ON A RECURSIVE METHODOLOGY FOR SEMI-ANALYTICAL SOLUTIONS OF SYMMETRIC AND UNSYMMETRIC LAMINATED THIN PLATES

Autores

  • Tales de Vargas Lisbôa Federal University of Rio Grande do Sul
  • Filipe Paixão Geiger

DOI:

https://doi.org/10.26512/ripe.v2i24.20977

Palavras-chave:

Recursive Methodology. Laminated Plates. Semi-analytical Solution. Rayleigh-Ritz Method.

Resumo

 The present paper has as objective the introduction and analysis of a new procedure in order to derive semi-analytical solutions of symmetric and unsymmetrical laminated rectangular thin plates in a recursive manner. The methodology is based on three main characteristics: (a) decomposition of the differential operator into two or more components, (b) an infinite expansion of the differential equation solution and, (c) determination of each superposed solution by a relationship between the divided operators and previous solutions. The first expanded term concerns to the plate’s isotropic solution and, in each step, orthorhombic laminae influence is inserted. In order to approximate the solutions, the pb-2 Rayleigh-Ritz Method is used. Obtained solutions are discussed and compared to those found in the literature.

Downloads

Não há dados estatísticos.

Referências

Abbasbandy, S., 2006, Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method. Applied Mathematics and Computation, vol. 172, n. 1, pp. 431”“438.

Adomian, G., 1994, Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Dordrecht.

Ansys R Inc., 2017, User Guide v. 17.0.

Altenbach, H., 1998, Theories for laminated and sandwich plates. Mechanics of Composite Materials, vol. 34, n. 3, pp. 243”“252.

Bhaskar, K., & Dhaoya, J., 2009, Straightforward power series solutions for rectangular plates. Composite Structures, vol. 89, n. 2, pp. 253”“261.

Bhaskar, K., & Kaushik, B., 2004, Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges. Composite Structures, vol. 63, n. 1, pp. 63”“68.

Bhat, R. B., 1985, Plate Deflections using Orthogonal Polynomials. Journal of Engineering Mechanics, vol. 111, n. 11, pp: 1301”“1309.

Browaeys, J. T.,& Chevrot, S., 2004, Decomposition fo the Elastic Tensor and Geophysical Applications. Geophysical Journal International, vol. 159, n. 2, pp. 667”“678.

Chadwick, P., Vianello, M., & Cowin, S. C., 2001, A New Proof that the Number of Linear Elastic Symmetries is Eight. Journal of the Mechanics and Physics of Solids, vol. 49, n. 11, pp. 2471”“2492.

Cheniguel, A., &Ayadi, A., 2011, Solving heat equation by the adomian decomposition method. Proceedings of the World Congress on Engineering (WCE 2011), vol. 1, n. 8, pp. 288”“290.

Kitipornchai, S., Xiang, Y., Liew, K. M., & Lim, M. K., 1994, A Global Approach for Vibration of Thick Trapezoidal Plates, Computers & Structures, vol. 53, n. 1, pp. 83”“92.

Li, J-., 2009, Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations. Journal of Computational and Applied Mathematics, vol. 228, n. 1, pp. 168”“173.

Liew, K. M., & Lam, K. Y., 1991, A Rayleigh-Ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions. International Journal of Solids and Structures, vol. 27, n. 2, pp. 189”“203.

Liew, K. M., & Wang, C. M., 1993, pb-2 Rayleigh-Ritz Method for General Plate Analysis, Engineering Structures, vol. 15, n. 1,pp. 55”“60.

McGee, O. G., Kim, J. W., Kim, Y. S., & Leissa, A. W., 1996, Corner stress singularity effects on the vibration of rhombic plates with combinations of clamped and simply supported edges. Journal of Sound and Vibration, vol. 193, n. 3, pp. 555”“580.

Rao, T. R. The Use of Adomian’s Decomposition Method for Solving Generalized Riccati Differential Equations. Proceedings of 6th IMT-GT (ICMSA 2010), pp. 935”“941.

Reddy, J. N., 1993, An evaluation of equivalent-single-layer and layerwise theories of composite laminates. Composites Structures, vol. 25, n. (1-4), pp. 21”“35.

Singh, A. V., & Elaghabash, Y., 2003, On Finite Displacement Analysis of Quadrangular Plates, International Journal of Non-Linear Mechanics, vol. 38, n. 8, pp. 1149”“1162.

Tabatabaei, K., 2010, Solution of differential equations by Adomian decomposition method. 2nd International Conference on Computer Engineering and Technology (ICCET), vol. 12, pp. 553”“555.

Ungbhakorn, V., & Wattanasakulpong, N., 2006, Bending Analysis of Symmetrically Laminated Rectangular Plates with Arbitrary Edge Supports by the Extended Kantorovich Method, Thammasat International Journal of Science and Technology, vol. 11, n. 1, pp. 33”“44.

Zhang, Y. X., & Kim, K. S., 2004, Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated plates. International Journal for Numerical Methods in Engineering, vol. 61, n. 11, pp. 1771”“1796.

Downloads

Publicado

2017-02-08

Como Citar

Lisbôa, T. de V., & Geiger, F. P. (2017). ON A RECURSIVE METHODOLOGY FOR SEMI-ANALYTICAL SOLUTIONS OF SYMMETRIC AND UNSYMMETRIC LAMINATED THIN PLATES. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(24), 13–26. https://doi.org/10.26512/ripe.v2i24.20977