BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM

Year 2020, Volume: 38 Issue: 2, 659 - 666, 01.06.2021

Akif Kutlu Mehmet H. Omurtag

Abstract

This study presents a mixed type finite element procedure for the linear buckling analysis of moderately thick plates lying on orthotropic elastic foundation. Kinematical expressions are due to the Mindlin plate theory and von Kármán strains. The force intensity exerted by orthotropic foundation on the plate is reflected according to the Pasternak model. Material directions of the foundation coincides with the global axes of the plate. The first variation of the systems nonlinear functional is obtained by following the Hellinger-Reissner principle. This expression is linearized according to the incremental formulation, thus the system and geometric matrices of the problem are obtained. Finite element equations are constructed by discretizing the plate domain with four noded isoparametric quadrilateral elements. After a static condensation procedure, force and couple type field variables are removed from the equations in order to reduce the problem into the solution of a standard Eigen-value system. Firstly, a convergence and comparison study is presented to verify the formulation and numerical procedure. The effects of foundation and plate parameters on the critical buckling loads are investigated.

Keywords

Mindlin plate, orthotropic pasternak foundation, Hellinger-Reissner, mixed finite elements, linear buckling

References

• [1] Dym C.L., (2002) Stability Theory and its Applications to Structural Mechanics, Courier Dover Publications.
• [2] Ugurlu B., Kutlu A., Ergin A., Omurtag M.H., (2008) Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid, J. Sound. Vib., 317 308–328. doi:10.1016/j.jsv.2008.03.022.
• [3] Xiang Y., Wang C.M., Kitipornchai S., (1994) Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations, International Journal of Mechanical Sciences, 36 311–316. doi:10.1016/0020-7403(94)90037-X.
• [4] Xiang Y., Kitipornchai S., Liew K. M., (1996) Buckling and vibration of thick laminates on Pasternak foundations, Journal of Engineering Mechanics, 122 54–63. doi:10.1061/(ASCE)0733-9399(1996)122:1(54).
• [5] Lam K.Y., Wang C.M., He X.Q., (2000) Canonical exact solutions for Levy-plates on two-parameter foundation using Green’s functions, Engineering Structures, 22 364–378. doi:10.1016/S0141-0296(98)00116-3.
• [6] Akhavan H., Hosseini Hashemi Sh., Damavandi Taher H.R., Alibeigloo A., Vahabi Sh., (2009) Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis, Computational Materials Science, 44 968–978. doi:10.1016/j.commatsci.2008.07.004.
• [7] Matsunaga H., (2000) Vibration and stability of thick plates on elastic foundations, Journal of Engineering Mechanics, 126 27–34. doi:10.1061/(ASCE)0733-9399(2000)126:1(27).
• [8] Park M., Choi D.-H., (2018) A simplified first-order shear deformation theory for bending, buckling and free vibration analyses of isotropic plates on elastic foundations, KSCE Journal of Civil Engineering, 22 1235–1249. doi:10.1007/s12205-017-1517-6.
• [9] Doğruoğlu A.N., Omurtag M.H., (2000) Stability analysis of composite-plate foundation interaction by mixed FEM, J. Eng. Mech, 126 928–936.
• [10] Setoodeh A.R., Karami G., (2004) Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM, Engineering Structures, 26 211–220. doi: 10.1016/j.engstruct.2003.09.009.
• [11] Kutlu A., Omurtag M.H., (2019) Elastik zeminle etkileşen nispeten kalın plağın karışık sonlu elemanlarla burkulma analizi, 21. Ulusal Mekanik Kongresi, 774–780, Niğde, Turkey.
• [12] Reddy J.N., (2006) Theory and Analysis of Elastic Plates and Shells, CRC Press.
• [13] Kutlu A., Omurtag M.H., (2012) Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method, International Journal of Mechanical Sciences, 65 64–74. doi:10.1016/j.ijmecsci.2012.09.004.
• [14] Kutlu A., Meschke G., Omurtag M.H., (2016) A new mixed finite-element approach for the elastoplastic analysis of Mindlin plates, Journal of Engineering Mathematics, 99 137–155. doi:10.1007/s10665-015-9825-7.
• [15] Aksoylar C., Ömercikoğlu A., Mecitoğlu Z., Omurtag M.H., (2012) Nonlinear transient analysis of FGM and FML plates under blast loads by experimental and mixed FE methods, Compos. Struct., 94 731–744. doi:10.1016/j.compstruct.2011.09.008.