Finite Difference Method for Biaxial and Uniaxial Buckling of Rectangular Silver Nanoplates Resting on Elastic Foundations in Thermal Environments Based on Surface Stress and Nonlocal Elasticity Theories
محورهای موضوعی : Engineering
M karimi
1
(Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran)
A.R Shahidi
2
(Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran)
کلید واژه: Nonlocal elasticity theory, Thermal environment, finite difference method, Biaxial and uniaxial buckling, Surface stress theory,
چکیده مقاله :
In this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the Gurtin-Murdoch’s theory. Using the principle of virtual work, the governing equations considering small scale for both nanoplate bulk and surface are derived. The influence of important parameters including, the Winkler and shear elastic moduli, boundary conditions, in-plane biaxial and uniaxial loads, and width-to-length aspect ratio, on the surface stress effects are also studied. The finite difference method, uniaxial buckling, nonlocal effect for both nanoplate bulk and surface, silver material properties, and below-mentioned results are the novelty of this investigation. Results show that the effects of surface elastic modulus on the uniaxial buckling are more noticeable than that of biaxial buckling, but the influences of surface residual stress on the biaxial buckling are more pronounced than that of uniaxial buckling.
[1] Sakhaee-Pour A., Ahmadian M. T., Vafai A., 2008, Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications 145:168-172.
[2] Ball P., 2001, Roll up for the revolution, Nature 414:142-144.
[3] Baughman R. H., Zakhidov A. A., DeHeer W. A., 2002, Carbon nanotubes–the route toward applications, Science 297: 787-792.
[4] Li C., Chou T. W., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 2487-2499.
[5] Govindjee S., Sackman J. L., 1999, On the use of continuum mechanics to estimate the properties of nanotubes, Solid State Communications 110: 227-230.
[6] He X. Q., Kitipornchai S., Liew K. M., 2005, Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, Journal of Mechanics and Physics of solids 53: 303-326.
[7] Gurtin M. E., Murdoch A. I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57: 291-323.
[8] Gurtin M. E, Murdoch A. I., 1978, Surface stress in solids, International Journal of Solids and Structures 14: 431-440.
[9] Assadi A., Farshi B., Alinia-Ziazi A., 2010, Size dependent dynamic analysis of nanoplates, Journal of Applied Physics 107: 124310.
[10] Assadi A., 2013, Size dependent forced vibration of nanoplates with consideration of surface effects, Applied Mathematical Modelling 37: 3575-3588.
[11] Assadi A., Farshi B., 2010, Vibration characteristics of circular nanoplates, Journal of Applied Physics 108: 074312.
[12] Assadi A., Farshi B., 2011, Size dependent stability analysis of circular ultrathin films in elastic medium with consideration of surface energies, Physica E 43: 1111-1117.
[13] Gheshlaghi B., Hasheminejad S. M., 2011, Surface effects on nonlinear free vibration of nanobeams, Composites Part B: Engineering 42: 934-937.
[14] Nazemnezhad R., Salimi M., Hosseini Hashemi S. h., Asgharifard Sharabiani P., 2012, An analytical study on the nonlinear free vibration of nanoscale beams incorporating surface density effects, Composites Part B: Engineering 43: 2893-2897.
[15] Hosseini-Hashemi S., Nazemnezhad R., 2013, An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects, Composites Part B: Engineering 52: 199-206.
[16] Asgharifard Sharabiani P., Haeri Yazdi M. R., 2013, Nonlinear free vibrations of functionally graded nanobeams with surface effects, Composites Part B: Engineering 45: 581-586.
[17] Ansari R., Sahmani S., 2011, Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories, International Journal of Engineering Science 49: 1244-1255.
[18] Karimi M., Shokrani M.H., Shahidi A.R., 2015, Size-dependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method, Journal of Applied and Computational Mechanics 1: 122-133.
[19] Challamel N., Elishakoff I., 2012, Surface stress effects may induce softening: Euler–Bernoulli and Timoshenko buckling solutions, Physica E 44: 1862-1867.
[20] Park H.S., 2012, Surface stress effects on the critical buckling strains of silicon nanowires, Computational Materials Science 51: 396-401.
[21] Ansari R., Shahabodini A., Shojaei M. F., Mohammadi V., Gholami R., 2014, On the bending and buckling behaviors of Mindlin nanoplates considering surface energies, Physica E 57: 126-137.
[22] Ansari R., Mohammadi V., Faghih Shojaei M., Gholami R., Sahmani S., 2014, On the forced vibration analysis of Timoshenko nanobeams based on the surface stress elasticity theory, Composites Part B: Engineering 60: 158-166.
[23] Mouloodi S., Khojasteh J., Salehi M., Mohebbi S., 2014, Size dependent free vibration analysis of Multicrystalline nanoplates by considering surface effects as well as interface region, International Journal of Mechanical Sciences 85: 160-167.
[24] Mouloodi S., Mohebbi S., Khojasteh J., Salehi M., 2014, Size-dependent static characteristics of multicrystalline nanoplates by considering surface effects, International Journal of Mechanical Sciences 79: 162-167.
