Influence Surface Coefficients of Plates Resting on Pasternak Foundation

Yıl 2022, Cilt: 13 Sayı: 2, 371 - 377, 28.06.2022

Ülkü Hülya Çalık Karaköse

https://doi.org/10.24012/dumf.1101167

Öz

In this study, internal force influence surface coefficients of plates resting on Pasternak foundation are obtained using the finite element method applying the classical Müller-Breslau Principle. The two-parameter elastic foundation is represented by the inclusion of the elastic bedding and shear parameter matrix terms of a 4-noded soil finite element to the corresponding stiffness matrix terms of the plate finite element used in the implementation. The loading matrices used to determine the influence surfaces directly are derived from the governing equations and the element matrices which are obtained using the Betti’s law. Internal force influence surface coefficients of plates with and without elastic foundation are given comparatively through numerical examples, confirming the values with another approach and the literature.

Anahtar Kelimeler

influence surface, Betti’s law, Müller-Breslau principle, plate finite element, Pasternak foundation

Teşekkür

Engin Orakdöğen is gratefully acknowledged for his fruitful suggestions on this study.

Pasternak Türü Zemine Oturan Plakların Tesir Yüzey Katsayıları

Öz

Bu çalışmada, Pasternak tipi zemine oturan plakların iç kuvvet tesir yüzey katsayıları sonlu elemanlar yöntemiyle klasik Müller-Breslau Prensibi uygulanarak elde edilmiştir. İki parametreli elastik zemin, 4 düğüm noktalı bir zemin sonlu elemanın elastik yataklanma ve kayma parametresi matris terimlerinin, kullanılan plak sonlu elemanın ilgili rijitlik matris terimlerine eklenmesiyle temsil edilmiştir. Tesir yüzeylerini doğrudan belirlemek için kullanılan yükleme matrisleri, ana denklemlerden ve Betti yasası kullanılarak elde edilen eleman matrislerinden türetilmiştir. Elastik zemine oturan ve zeminsiz plakların iç kuvvet tesir yüzey katsayıları, sayısal örneklerle karşılaştırmalı olarak verilmiş, elde edilen değerler başka bir yaklaşımla ve literatürle doğrulanmıştır.

Anahtar Kelimeler

tesir yüzeyi, Betti kanunu, Müller-Breslau prensibi, plak sonlu eleman, Pasternak tipi zemin

Kaynakça

• [1] A. Cifuentes, M. Paz, “A note on the determination of influence lines and surfaces using finite elements”, Finite Elements in Analysis and Design, vol. 7, pp. 299-305, 1991.
• [2] E. Orakdöğen, K. Girgin, “Direct determination of influence lines and surfaces by F.E.M.”, Structural Engineering and Mechanics, vol. 20, no. 3, pp. 279-292, 2005.
• [3] W. Shen, “The generalized Müller-Breslau principle for higher-order elements”, Computers & Structures, vol. 44, pp. 207-212, 1992.
• [4] A. Ghali, A.M. Neville, Structural Analysis, Chapman and Hall, London, 1978.
• [5] T.M. Charlton, “The principle of virtual work in relation to Müller-Breslau’s principle”, International Journal of Mechanical Sciences, vol. 22, no. 2, pp. 523-525, 1980.
• [6] A.D. Belegundu, “Interpreting adjoint equations in structural optimization”, Journal of Structural Engineering, ASCE, vol. 112, no. 8, pp. 1971-1976, 1986.
• [7] A.D. Belegundu, “The adjoint method for determining influence lines”, Computers & Structures, vol. 29, no. 2, pp. 345-350, 1988.
• [8] A.M. Memari, H.H. West, “Computation of bridge design forces from influence surfaces”, Computers & Structures, vol. 38, pp. 547-556, 1991.
• [9] A.A.A. Albuquerque, V.G. Haach, R.R. Paccola, “Dependency of modeling parameters for the construction of influence surfaces by the finite element method”, Engineering with Computers, vol. 34, pp. 143-154, 2018.
• [10] M. Çelik, A. Saygun, “A method for the analysis of plates on a two-parameter foundation”, International Journal of Solids and Structures, vol. 36, pp. 2891-2915, 1999.
• [11] R.J. Melosh, “Structural analysis of solids”, Journal of Structural Engineering, ASCE, vol. 4, pp. 205-223, 1963.
• [12] O.C. Zienkiewicz, Y.K. Cheung, “The finite element method for analysis of elastic isotropic and orthotropic slabs”, Proceedings of the Institution of Civil Engineers, vol. 28, pp. 471-88, 1964.
• [13] O.C. Zienkiewicz, Y.K. Cheung, “Finite element procedures in the solution of plate and shell problems in stress analysis”, Chapter 8. John Wiley & Sons, Chichester, 1965.
• [14] K.Y. Lam, C.M. Wang, X.Q. He, “Canonical exact solutions for Levy-plates on two parameter foundation using Green’s functions”, Engineering Structures, vol. 22, no. 4, pp. 364-378, 2000.
• [15] Z.Y. Huang, C.F. Lü, W.Q. Chen, “Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations”, Composite Structures, vol. 85, pp. 95-104, 2008.
• [16] Ü.H. Çalık Karaköse, FE Analysis of FGM Plates on Arbitrarily Orthotropic Pasternak Foundations for Membrane Effects, Teknik Dergi, vol. 33, no. 2, pp. 11799-11822, 2022.