Dairesel delikli dikdörtgen levhanın H-tipi sonlu elemanlar ile uyarlamalı analizi

H-tipi elemanlar kullanılarak dairesel bir boşluk içeren levhaların gerilme analizi uyarlamalı sonlu elemanlar metoduyla MATLAB® ortamında yazılan bir programla yapılmıştır. Yük etkisindeki levhanın uyarlamalı sonlu elemanlarla iteratif çözümünde iki tip yaklaşım kullanılmıştır. Bunlardan ilkinde sisteme ait başlangıç çözüm ağı teşkil edilip gerilme analizi yaptıktan sonra, Zienkiewicz ve Zhu tarafından oluşturulmuş olan hızlı yakınsayan yama düzeltmesi (HYD) kullanılmakta ve sonlu elemanlar çözümünden elde edilen gerilmeler iyileştirilmektedir. İkinci yaklaşımda, seçilen bir gerilme bileşeninin komşu noktalar arasındaki değişimini dikkate alarak sonlu elemanlar ağı sıklaştırılmaktadır. Sonlu elemanlar çözüm ağının oluşturulmasında Delaunay kriteri kullanılmıştır. HYD iyileştirmesi kullanarak optimum sayıda sonlu elemanla uyarlamalı analiz yapılmıştır. İkinci yöntemde elde edilen üçgen eleman sayısı birinci yöntemdekine göre yaklaşık yüzde 50 daha fazla olmaktadır.

H-versiyon adaptive finite element analysis of plate with circular hole

Stress analysis of rectangular plates with a circular hole is carried out by a program written in MATLAB® environment and iterative h-version adaptive finite element method. Two different approaches were used in th adaptive solution of loaded plate. In the first one, stress calculation was made using initial course mesh and superconvergent patch recovery technique (SPR) proposed by Zienkiewicz ve Zhu was employed to refine th stress values. In second approach, finite element mesh was refined considering the variation of a chosen stres component between adjacent nodes. Triangular mesh was obtained using Delaunay criterion. Adaptive analyse were carried out using SPR technique with optimum number of finite elements. Number of triangular element obtained from second approach was about 50 percent greater than the number of elements in the first approach.

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