Pasternak türü zemin üzerindeki ince plakların statik analizi için yakınsama çalışmaları

Öz

Pasternak türü zemin üzerine oturan ince plakların statik analizi için yakınsama çalışmaları yapılmıştır. Plaklar, formülasyonları Kirchhoff ve Reissner-Mindlin plak teorilerine dayanan iki farklı sonlu eleman kullanılarak modellenmiştir. Reissner-Mindlin plak teorisinin sonlu elemanlar uygulamasında tam integrasyon kullanıldığında ortaya çıkan kayma kilitlenmesi sorunu, selektif integrasyon ile ortadan kaldırılmıştır. Pasternak zemini, mevcut bir zemin sonlu elemana ait parametre matrislerinin, plak sonlu elemanların çökmelere karşılık gelen rijitlik matrisi terimlerine eklenmesiyle tanımlanmıştır. Farklı sınır koşulları, plak kalınlıkları ve zemin parametreleri için yakınsama oranları elde edilmiş ve sayısal örneklerle karşılaştırmalı olarak verilmiştir.

Anahtar Kelimeler

• Kirchhoff plate element
• Reissner-Mindlin plate element
• Pasternak foundation
• shear locking
• convergence

Convergence studies for static analysis of thin plates on Pasternak Foundations

Abstract

Convergence studies for the static analysis of thin plates resting on Pasternak foundations is performed. The plates are discretized using two different finite elements, the formulations of which are based on the Kirchhoff and Reissner-Mindlin plate theories. The shear locking problem which arises when full integration is used in the finite element implementation of Reissner-Mindlin plate theory is eliminated with selective integration. The Pasternak foundation is accounted for by adding the parameter matrices of an existing soil finite element to the stiffness matrix terms of the plate finite elements corresponding to deflections. Convergence rates for different boundary conditions, plate thicknesses and soil parameters are obtained and given comparatively through numerical examples.

Keywords

• Kirchhoff plate element
• Reissner-Mindlin plate element
• Pasternak foundation
• shear locking
• convergence

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