Abstract
In this paper, a simple 2D quadrilateral finite element has been developed based on Reddy’s third order shear deformation theory for the buckling behavior analysis of isotropic and composites laminated plates. The developed element is a C0 four-nodded isoparametric with seven degrees of freedom (7DOF) at each node. Each node has only three translation components, two rotations and two higher order rotational degrees. The nodal approximation is expressed from the Lagrange interpolation for the considered degrees of freedom in each node and for the element geometry through all coordinates. In particular, the selective numerical integration is introduced for the present FE formulation in order to achieve good results and to alleviate the shear locking problem. The model is able to provide a parabolic distribution transverse shear stress through the thickness and satisfying zero boundary conditions at the top and bottom surfaces of the plate without any remedy to correction factors. The performance and reliability of the proposed formulation are proved by comparing with those obtained analytically by three-dimensional theories and those obtained by the same order models in the literature. The results indicate that the proposed formulation is promising in terms of the accuracy and the convergence speed for both thin and thick plates.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Averill R, Reddy JN (1992) An assessment of four-noded plate finite elements based on a generalized third-order theory. Int J Numer Meth Eng 33(8):1553–1572
Belkaid K, Tati A (2015) Analysis of laminated composite plates bending using a new simple finite element based on Reddy’s third order theory. Revue Des Composites et des Materiaux Avancés 25(1):89–106
Belkaid K, Tati A et al (2016) A simple finite element with five degrees of freedom based on Reddy’s third-order shear deformation theory. Mech Compos Mater 52(2):257–270
Chakrabarti A, Sheikh AH (2003) Buckling of laminated composite plates by a new element based on higher order shear deformation theory. Mech Adv Mater Struct 10(4):303–317
Ferreira AJM, Roque CMC et al (2011) Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory. Thin-Walled Structures 49(7):804–811. https://doi.org/10.1016/j.tws.2011.02.005
Gerard G, Becker H (1957) Handbook of structural stability part III: buckling of curved plates and shells
Ghosh AK, Dey SS (1994) Buckling of laminated plates-A simple finite element based on higher-order theory. Finite Elem Anal Des 15(4):289–302
Ghugal Y, Shimpi R (2002) A review of refined shear deformation theories of isotropic and anisotropic laminated plates. J Reinf Plast Compos 21(9):775–813
Hughes TJ, Cohen M et al (1978) Reduced and selective integration techniques in the finite element analysis of plates. Nucl Eng Des 46(1):203–222
Leissa AW (1987a) An overview of composite plate buckling. Compos Struct 4:1–29. (Springer)
Leissa AW (1987b) A review of laminated composite plate buckling. Appl Mech Rev 40(5):575–591
Moita J, Soares CMM et al (1996) Buckling behaviour of laminated composite structures using a discrete higher-order displacement model. Compos Struct 35(1):75–92
Moita JS, Soares CMM et al (1999) Buckling and dynamic behaviour of laminated composite structures using a discrete higher-order displacement model. Comput Struct 73(1):407–423
Noor AK (1975) Stability of multilayered composite plates. Fibre Sci Technol 8(2):81–89. https://doi.org/10.1016/0015-0568(75)90005-6
Putcha N, Reddy JN (1986) Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory. J Sound Vib 104(2):285–300
Reddy JN (1984a) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745–752
Reddy JN (1984b) A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct 20(9):881–896
Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton, FL
Reddy JN, Phan N (1985) Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J Sound Vib 98(2):157–170
Reddy JN, Robbins D (1994) Theories and computational models for composite laminates. Appl Mech Rev 47(6):147–169
Singh SK, Chakrabarti A (2012) Buckling analysis of laminated composite plates using an efficient C0 FE model. Latin Am J Solids Struct 9:1–13
Singh SNLG, Rao GV (1996) Stability of laminated composite plates subjected to various types of in-plane loadings. Int J Mech Sci 38(2):191–202
Xu J, Zhao Q, et al (2013) A critical review on buckling and post-buckling analysis of composite structures
Zienkiewicz OC, Cheung YK (1964) The finite element method for analysis of elastic isotropic and orthotropic slabs, ICE proceedings, Thomas Telford
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Belkaid, K. (2019). Buckling Analysis of Isotropic and Composite Laminated Plates: New Finite Element Formulation. In: Boukharouba, T., Chaari, F., Ben Amar, M., Azouaoui, K., Ouali, N., Haddar, M. (eds) Computational Methods and Experimental Testing In Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-11827-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-11827-3_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11826-6
Online ISBN: 978-3-030-11827-3
eBook Packages: EngineeringEngineering (R0)