Abstract
In this paper we use a trigonometric layerwise deformation theory for modelling symmetric composite plates. We use a meshless discretization method based on global multiquadric radial basis functions. The results obtained are compared with solutions derived from other models and numerical techniques. The results show that the use of trigonometric layerwise deformation theory discretized with multiquadrics provides very good solutions for composite plates and excellent solutions for sandwich plates.
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References
J.M. Whitney and N.J. Pagano. Shear deformation in heterogeneous anisotropic plates. ASME J. of Appl. Mech., 37:1031–1036, 1970.
E. Reissner. A consistment treatment of transverse shear deformations in laminated anisotropic plates. AIAA J., 10(5):716–718, 1972.
J.N. Reddy. Energy and Variational Methods in Applied Mechanics. John Wiley, New York, 1984.
C.T. Sun. Theory of laminated plates. J. of Applied Mechanics, 38:231–238, 1971.
J.M. Whitney and C.T. Sun. A higher order theory for extensional motion of laminated anisotropic shells and plates. J. of Sound and Vibration, 30:85–97, 1973.
J.N. Reddy. A simple higher-order theory for laminated composite plates. J. of Applied Mechanics, 51:745–752, 1984.
M. Di Sciuva. An improved shear-deformation theory for moderately thick multilayered shells and plates. J. of Applied Mechanics, 54:589–597, 1987.
H. Murakami. Laminated composite plate theory with improved in-plane responses. Journal of Applied Mechanics, 53:661–666, 1986.
J.G. Ren. A new theory of laminated plate. Composite Science and Technology, 26:225–239, 1986.
A.J.M. Ferreira. Analysis of composite plates using a layerwise shear deformation theory and multiquadrics discretization. Mechanics of Advanced Materials and Structures, 2004, to appear.
D.H. Robbins and J.N. Reddy. Modelling of thick composites using a laminate layerwise theory. Int. J. Num. Meth. Eng., 36:655–677, 1993.
E. Carrera. C0 reissner-mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. International Journal of Numerical Methods in Engineering, 39:1797–1820, 1996.
H. Arya, R.P. Shimpi, and N.K. Naik. A zigzag model for laminated composite beams. Composite structures, 56:21–24, 2002.
R.P. Shimpi and A.V. Ainapure. A beam finite element based on layerwise trigonometric shear deformation theory. Composite structures, 53:153–162, 2001.
R.L. Hardy. Multiquadric equations of topography and other irregular surfaces. Geophys. Res., 176: 1905–1915, 1971.
R.L. Hardy. Theory and applications of the multiquadric-biharmonic method: 20 years of discovery. Computers Math. Applic., 19(8/9):163–208, 1990.
E.J. Kansa. Multiquadrics— a scattered data approximation scheme with applications to computational fluid dynamics. i: Surface approximations and partial derivative estimates. Comput. Math. Appl., 19(8/9): 127–145, 1990.
E.J. Kansa. Multiquadrics— a scattered data approximation scheme with applications to computational fluid dynamics. ii: Solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput. Math. Appl., 19(8/9):147–161, 1990.
A.J.M. Ferreira. A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Composite Structures, 59:385–392, 2003.
A.J.M. Ferreira. Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mechanics of Advanced Materials and Structures, 10:271–284, 2003.
A.J.M. Ferreira, C.M.C. Roque, and 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, 34:627–636, 2003.
A.J.M. Ferreira, C.M.C. Roque, and R.M.N. Jorge. Analysis of composite plates by trigonometric shear deformation theory and multiquadrics. submitted, 2004.
G. Akhras, M.S. Cheung, and W. Li. Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory. Computers & Structures, 52(3):471–477, 1994.
G. Akhras, M.S. Cheung, and W. Li. Static and vibrations analysis of anisotropic laminated plates by finite strip method. Int. J. Solids Struct, 30(22):3129–3137, 1993.
J.N. Reddy. A simple higher-order theory for laminated composite plates. J. Appl. Mech., 51: 745–752, 1984.
N.J. Pagano. Exact solutions for rectangular bidirectional composites and sandwich plates. J. Compos. Mater, 4:20–34, 1970.
S. Srinivas. A refined analysis of composite laminates. J. Sound and Vibration, 30:495–507, 1973.
B.N. Pandya and T. Kant. Higher-order shear deformable theories for flexure of sandwich plates finite element evaluations. Int. J. Solids and Structures, 24:419–451, 1988.
A.J.M. Ferreira and J.T. Barbosa. Buckling behaviour of composite shells. Composite Structures, 50:93–98, 2000.
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Roque, C.M., Ferreira, A.J., Jorge, R.M. (2005). Modelling of Composite and Sandwich Plates by a Trigonometric Layerwise Theory and Multiquadrics. In: Thomsen, O., Bozhevolnaya, E., Lyckegaard, A. (eds) Sandwich Structures 7: Advancing with Sandwich Structures and Materials. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3848-8_23
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DOI: https://doi.org/10.1007/1-4020-3848-8_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3444-2
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