Non-Linear Response of Torsional Buckling Piezoelectric Cylindrical Shell Reinforced with DWBNNTs Under Combination of Electro-Thermo-Mechanical Loadings in Elastic Foundation
الموضوعات :
M Sarvandi
1
(Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran)
M.M Najafizadeh
2
(Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran)
H Seyyedhasani
3
(School of Plant and Environmental Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA)
الکلمات المفتاحية: Elastic foundation, Piezoelectric, Torsional Buckling, Electro-thermo-mechanic, Cylindrical shell,
ملخص المقالة :
Nanocomposites provide new properties and exploit unique synergism between materials. Polyvinylidene fluoride (PVDF) is an ideal piezoelectric matrix applicable in nanocomposites in a broad range of industries from oil and gas to electronics and automotive. And boron nitride nanotubes (BNNTs) show high mechanical, electrical and chemical properties. In this paper, the critical torsional load of a composite tube made of PVDF reinforced with double-walled BNNTs is investigated, under a combination of electro-thermo-mechanical loading. First, a nanocomposite smart tube is modeled as an isotropic cylindrical shell in an elastic foundation. Next, employing the classical shell theory, strain-displacement equations are derived so loads and moments are obtained. Then, the total energy equation is determined, consisting of strain energy of shell, energy due to external work, and energy due to elastic foundation. Additionally, equilibrium equations are derived in cylindrical coordinates as triply orthogonal, utilizing Euler equations; subsequently, stability equations are developed through the equivalent method in adjacent points. The developed equations are solved using the wave technique to achieve critical torsional torque. Results indicated that critical torsional buckling load occurred in axial half-wave number m = 24 and circumferential wave number n = 1, for the investigated cylindrical shell. The results also showed that with the increase in the length-to-radius ratio and in the radius-to-shell thickness ratio, the critical torsional buckling load increased and decreased, respectively. Lastly, results are compared in various states through a numerical method. Moreover, stability equations are validated via comparison with the shell and sheet equations in the literature.
[1] Brockmann T.H., 2009, Theory of Adaptive Fiber Composites: From Piezoelectric Material Behavior to Dynamics of Rotating Structures, Springer Science & Business Media.
[2] Uzun B., Numanoglu H., Civalek O., 2018, Free vibration analysis of BNNT with different cross-Sections via nonlocal FEM, Journal of Computational Applied Mechanics 49(2): 252-260.
[3] Sofiyev A., 2010, Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation, Mechanics Research Communications 37(6): 539-544.
[4] Miraliyari O., Najafizadeh M.M., Rahmani A.R., Momeni Hezaveh A., 2011, Thermal and mechanical buckling of short and long functionally graded cylindrical shells using third order shear deformation theory, World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering 5(2): 518-522.
[5] Bagherizadeh E., Kiani Y., Eslami M., 2011, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures 93(11): 3063-3071.
[6] Najafizadeh M.M., Hasani A., Khazaeinejad P., 2009, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling 33(2): 1151-1157.
[7] Sheng G., Wang X., 2010, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, Applied Mathematical Modelling 34(9): 2630-2643.
[8] Shen H.-S., Yang J., Kitipornchai S., 2010, Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium, European Journal of Mechanics-A/Solids 29(3): 448-460.
[9] Najafizadeh M.M., Khazaeinejad P., 2011, Buckling of nonhomogeneous cylindrical shells under torsion using first order shear deformation theory, National Conference on New Technologies in Mechanical Engineering, Iran.
[10] Hassani H.S., 2010, Transient heat transfer analysis of hydraulic system for JD 955 harvester combine by finite element method, Journal of Food, Agriculture & Environment 8(2): 382-385.
[11] Arani A.G., 2012, Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory, Composites Part B: Engineering 43(2): 195-203.
[12] Shadmehri F., Hoa S., Hojjati M., 2012, Buckling of conical composite shells, Composite Structures 94(2): 787-792.
[13] Arani A.G., 2011, Semi-analytical solution of time-dependent electro-thermo-mechanical creep for radially polarized piezoelectric cylinder, Computers & Structures 89(15): 1494-1502.
[14] Khazaeinejad P., 2010, On the buckling of functionally graded cylindrical shells under combined external pressure and axial compression, Journal of Pressure Vessel Technology 132(6): 064501.
[15] Zargaripoor A., 2018, Free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory using finite element method, Journal of Computational Applied Mechanics 49(1): 86-101.
[16] Moradi A., 2018, Magneto-thermo mechanical vibration analysis of FG nanoplate embedded on Visco Pasternak foundation, Journal of Computational Applied Mechanics 49(2): 395-407.
[17] Mohammadi M., 2013, Temperature effect on vibration analysis of annular graphene sheet embedded on visco-Pasternak foundation, Journal of Solid Mechanics 5(3): 305-323.
[18] Goodarzi M., 2014, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, Journal of Solid Mechanics 6(1): 98-121.
[19] Shen H.-S., Zhang C.-L., 2010, Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model, Composite Structures 92(5): 1073-1084.
[20] Mantari J., Oktem A., Soares C.G., 2012, A new higher order shear deformation theory for sandwich and composite laminated plates, Composites Part B: Engineering 43(3): 1489-1499.
[21] Hassani H.S., 2011, Fatigue analysis of hydraulic pump gears of JD 1165 harvester combine through finite element method, Trends in Applied Sciences Research 6(2): 174.
[22] Arani A.G., Kolahchi R., Barzoki A.M., 2011, Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling 35(6): 2771-2789.
[23] Arani A.G., 2013, Electro-thermo-torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composites Part B: Engineering 51: 291-299.
[24] Arani A.G., 2012, Electro-thermo-mechanical nonlinear nonlocal vibration and instability of embedded micro-tube reinforced by BNNT, conveying fluid, Physica E: Low-Dimensional Systems and Nanostructures 45: 109-121.
[25] Ansari R., Rouhi S., Ahmadi M., 2018, On the thermal conductivity of carbon nanotube/polypropylene nanocomposites by finite element method, Journal of Computational Applied Mechanics 49(1): 70-85.
[26] Barzoki A.M., 2012, Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 36(7): 2983-2995.
[27] Kargarnovin M., Shahsanami M., 2012, Buckling analysis of a composite cylindrical shell with fiber’s material properties changing lengthwise using first-order shear deformation theory, International Conference on Mechanical, Automotive and Materials Engineering.
[28] Barzoki A.M., 2013, Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro–thermo-mechanical loadings using HDQM, Composites Part B: Engineering 44(1): 722-727.
[29] Tan P., Tong L., 2001, Micro-electromechanics models for piezoelectric-fiber-reinforced composite materials, Composites Science and Technology 61(5): 759-769.
[30] Brush D.O., Almroth O., 1975, Buckling of Bars, Plates and Shells, New York, McGraw Hill.
