A Semi-Analytical Model for Buckling of Laminated Plates with the NKQ Method

Abstract:

A semi-analytical approach for analysis of laminated plates with general boundary conditions under a general distribution of loads is developed. The non-linear equations are solved by the Newton-Kantorovich-Quadrature (NKQ) method which is a combination of well-known Newton-Kantorovich method and the Quadrature method. This method attempts to solve a sequence of linear integral equations. In this paper this method is used to propose a semi-analytical model for buckling of laminated plates. The convergence of the proposed method is investigated and the validation of the method is explored through numerical examples and the results compared with finite element method (FEM). There is a good agreement between the NKQ model and FEM results.

• Periodical: Applied Mechanics and Materials (Volume 232)
• Pages: 68-72
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.232.68
• Online since: November 2012
• Authors: Rasoul Khandan, Siamak Noroozi, John Vinney, Philip Sewell, Mehran Koohgilani
• Keywords: Buckling, Composite, NKQ Method, Semi-Analytical Model

References

[1] Khandan R, Noroozi S, Sewell P, Vinney J, Ramazani MR. Optimum Design of Fibre Orientation Angles in Composite Laminate Plates for Minimum Thickness. ASME 2010 International Mechanical Engineering Congress & Exposition, 2010 Canada.

DOI: 10.1115/imece2010-40424

[2] Reissner E, Stavsky Y. Bending and Stretching of Certain Types of Aeolotropic Elastic Plates. Journal of Applied Mechanics 1961; 28: 402–408.

DOI: 10.1115/1.3641719

[3] Reddy JN. Mechanics of Laminated Composite Plates And Shells. 2004 Second Edition, CRC Press, New York.

[4] Mindlin RD. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J Appl Mech ASME 1951; 18: 31–36.

DOI: 10.1115/1.4010217

[5] Liew KM, Wang J, Tan MJ, Rajendran S. Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT. Comput. Methods Appl. Mech. Eng. 2004: 193; 4763–4779.

DOI: 10.1016/j.cma.2004.03.013

[6] Savithri S, Varadan TK. Large deflection analysis of laminated composite plates. Int. J. Non-Linear Mech. 1993; 28(1): 1–12.

DOI: 10.1016/0020-7462(93)90002-3

[7] Ovesy HR, Assaee H. The influence of bend-twist coupling on the post-buckling characteristics of composite laminated plates using semi-energy finite strip approach. Thin-Wall Struct 2007; 45: 209–20.

DOI: 10.1016/j.tws.2007.01.016

[8] Shufrin I, Rabinovitch O, Eisenberger M. Buckling of symmetrically laminated rectangular plates with general boundary conditions – a semi analytical approach. Composite Structures 2008: 82; 521–531.

DOI: 10.1016/j.compstruct.2007.02.003

[9] Bisagni C, Vescovini R. Analyticalformulationforlocalbucklingandpost-bucklinganalysis of stiffenedlaminatedpanels. Thin-Walled Structures 2009; 47: 318–334.

[10] Lopatin AV, Morozov EV. Buckling of the SSCF rectangular orthotropic plate subjected to linearly varying in-plane loading. Composite Structures 2011; 93: 1900–(1909).

DOI: 10.1016/j.compstruct.2011.01.024

[11] Daniel IM, Ishai O. Engineering Mechanics of Composite Materials. 2006 Second Edition, Oxford University Press.

[12] Saberi-Nadjafi J, Heidari M. Solving nonlinear integral equations in the Urysohn form by Newton-Kantorovich-quadrature method. Computers and Mathematics with Applications 2010; 60: 2058-(2065).

DOI: 10.1016/j.camwa.2010.07.046