EARTQUAKE BEHAVIOUR OF THICK PLATES RESTING ON ELASTIC FOUNDATION WITH FIRST ORDER FINITE ELEMENT

Yıl 2018, Cilt: 36 Sayı: 4, 935 - 950, 01.12.2018

Yaprak Itır Özdemir

Öz

This paper focus on to study dynamic analysis of thick plates resting on Winkler foundation. The governing equation is derived from Mindlin’s theory. This study is a parametric analysis therefore, the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to earthquake excitations is studied. In the analysis, as a dynamic solution the Newmark-β method is used for the time integration and finite element method is used for spatial integration. While using finite element method first order element is used. This element is 4-noded and it’s formulation is derived by using first order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 4-noded finite element can be effectively used in the earthquake analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

Anahtar Kelimeler

Parametric forced vibration analysis, thick plate, mindlin’s theory, first order finite element, winkler foundation.

Kaynakça

• [1] Winkler, E. (1867), Theory of Elasticity and Strength, Dominicus Pague, Czechoslovakia
• [2] Hetenyi, M. (1950), “A general solution for the bending of beams on an elastic foundation of arbitrary continuity.” J.Appl. Phys.. 21, 55-58.
• [3] Pasternak, PL. (1954) “New method of calculation for flexible substructures on two-parameter elastic foundation”. Gasudarstvennoe Izdatelstoo. Literatury po Stroitelstvu I Architekture, 1-56, Moskau.
• [4] Vlasov, VZ., Leont’ev, NN. (1989) Beam, plates and shells on elastic foundations. GIFML, Moskau.
• [5] Ugural A.C. (1981), Stresses in Plates and Shells, McGraw-Hill., New York.
• [6] Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells. Second edition, McGraw-Hill., New York.
• [7] Leissa A. W. The free vibration of rectangular plates. J Sound Vib 1973; 31 (3): 257-294.
• [8] Providakis C. P., Beskos D. E. Free and forced vibrations of plates by boundary elements. Comput Meth Appl Mech Eng 1989;, 74: 231-250.
• [9] Qiu J. and Feng Z. C. (2000), “Parameter dependence of the impact dynamics of thin plates,” Comput. Struct., 75(5), 491-506.
• [10] Grice R. M. and Pinnington R. J. (2002), “Analysis of the flexural vibration of a thin-plate box using a combination of finite element analysis and analytical impedances,” J Sound Vib., 249(3), 499-527.
• [11] Lok T. S. and Cheng Q. H. (2001), “Free and forced vibration of simply supported, orthotropic sandwich panel,” Comput. Struct., 79(3), 301-312.
• [12] Si W.J., Lam K. Y. and Gang S. W. (2005), “Vibration analysis of rectangular plates with one or more guided edges via bicubic B-spline method,” Shock Vib., 12(5).
• [13] Wu L.H. (2012), “Free vibration of arbitrary quadrilateral thick plates with internal colums and uniform elastic edge supports by pb-2 Ritz method,” Struct. Eng. Mech., 44(3), 267-288.
• [14] Kutlu A., Uğurlu B., Omurtag M.H. (2012), “Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid”, Ocean Eng.. 42, 112-125.
• [15] Sheikholeslami S.A., Saidi A.R. (2013), “Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory,” Comput. Struct., 106, 350-361.
• [16] Senjanovic I.; Tomic M., Hadzic N., Vladimir N. (2017), “Dynamic finite element formulations for moderately thick plate vibrations based on the modified Mindlin theory,” Eng. Struct., 136, 100-113.
• [17] Tahouneh V. (2014), “Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations,” Struct. Eng. Mech., 50(6), 773-796.
• [18] Zamani H.A., Aghdam M.M., Sadighi M. (2017), “Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory,” Comput. Struct., 182, 25-35.
• [19] Ayvaz Y., Daloğlu A. and Doğangün A. (1998) “Application of a modified Vlasov model to earthquake analysis of the plates resting on elastic foundations,” J Sound Vib., 212(3), 499-509.
• [20] Omurtag, M.H., and Kadıoğlu, F. (1998), “Free vibration analysis of orthotropic plates resting on Pasternak foundation by mixed finite element formulation,” Comput. Struct., 67, 253-265.
• [21] Ayvaz Y. and Oguzhan C.B. (2008) “Free vibration analysis of plates resting on elastic foundations using modified Vlasov model.,” Struct. Eng. Mech., 28(6), 635-658.
• [22] Özgan K., Daloglu A. T. (2012), “Free vibration analysis of thick plates on elastic foundations using modified Vlasov model with higher order finite elements”, Int. J. Eng.. Materials Sciences., 19, 279-291.
• [23] Zienkiewich O.C., Taylor RL. and Too JM. (1971), “Reduced integration technique in general analysis of plates and shells,” Int. J. Numer. Meth. Eng., 3, 275-290.
• [24] Zienkiewich O.C., Taylor RL. and Too JM. (1989), The Finite Element Method, fourth ed., McGraw-Hill, New York.
• [25] Özdemir Y. I., Bekiroğlu S. and Ayvaz Y. (2007), “Shear locking-free analysis of thick plates using Mindlin’s theory,” Struct. Eng. Mech., 27(3), 311-331.
• [26] Özdemir Y. I., (2012), “Development of a higher order finite element on a Winkler foundation”, Finite Elem. Anal.. Des.., 48, 1400-1408.
• [27] Özdemir Y. I. (2007), “Parametric Analysis of Thick Plates Subjected to Earthquake Excitations by Using Mindlin’s Theory”, Ph. D. Thesis, Karadeniz Technical University, Trabzon.
• [28] Tedesco J. W., McDougal W. G., Ross C.A. (1999), Structural Dynamics, Addison Wesley Longman Inc., California.
• [29] Mindlin, R.D. (1951),” Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates”, J. Appl. M.; 18, 31-38.
• [30] Cook, R.D. and Malkus, D.S. and Michael, E.P. (1989), Concepts and Applications of Finite Element Analysis. John Wiley & Sons, Inc., Canada.
• [31] Weaver W. and Johnston P. R. (1984), Finite Elements for Structural Analysis, Prentice Hall, Inc., Englewood Cliffs, New Jersey.
• [32] Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey.