An analytical approach for bending and stress analysis of cross/angle-ply laminated composite plates under arbitrary non-uniform loads and elastic foundations

• Autorzy: Alipour M. M.

Identyfikatory

DOI

10.1016/j.acme.2015.11.001

• Języki publikacji: EN

Abstrakty

EN

In the present study, a new analytical approach is developed for bending and stress analysis of angle-ply laminated composite and sandwich plates subjected to arbitrary non-uniform loads. Governing equations are derived based on the Mindlin–Reissner plate theory. For the first time, a system of three second order coupled partial differential equations is analytically solved by using power-series solution. The transverse shear stress is determined based on the three-dimensional theory of elasticity. Most of the available analytical solutions of the rectangular plates were presented for specific load and edge conditions. The proposed method can be applied for plates with arbitrary boundary conditions and various distributed loads. To demonstrate the generality and accuracy of the present method, comprehensive numerical examples are presented and compared with other available published results. The results show that the proposed solution can be applied for analysis of cross/angle-ply laminated composite and sandwich plates with various combinations of the edge conditions, orientation angle of the laminated composite plate, arbitrary non-uniform transversely distributed loads and non-uniform elastic foundation. The proposed method predicts excellent results for laminated composite plates. Also even for moderately thick sandwich plates, accuracy of the present results are in a good agreement with the exact solutions.

Słowa kluczowe

EN

analytical approach; laminated composite plates; sandwich plates; non-uniform loads; non-uniform elastic foundation

PL

laminowane płyty kompozytowe; płyty warstwowe; nierównomierne obciążenie

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2016
• Tom: Vol. 16, no. 2
• Strony: 193--210
• Opis fizyczny: Bibliogr. 36 poz., rys., tab., wykr.

Twórcy

autor

Alipour M. M.

• Department of Mechanical Engineering, University of Mazandaran, Babolsar 47416-13534, Iran

