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

Akif Kutlu; Mehmet H. Omurtag

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

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

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.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Akif Kutlu This is me
0000-0001-6865-3022
Türkiye

Mehmet H. Omurtag This is me
0000-0003-2669-6459
Türkiye

Publication Date

June 1, 2021

Submission Date

October 13, 2019

Acceptance Date

March 5, 2020

Published in Issue

Year 2020 Volume: 38 Number: 2

IZ

https://izlik.org/JA66PJ37GU

Cite

RIS / Bibtex

APA

Kutlu, A., & Omurtag, M. H. (2021). BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM. Sigma Journal of Engineering and Natural Sciences, 38(2), 659-666. https://izlik.org/JA66PJ37GU

AMA

1.Kutlu A, Omurtag MH. BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM. SIGMA. 2021;38(2):659-666. https://izlik.org/JA66PJ37GU

Chicago

Kutlu, Akif, and Mehmet H. Omurtag. 2021. “BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM”. Sigma Journal of Engineering and Natural Sciences 38 (2): 659-66. https://izlik.org/JA66PJ37GU.

EndNote

Kutlu A, Omurtag MH (June 1, 2021) BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM. Sigma Journal of Engineering and Natural Sciences 38 2 659–666.

IEEE

[1]A. Kutlu and M. H. Omurtag, “BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM”, SIGMA, vol. 38, no. 2, pp. 659–666, June 2021, [Online]. Available: https://izlik.org/JA66PJ37GU

ISNAD

Kutlu, Akif - Omurtag, Mehmet H. “BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM”. Sigma Journal of Engineering and Natural Sciences 38/2 (June 1, 2021): 659-666. https://izlik.org/JA66PJ37GU.

JAMA

1.Kutlu A, Omurtag MH. BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM. SIGMA. 2021;38:659–666.

MLA

Kutlu, Akif, and Mehmet H. Omurtag. “BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM”. Sigma Journal of Engineering and Natural Sciences, vol. 38, no. 2, June 2021, pp. 659-66, https://izlik.org/JA66PJ37GU.

Vancouver

1.Akif Kutlu, Mehmet H. Omurtag. BUCKLING OF RECTANGULAR FSDT PLATES RESTING ON ORTHOTROPIC FOUNDATION BY MIXED FEM. SIGMA [Internet]. 2021 Jun. 1;38(2):659-66. Available from: https://izlik.org/JA66PJ37GU