BUCKLING ANALYSIS OF PLATES USING AN EFFICIENT SINUSOIDAL SHEAR DEFORMATION THEORY
DOI:
https://doi.org/10.4314/jfas.v14i1.11Keywords:
Buckling analysis; Refined plate theory; The nonlinear strain-displacement of Von Karman relations; Isotropic plate; Orthotropic plate; Navier method.Abstract
Mechanical buckling response of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The nonlinear strain-displacement of Von Karman relations are also taken into consideration.The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.
Downloads
References
S K. Singh and A, Chakrabarti. Buckling analysis of laminated composite plates using an efficient C0 FE model. Latin American Journal of Solids and Structures.,1(2012) 1 – 13
S.E. Kim, H.T. Thai, J. Lee. Buckling analysis of plates using the two variable refined plate theory. Thin-Walled Structures, 47, 455–462 (2009).
Timoshenko SP, Woinowsky-Krieger S. Theory of plates and shells. NewYork: McGraw-Hill;1959.
Timoshenko SP, Gere JM. Theory of elastic stability. New York: McGraw-Hill;1961.
Bank L, Yin J. Buckling of orthotropic plates with free and rotationally restrained unloaded edges. Thin Wall Struct 1996; 24(1): 83–96.
Kang JH, Leissa AW. Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges. Int J Solids Struct 2005;42(14):4220–38.
Aydogdu M, Ece MC. Buckling and vibration of non-ideal simply supported rectangular isotropic plates. Mech Res Commun 2006;33(4):532–40.
Hwang I, Lee JS. Buckling of orthotropic plates under various in plane loads. KSCE J Civ Eng 2006;10(5):349–56.
Reissner E. The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech-TASME 1945;12(2):69–77.
Mindlin RD. Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech-TASME 1951;18(1):31–8.
Levinson M. An accurate simple theory of the statics and dynamics of elastic plates. Mech Res Commun 1980;7(6): 343–50.
Reddy JN. A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct 1984 ;20(9):881–96.
Shimpi RP, Patel HG. A two variable refined plate theory for orthotropic plate analysis. Int J Solids Struct 2006;43(22–23):6783–99.
Khalfi Y, Bouchikhi AS, and Bellebna Y. (2019). Mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory. Frattura ed Integrita Strutturale, 48: 208-221
Reddy JN. Mechanics of laminated composite plate: theory and analysis. New York: CRC Press;1997.
Srinivas S, Rao AK. Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int J Solids Struct1970;6(11): 1463–81.
Huu-Tai Thai, Seung-Eock Kim. Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory. Composite Structures 93 (2011) 1738–1746.
Submissions
