Stress Analysis of Skew Nanocomposite Plates Based on 3D Elasticity Theory Using Differential Quadrature Method

Document Type : Research Paper


School of Mechanical Engineering, Shiraz University


In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results for skew nanocomposite plates are investigated. The differential quadrature method (DQM) is used to solve these equations. In order to show the accuracy of present work, our results are compared with other numerical solution for skew plates. From the knowledge of author, it is the first time that the stress analysis of arbitrary straight-sided quadrilateral nanocomposite plates is investigated. It is shown that increasing the skew angle and thickness of nanocomposite skew plate will decrease the vertical displacements. It is also noted that the thermal effects are also added in the governing equations.


[1] Rieth M., Schommers W., 2005, Handbook of Theoretical and Computational Nanotechnology, Basic Concepts, Nanomachines and Bionanodevices, Forschungszentrum Karlsruhe, Germany 1:1-33.
[2] Shariyat M., Darabi E.A., 2013, Variational iteration solution for elastic–plastic impact of polymer/clay nanocomposite plates with or without global lateral deflection, employing an enhanced contact law, International Journal of Mechanics and Scienc 67:14-27.
[3] Jafari Mehrabadi S., Sobhani Aragh B., Khoshkhahesh V., 2012, Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes ,Composite Part B: Engineering 43:2031-2040.
[4] Belay O.V., Kiselev S.P., 2011, Molecular dynamics simulation of deformation and fracture of a “copper- molybdenum” nanocomposite plate under uniaxial tension, Physical Mesomechanics 14:145-153.
[5] Yas M.H., Pourasghar A., Kamarian S., 2013, Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube , Material Design 49:583-590.
[6] Moradi-Dastjerdi R., Foroutan M., Pourasghar A., 2013, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method, Material Design 44:256-266.
[7] Heshmati M., Yas M.H., 2013, Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads, Material Design 49:894-904.
[8] Shen H.S., Xiang Y., 2013, Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment Composite Part B: Engineering 52:311-322.
[9] Eftekhari S.A., Jafari A.A., 2013, Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions , Applied Mathematical Modelling 37(12–13):7398–7426.
[10] Upadhyay A.K., Shukla K.K., 2013, Geometrically nonlinear static and dynamic analysis of functionally graded skew plates, Communications in Nonlinear Science and Numerical Simulation 18:2252-2279.
[11] Jaberzadeh E., Azhari M., Boroomand B., 2013, Inelastic buckling of skew and rhombic thin thickness-tapered plates with and without intermediate supports using the element-free Galerkin method, Applied Mathematical Modelling 37(10–11):6838–6854.
[12] Daripa R., Singha M.K., 2009, Influence of corner stresses on the stability characteristics of composite skew plates, International Journal of Non-Linear Mechanics 44(2):138-146.
[13] Kumar N., Sarcar M.S.R., Murthy M.M.M., 2009, Static analysis of thick skew laminated composite plate with elliptical cutout, Indian Journal of Engineering Material Science 16:37-43.
[14] Karami G., Shahpari S.A., Malekzadeh P., 2003, DQM analysis of skewed and trapezoidal laminated plates, Composite Structure 59:393-402.
[15] Malekzadeh P., Karami G., 2006, Differential quadrature nonlinear analysis of skew composite plates based on FSDT, Engineering Structure 28(9):1307-1318.
[16] Malekzadeh P., 2007, A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates, Thin-Walled Structure 45(2):237-250.
[17] Malekzadeh P., 2008, Differential quadrature large amplitude free vibration analysis of laminated skew plates, on FSDT, Composite Structure 83(2):189-200.
[18] Das D., Sahoo P., Saha K.A., 2009, Variational analysis for large deflection of skew under uniformly distributed load through domain mapping technique, International Journal of Engineering Science and Technology 1:16-32.
[19] Griebal M., Hamaekers J., 2005, Molecular dynamics simulations of the mechanical properties of polyethylene-carbon nanotube composites, Institut fur Numerische Simulation, Germani.
[20] Malekzadeh P., 2008, Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM, Thin-Walled Structure 46:11-26.
[21] Hashemi M.R., Abedini M.j., Neill S.p., Malekzadeh P., 2008, Tidal and surge modelling using differential quadrature: A case study in the Bristol Channel, Coastal Engineering 55:811-819.
[22] Alibeygi Beni A., Malekzadeh P., 2012, Nonlocal free vibration of orthotropic non-prismatic skew nanoplates, Composite Structure 94:3215-3222.
[23] Malekzadeh P., Heydarpour Y., 2013, Free vibration analysis of rotating functionally graded truncated conical shells, Composite Structure 97:176-188.
[24] Sadd M.H., 2009, Elasticity, Theory, Applications, and Numerics, Elsevier.
[25] Griebel M., Hamaekers J., 2004, Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites, Computer Methods in Applied Mechanics and Engineering 193:1773-1788.