Bibliografia

• [1] N.J. Pagano, Exact solutions for composite laminates in cylindrical bending, Journal of Composite Materials 3 (3) (1969) 398–411.
• [2] N.J. Pagano, Exact solutions for rectangular bidirectional composites and sandwich plates, Journal of Composite Materials 4 (1970) 20–34.
• [3] S. Srinivas, A refined analysis of composite laminates, Journal of Sound and Vibration 30 (1973) 495–507.
• [4] J.N. Reddy, C.F. Liu, A higher-order shear deformation theory of laminated elastic shells, International Journal of Engineering Science 23 (1985) 319–330.
• [5] M. Touratier, An efficient standard plate theory, International Journal of Engineering Science 29 (8) (1991) 901–916.
• [6] E. Altunsaray, I. Bayer, Deflection and free vibration of symmetrically laminated quasi-isotropic thin rectangular plates for different boundary conditions, Ocean Engineering 57 (2013) 197–222.
• [7] M. Somireddy, A. Rajagopal, Meshless natural neighbor Galerkin method for the bending and vibration analysis of composite plates, Composite Structures 111 (2014) 138–146.
• [8] B. Tian, R. Li, Y. Zhong, Integral transform solutions to the bending problems of moderately thick rectangular plates with all edges free resting on elastic foundations, Applied Mathematical Modelling 39 (1) (2015) 128–136.
• [9] B. Pan, R. Li, Y. Su, B. Wang, Y. Zhong, Analytical bending solutions of clamped rectangular thin plates resting on elastic foundations by the symplectic superposition method, Applied Mathematics Letters 26 (3) (2013) 355–361.
• [10] M. Karama, K.S. Afaq, S. Mistou, A new theory for laminated composite plates, Journal of Materials Design and Applications 23 (2) (2009) 53–62.
• [11] J.L. Mantari, A.S. Oktem, C.G. Soares, A new higher order shear deformation theory for sandwich and composite laminated plates, Composites: Part B 43 (2012) 1489–1499.
• [12] H.T. Thai, D.H. Choi, Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates, Applied Mathematical Modelling 37 (18-19) (2013) 8310–8323.
• [13] M.A. Zenkour, Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates, Applied Mathematical Modelling 27 (2003) 515–534.
• [14] T.H. Daouadji, A. Tounsi, E.A.A. Bedia, Analytical solution for bending analysis of functionally graded plates, Scientia Iranica B 20 (3) (2013) 516–523.
• [15] L. Demasi, Three-dimensional closed form solutions and exact thin plate theories for isotropic plates, Composite Structures 80 (2007) 183–195.
• [16] A. Arikoglu, I. Ozkol, Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method, Composite Structures 92 (12) (2010) 3031–3039.
• [17] H.S. Yalcin, A. Arikoglu, I. Ozkol, Free vibration analysis of circular plates by differential transformation method, Applied Mathematics & Computations 212 (2009) 377–386.
• [18] M.M. Alipour, M. Shariyat, Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations, Mechanics Research Communications 38 (2011) 594–601.
• [19] M.M. Alipour, M. Shariyat, A semi-analytical solution for buckling analysis of variable thickness two-directional functionally graded circular plates with non-uniform elastic foundations, Journal of Engineering Mechanics 139 (2013) 664–676.
• [20] M.M. Alipour, M. Shariyat, An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution, European Journal of Mechanics A/Solids 34 (2012) 78–101.
• [21] M.M. Alipour, M. Shariyat, Stress analysis of two-directional FGM moderately thick constrained circular plates with non- uniform load and substrate stiffness distributions, Journal of Solid Mechanics 2 (2010) 316–331.
• [22] M.M. Alipour, M. Shariyat, Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a 3D elasticity-type double superposition zigzag theory, Aerospace Science and Technology 32 (2014) 235–259.
• [23] M.M. Alipour, M. Shariyat, An analytical global-local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations, Archives of Civil and Mechanical Engineering 14 (2014) 6–24.
• [24] M.M. Alipour, M. Shariyat, Semi-analytical consistent zigzag-elasticity formulations with implicit layerwise shear correction factors for dynamic stress analysis of sandwich circular plates with FGM layers, Composites Part B 49 (2013) 43–64.
• [25] M.M. Alipour, M. Shariyat, Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates, Composite Structures 106 (2013) 426–445.
• [26] K. Bhaskar, J. Dhaoya, Straightforward power series solutions for rectangular plates, Composite Structures 89 (2) (2009) 253–261.
• [27] L.M.S. Castro, A.J.M. Ferreira, S. Bertoluzza, R.C. Batra, J.N. Reddy, A wavelet collocation method for the static analysis of sandwich plates using a layerwise theory, Composite Structures 92 (2010) 1786–1792.
• [28] A.J.M. Ferreira, C.M.C. Roque, P.A.L.S. Martins, Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method, Composites: Part B 34 (2003) 627–636.
• [29] B.N. Pandya, T. Kant, Higher-order shear deformable theories for flexure of sandwich plates – finite element evaluations, International Journal of Solids and Structures 24 (1988) 419–451.
• [30] C.M.C. Roque, A.J.M. Ferreira, R.M.N. Jorge, Modeling of composite and sandwich plates by a trigonometric layerwise deformation theory and radial basis functions, Composite Part B 36 (2005) 559–572.
• [31] J.L. Mantari, A.S. Oktem, C.G. Soares, A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates, Computers and Structures 94-95 (2012) 45–53.
• [32] A.J.M. Ferreira, C.M.C. Roque, R.M.N. Jorge, Analysis of composite plates by trigonometric shear deformation theory and multiquadrics, Computers and Structures 83 (2005) 2225–2237.
• [33] J.L. Mantari, A.S. Oktem, C.G. Soares, Static, dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory, Composite Structures 94 (2011) 37–49.
• [34] A.J.M. Ferrira, Analysis of composite plates using a layerwise shear deformation theory and multiquadrics discretization, Mechanics of Advanced Materials and Structures 12 (2005) 99–112.
• [35] S. Xiang, K. Wang, Y. Ai, Y. Sha, H. Shi, Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories, Composite Structures 91 (2009) 31–37.
• [36] C.M. Wang, Deducing thick plate solutions from classical thin plate solutions, Structural Engineering and Mechanics 11 (2001) 89–104.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę