Influence Surface Coefficients of Plates Resting on Pasternak Foundation

Year 2022, Volume: 13 Issue: 2, 371 - 377, 28.06.2022

Ülkü Hülya Çalık Karaköse

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

Abstract

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.

Keywords

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

Thanks

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

Pasternak Türü Zemine Oturan Plakların Tesir Yüzey Katsayıları

Abstract

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.

Keywords

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

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