AN IMPROVED FORMULATION OF NONLINEAR STRAIN-DISPLACEMENT RELATIONS AND SPECIFIC MATHEMATICAL MODELS FOR STABILITY ANALYSIS OF THIN RECTANGULAR PLATES
Abstract
ABSTRACT:Â The present work is aimed at deriving from the first principle the strain-displacement relations, and to develop specific stability equations for five (5) plate types using polynomial displacement shape functions for large deflection analysis of thin rectangular plates. This was done by looking at the deformation of a cube and formulating the new nonlinear strain-displacement relations, and substituting the new relations together with stress-strain relations into the total potential energy functional equation to arrive at the general stress parameter equation. From this equation, the general mathematical model for stability analysis of thin rectangular plates was formulated. The polynomial displacement shape function for each of the five plate types considered here was evaluated to obtain the individual stiffness. The obtained stiffnesses were substituted into the general stability model and evaluated to obtain specific mathematical models for the five plate types. The observed numerical values indicate that the frequency increases as the displacement increases and decreases as the aspect ratio increases. This conforms with existing works in literature and the behavior of plates. Therefore, the conclusion is that these newly formulated mathematical models are adequate for these analyses.
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KEYWORDS:Â Strain-displacement relations, Stress parameter, Buckling and Postbuckling loads, Stability, Large deflection, Specific Models
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Adah, E. I., (2016). “Development of Computer Programs for Analysis of Single Panel and Continuous Rectangular Platesâ€. M. Eng. Thesis submitted to Postgraduate School, Federal University of Technology Owerri. (www.library.futo.edu.ng-Adah, Edward, I. 2016)
Bloom, F., Coffin, D., (2001). “Thin Plate Buckling and Postbucklingâ€. London: Chapman & Hall/CRC (2001).
Byklum, E. and Amdahl, J., (2002). “A simplified method for elastic large deflection analysis of plates and stiffened panels due to local bucklingâ€. Thin-Walled Structures, 40 (11), 925–953 (2002).
Civalek, O. and Yavas, A., (2006). “Large Deflection Static Analysis of Rectangular Plates on Two Parameters Elastic Foundationsâ€. International Journal of Science and Technology, 1(1), 43-50, (2006).
Chajes, A., (1974). “Principles of Structural Stability Theoryâ€. London: Prentice-Hall Inc (1974).
Elsami, M. R., (2018). “Buckling and Postbuckling of Beams, Plates, and Shellsâ€. Springer International Publishing AG (2018).
Elsheikh, A., Wang, D., (2005). “Large-Deflection Mathematical Analysis of Rectangular Platesâ€. Journal of Engineering Mechanics, 131 (8), (2015).
Enem J. I., (2018). “Geometrically Nonlinear Analysis of Isotropic Rectangular Thin Plates Using Ritz Methodâ€. PhD Thesis: Department of Civil Engineering Federal University of Technology, Owerri Nigeria (www.library.futo.edu.ng-Enem, J, I. 2018)
GhannadPour, S. A. M., Alinia, M. M., (2006). “Large deflection behavior of functionally graded plates under pressure loadsâ€. Composite Structures, 75, 67–71, (2018).
Ibearugbulem, O.M., Ezeh, J.C., Ettu, L. O., (2014). “Energy Methods in Theory of Rectangular Plates: Use of Polynomial Shape Functionsâ€. Owerri, Liu House of Excellence Ventures, (2014).
Ibearugbulem, O. M., Adah, E. I., Onwuka, D. O. & C. E. Okere, (2020). “Simple and Exact Approach to Postbuckling Analysis of Rectangular Plateâ€, SSRG International Journal of Civil Engineering, 7 (6): 54-64, (2020). www.internationaljournalssrg.org.
Iwuoha, S. E., (2016). “Buckling Analysis of Plates Subjected to Biaxial Forces using Galerkin’s 1 Methodâ€. An M. Eng. Thesis submitted to Postgraduate School, Federal University of Technology Owerri. (www.library.futo.edu.ng-Iwuoha. 2016)
Iyengar, N. G., (1988). “Structural Stability of Columns and Plateâ€. Chichester, Ellis Horwood (1988).
Katsikadelis, J. T., Babouskos, N., (2007). “The Postbuckling Analysis of Plates: A BEM Based Meshless Variational Solution. Mechanical Automatic Control and Roboticsâ€. 6(1), 113-118, (2007).
Levy, S., (1942). “Bending of rectangular plates with large deflectionsâ€. Technical notes: National Advisory Committee for Aeronautics (NACA), N0. 846 (1942).
Lee, H., (1977). “Nonlinear Finite Element Analysis of Thin-Walled Membersâ€. A PhD Thesis submitted to the Faculty of Graduate Studies and Research, McGill University, Montreal, Canada, (1977).
Oguaghamba, O. A., (2015). “Analysis of buckling and postbuckling loads of Isotropic thin rectangular platesâ€. PhD Thesis: Department of Civil Engineering Federal University of Technology, Owerri Nigeria (www.library.futo.edu.ng-Oguaghamba, O. A. 2015)
Oguaghamba, O. A., Ezeh, J. C., Ibearugbulem, O.M., Ettu, L. O., (2015). “Buckling and Postbuckling Loads Characteristics of All Edges Clamped Thin Rectangular Plateâ€. The International Journal of Engineering and Science, 4(11), 55-61, (2015).
Onwuka, D. O., Ibearugbulem O. M. and Adah, E. I., (2016). “Stability analysis of axially compressed SSSS & CSCS plates using Matlab programmingâ€. International Journal of Science and Technoledge, 4(1), 66-71, (2016).
Shufrin, I., Rabinovitch O., Eisenberger, M., (2008). “A semi-analytical approach for the nonlinear large deflection analysis of laminated rectangular plates under general out-of-plane loading. International Journal of Non-Linear Mechanicsâ€. 43, 328–340, (2008).
Stein, M., (1984). “Analytical results for postbuckling behavior of plates in compression and in shearâ€. National Aeronautics and Space Administration (NASA). NASA Technical Memorandum 85766 S, (1984).
Tanriöver, H. and Senocak, E., (2004). “Large deflection analysis of unsymmetrically laminated composite plates: analytical–numerical type approachâ€. International Journal of Non-linear Mechanics. 39, 1385–1392, (2004).
Timoshenko, S. P., Woinowsky-Krieger, S. (1959). “Theory of plates and shellsâ€, 2nd ed, McGraw-Hill, New York, (1959).
Ventsel, E and Krauthamer, T., (2001). “Thin Plates and Shells: Theory, Analysis and Applicationâ€. Marcel Dekker, New York (2001)
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