[25] Wang K. F., Wang B. L., 2013, A finite element model for the bending and vibration of nanoscale plates with surface effect, Finite Elements in Analysis and Design 74: 22-29.
[26] Wang K.F., Wang B.L., 2011, Combining effects of surface energy and non-local elasticity on the buckling of nanoplates, Micro and Nano Letters 6: 941-943.
[27] Wang K.F., Wang B.L., 2011, Vibration of nanoscale plates with surface energy via nonlocal elasticity, Physica E 44: 448-453.
[28] Farajpour A., Dehghany M., Shahidi A. R., 2013, Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment, Composites Part B: Engineering 50: 333-343.
[29] Asemi S. R., Farajpour A., 2014, Decoupling the nonlocal elasticity equations for thermo-mechanical vibration of circular graphene sheets including surface effects, Physica E 60: 80-90.
[30] Juntarasaid C., Pulngern T., Chucheepsakul S., 2012, Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity, Physica E 46: 68-76.
[31] Mahmoud F.F., Eltaher M.A., Alshorbagy A.E., Meletis E.I., 2012, Static analysis of nanobeams including surface effects by nonlocal finite element, Journal of Mechanical Science and Technology 26: 3555-3563.
[32] Eltaher M.A., Mahmoud F.F., Assie A.E., Meletis E.I., 2013, Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams, Applied Mathematics and Computation 224:760-774.
[33] Karimi M., Haddad H.A., Shahidi A.R., 2015, Combining surface effects and non-local two variable refined plate theories on the shear/biaxial buckling and vibration of silver nanoplates, Micro and Nano Letters 10: 276-281.
[34] Hosseini–Hashemi S. h., Fakher M., Nazemnezhad R., 2013, Surface effects on free vibration analysis of nanobeams using nonlocal elasticity: a comparison between Euler-Bernoulli and Timoshenko, Journal of Solid Mechanics 5: 290-304.
[35] Ghorbanpour Arani A., Kolahchi R., Hashemian M.,2014, Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 203:228-245.
[36] Ghorbanpour Arani A., Fereidoon A., Kolahchi R., 2014, Nonlinear surface and nonlocal piezoelasticity theories for vibration of embedded single-layer boron nitride sheet using harmonic differential quadrature and differential cubature methods, Journal of Intelligent Material Systems and Structures 26:1150-1163.
[37] Mohammadi M., Moradi A., Ghayour M., Farajpour A., 2014, Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11: 437-458.
[38] Mohammadi M., Farajpour A., Goodarzi M., Dinari F., 2014, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11: 659-682.
[39] Mohammadi M., Farajpour A., Goodarzi M., Heydarshenas R., 2013, Levy type solution for nonlocal thermomechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics 5: 116-132.
[40] Asemi S. R., Farajpour A., Borghei, M., Hassani A. H., 2014, Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics, Latin American Journal of Solids and Structures 11: 704-724.
[41] Ghorbanpour Arani A.H., Maboudi M.J., Ghorbanpour Arani A., Amir S., 2013, 2D-magnetic field and biaxiall in-plane pre-load effects on the vibration of double bonded orthotropic graphene sheets, Journal of Solid Mechanics 5: 193-205.
[42] Ghorbanpour Arani A., Amir S., 2013, Nonlocal vibration of embedded coupled CNTs conveying fluid Under thermo-magnetic fields via Ritz method, Journal of Solid Mechanics 5:206-215.
[43] Ghorbanpour Arani A., Kolahchi R., Allahyari S.M.R., 2014, Nonlocal DQM for large amplitude vibration of annular boron nitride sheets on nonlinear elastic medium, Journal of Solid Mechanics 6:334-346.
[44] Anjomshoa A., Shahidi A.R., Shahidi S.H., Nahvi H., 2015, Frequency analysis of embedded orthotropic circular and elliptical micro/nano-plates using nonlocal variational principle, Journal of Solid Mechanics 7:13-27.
[45] Naderi A., Saidi A.R., 2014, Nonlocal postbuckling analysis of graphene sheets in a nonlinear polymer medium, International Journal of Engineering Science 81: 49-65.
[46] Naderi A., Saidi A.R., 2013, Modified nonlocal mindlin plate theory for buckling analysis of nanoplates, Journal of Nanomechanics and Micromechanics 4:130150-130158.
[47] Eringen A.C., Edelen D.G.B., 1972, On nonlocal elasticity, International Journal of Engineering Science 10: 233-248.
[48] Malekzadeh P., Shojaee M., 2013, A two-variable first-order shear deformation theory coupled with surface and nonlocal effects for free vibration of nanoplates, Journal Vibration and Control 21(14): 2755-2772.
[49] Karamooz Ravari M. R., Talebi S. A., Shahidi R., 2014, Analysis of the buckling of rectangular nanoplates by use of finite-difference method, Meccanica 49: 1443-1455.
[50] Karamooz Ravari M.R., Shahidi R., 2013, Axisymmetric buckling of the circular annular nanoplates using finite difference method, Meccanica 48: 135-144.
[51] GreeJ.R, Street R.A., 2007, Mechanical characterization of solution-derived nanoparticle silver ink thin films, Journal of Applied Physics 101: 103529.
