Enine Yük Altında Merkezi Delik İçeren Ortotropik Plakanın Gerilme ve Deformasyon Analizi

Abstract

Bu çalışmada, merkezi dairesel deliğe sahip dikdörtgen ortotropik bir plakanın gerilme ve deformasyon analizi, sonlu elemanlar metodu (SEM) temel alınarak gerçekleştirilmiştir. Analizde, AS4 karbon fiber/epoksi malzemesi seçilmiştir çünkü bu malzeme havacılık, uzay, otomotiv ve denizcilik endüstrilerinde yaygın olarak kullanılmaktadır. Ortotropik plakanın eğilme probleminin fiziğini ifade eden analitik formülasyonlar, deliksiz bir kare plaka (yani deliksiz plakalar olarak adlandırılan) dikkate alınarak türetilmiştir. Plakanın deformasyonu, çift serili bir çözüm kullanılarak ifade edilmiştir. Ayrıca, genel amaçlı sonlu elemanlar analizi yazılımı ANSYS kullanılarak bir sayısal model oluşturulmuştur. Uygun ağ yapısını seçmek için yakınsama çalışmaları yapılmıştır. Uygun sayısal model belirlendikten sonra, elde edilen sayısal sonuçlar MATLAB yardımıyla analitik yöntemle elde edilen sonuçlarla karşılaştırılmış ve sonuçlar arasında oldukça iyi bir uyum sağlanmıştır. Geliştirilen sayısal model doğrulandıktan sonra, elastik modül oranlarının Exx⁄Eyy , Exx⁄Ezz ve delik çapının kenar uzunluğuna oranının R⁄a von-Mises gerilmesi ve deformasyon dağılımları üzerindeki etkileri incelenmiştir. Elastik modül oranlarındaki değişimin Exx⁄Eyy , Exx⁄Ezz von-Mises gerilmesi ve deformasyon dağılımları üzerinde benzer etkilerinin olduğu gözlemlenmiştir. Plaka üzerindeki deliğin büyüklüğünün artması, R⁄a artışını ima etmiş ve aynı basınç altında daha düşük enine yük, daha az gerilme ve deformasyona neden olmuştur. Delik çevresindeki ve plaka sınırlarına yakın bölgelerdeki gerilme ve deformasyonların, uygun kompozit malzeme seçimi ile ayarlanabileceği tespit edilmiştir.

Keywords

• Ortotropik plaka
• dairesel delik
• enine yükleme
• deformasyon
• Sonlu Elemanlar Analizi (SEM)

Stress and Deformation Analysis of an Orthotropic Plate Including a Central Hole Under Transverse Load

Abstract

In this study, stress and deformation analysis of a rectangular orthotropic plate with a central circular hole has been conducted based on finite element method (FEM). In the analysis, AS4 Carbon fiber/epoxy material was selected since this material has widely been used in aerospace, automotive and marine industries. Analytical formulation expressing the physics of the bending problem of the orthotropic plate was presented as a double series solution for a square rectangular plate without any hole, i.e. called as non-perforated plates using the literature. A computational model is constructed using general purpose finite element analysis software ANSYS. In order to select the proper mesh, convergence studies were carried out. Then, computational results were compared with those obtained by analytical method and a very good agreement was achieved between results. After verification of the developed computational model, the influences of elastic modulus ratios E_xx⁄E_yy , E_xx⁄E_zz and the ratio of hole radius to edge length R⁄a on Von-Mises stress and plate deformation were examined. It was observed that change in elastic modulus ratios E_xx⁄E_yy and E_xx⁄E_zz had a similar effect on Von-Mises stress and deformation distributions. Increase in E_xx⁄E_yy and E_xx⁄E_zz alleviates stress level around the hole and escalates the stress level around boundaries in x-direction. However, the reverse trend was observed around boundaries in y-direction as these ratios were increased. The number of stress peaks and their levels were changed due to utilization of different E_xx⁄E_yy and E_xx⁄E_zz values. The use of greater hole within a plate induced an increase in R⁄a and caused less transverse load under same pressure and resulted in a less stress and deformation on the plate. It has been observed that stress and deformation near the hole and edges of the plate under transverse load can be adjusted by appropriate selection of composite material properties.

Keywords

• Orthotropic plate
• Circular hole
• Transverse load
• Deformation
• Finite element method

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