckling, FGM,
چکیده مقاله :
In the present work, the symmetric thermal buckling behavior of shear deformable heterogonous nano/micro circular porous plates resting on a two parameter foundation is studied. The material behavior of the nano plate is modeled by the modified couple stress theory. The plate material properties assumed to be graded across the thickness direction according to a simple power law, and has a uniform porosity. Using Mindlin’s plate theory and the nonlinear von-Karman strain field and implementing the energy method, the plate stability equations together with the membrane equilibrium equation are derived and expressed in terms of the displacement field components. Then the nondimensionalized forms of the equations are discretized using differential quadrature method (DQM). The resulting eigenvalue problem is solved to evaluate the plate critical buckling temperature difference. Comparative studies are carried out. Also the influences of some important parameters including length scale factor, porosity factor and Winkler& Pasternak stiffness coefficients are investigated..
In the present work, the symmetric thermal buckling behavior of shear deformable heterogonous nano/micro circular porous plates resting on a two parameter foundation is studied. The material behavior of the nano plate is modeled by the modified couple stress theory. The plate material properties assumed to be graded across the thickness direction according to a simple power law, and has a uniform porosity. Using Mindlin’s plate theory and the nonlinear von-Karman strain field and implementing the energy method, the plate stability equations together with the membrane equilibrium equation are derived and expressed in terms of the displacement field components. Then the nondimensionalized forms of the equations are discretized using differential quadrature method (DQM). The resulting eigenvalue problem is solved to evaluate the plate critical buckling temperature difference. Comparative studies are carried out. Also the influences of some important parameters including length scale factor, porosity factor and Winkler& Pasternak stiffness coefficients are investigated..
[1] Fleck, N.A., and Hutchinson, J.W., 1993, A Phenomenological Theory for Strain Gradient Effects in Plasticity, Journal of Mechanics and Physics of Solids, 41(12): 1825–57.
[2] Yang, F., Chong, A.C.M. , Lam, D.C.C., 2002, Tong, P., Couple Stress Based Strain Gradient Theory for Elasticity, International Journal of Solids and Structures, 39: 2731–43
[3] Duan W.H., Wang C.M., 2009, Nonlinear bending and stretching of a circular graphene sheet under a central point load, Nanotechnology, 20: 1-7.
[4] Shen L., Shen H.S. Zhang C.L., 2010, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Computational Materials Science, 48: 680–685.
[5] Jabbarzadeh, M., Talati, H., Noroozi, A.R., 2013, Nonlinear Analysis of Circular Graphene Sheet Using Nonlocal Continuum Mechanic Theory, Journal of Modares Mechanical Engineering, 13(13): 57-66 (In Persian).
[6] Wang, Y.G., Lin, W.H., Liu, N., 2013, Large Amplitude Free Vibration of Size-Dependent Circular Microplates Based on the Modified Couple Stress Theory, International Journal of Mechanical Science., 71: 51-57.
[7] Ghiasian, S.E., Kiani, Y., Sadighi, M., Eslami, M.R., 2014. Thermal Buckling of Shear Deformable Temperature Dependent Circular/Annular FGM Plates, International Journal of Mechanical Science, 81: 137-148.
[8] Jabbari, M., Hashemitaheri, M, Mojahedin, A, 2014, Thermal Buckling Analysis of Functionally Graded Thin Circular Plate Made of Saturated Porous Materials, Journal of Thermal Stress, 3: 202–220.
[9] Ansari R., Gholami R, Faghih Shojaei M., Mohammadi V., Sahmani S., 2015, Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory, European Journal of Mechanics A/Solids, 49: 251-267.
[10] Eshraghi, I., Dag, S., Soltani, N., 2016, Bending and Free Vibrations of Functionally Graded Annular and Circular Micro-Plates under Thermal Loading, Composite Structure, 137: 196-207.
[11] Shojaeefard M.H., Saeidi Googarchin, H, Ghadiri M., Mahinzare, M., 2017, Micro temperature-dependent FG porous plate: Free vibration and thermal buckling analysis using modifed couple stress theory with CPT and FSDT, Applied Mathematical Modeling, 50: 633-655.
[12] Lin, M.X., Lai, H.Y., Chen, C.K., 2017, Analysis of Nonlocal Nonlinear Behavior of Graphene Sheet Circular Nanoplate Actuators Subject to Uniform Hydrostatic Pressure, Microsystem Technology, 24: 919–928.
[13] Farzam, A., and Hassani, B., 2019, Size-Dependent Analysis of FG Microplates with Temperature-Dependent Material Properties Using Modified Strain Gradient Theory and Isogeometric Approach, Composites Part B, 161: 150-168.
[14] Gobadi. A, Tadi Beni, Y., Golestanian, H., 2020 , Size Dependent Nonlinear Bending Analysis of a Flexoelectric Functionally Graded Nano-Plate Under Thermo-Electro-Mechanical Loads, Journal of Solid Mechanics, 12( 1) : 33-56.
[15] Ahmadpour, M., Golmakani, M.E., Malikan, M., 2021,Thermal Buckling Analysis of Circular Bilayer Graphene Sheets Resting on An Elastic Matrix Based on Nonlocal Continuum Mechanics, Journal of Applied Computational Mechanics, 7(4): 1862-1877.
[16] Rajabi M., Lexian , Rajabi A, 2021, Analysis of Nanoplate with a Central Crack Under Distributed Transverse Load Based on Modified Nonlocal Elasticity Theory, Journal of Solid Mechanics, 13( 2): 213-232.
[17] Kiarasi F., Babaei M., Kamran Asemi K., Dimitri R., Tornabene F., 2021, Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions, Applied Sciences, 11(21): 1-21.
[18] Saini R., Ahlawat N., Rai P., Khadimallah M.A., 2022, Thermal stability analysis of functionally graded non-uniform asymmetric circular and annular nano discs: Size-dependent regularity and boundary conditions, Europian Journal of Mechanics-A/Solids, 94:51-65.
[19] Jalali, S.K., and Heshmati, M.,2020, Vibration Analysis of Tapered Circular Poroelastic Plates with Radially Graded Porosity Using Pseudo-Spectral Method, Mechanics of Materials, 140.
[20] Jalali, S.K., Naei, M.H., Poorsolhjouy, A., 2010, Thermal Stability Analysis of Circular Functionally Graded Sandwich Plates of Variable Thickness Using Pseudo-Spectral Method, Materials and Design, 31: 4755-4763.
[21] Brush, D.O, and Almroth, B.O., 1975,Buckling of Bars Plates and Shells, McGraw-Hill, New York, Second Edition.
