A Comparative Assessment of Plane Stress Finite Elements for Stress Analysis in a Rectangular Plate with a Central Circular Hole under Uniaxial Tension

Öz

This study presents a comparative assessment of three various plane stress finite element formulations—CPS4, CPS4R, and CPS4I—implemented in ABAQUS for the prediction of maximum stress in a rectangular plate with a central circular hole subjected to uniaxial tension. Numerical results were benchmarked against the theoretical solution based on the gross-section stress concentration factor over hole diameter-to-width ratios up to 0.8. The primary objective was to quantify the influence of element formulations on maximum stress estimation with increasing hole diameter-to-width ratio. Numerical results suggested that all element types successfully captured the progressive increase in maximum stress with increasing hole size. Nevertheless, systematic differences in accuracy were observed. The CPS4 element produced slight overestimations, whereas CPS4R consistently underestimated the reference solution, with discrepancies becoming more noticeable at higher geometric ratios where stress gradients are more pronounced. Among the examined formulations, CPS4I exhibited the most consistent and accurate agreement with the theoretical results, maintaining small and stable error levels across the entire investigated range. This was attributed to its incompatible mode enhancement that provides improved strain field representation, enabling more reliable resolution of localized stress peaks. The findings underscored the critical role of element formulation in ABAQUS for achieving accurate maximum stress predictions in perforated structural components subjected to uniaxial tensile loading.

Anahtar Kelimeler

• Stress concentration
• Finite element analysis (FEA)
• Plane stress elements
• Element formulation accuracy
• Uniaxial tension
• Finite-width perforated plates

Tek Eksen Çekmede Merkezi Dairesel Delikli Dikdörtgen Bir Plakada Gerilme Analizi için Düzlem Gerilme Sonlu Elemanlarının Karşılaştırmalı Değerlendirmesi

Öz

Bu çalışma, tek eksenli çekme yüküne maruz bırakılmış, ortasında dairesel delik bulunan dikdörtgen bir plakanın maksimum gerilmesinin tahmini için ABAQUS’te uygulanan üç farklı düzlem gerilme sonlu eleman formülasyonunun—CPS4, CPS4R ve CPS4I—karşılaştırmalı bir değerlendirmesini sunmaktadır. Sayısal sonuçlar, delik çapının plaka genişliğine oranının 0.8’e kadar olan değerleri için, brüt kesit gerilme yığılma katsayısına dayanan teorik çözümle karşılaştırılmıştır. Çalışmanın temel amacı, delik çapı/genişlik oranının artmasıyla birlikte eleman formülasyonlarının maksimum gerilme tahmini üzerindeki etkisini nicel olarak belirlemektir. Sayısal sonuçlar, tüm eleman tiplerinin delik boyutu arttıkça maksimum gerilmedeki kademeli artışı başarıyla yakaladığını göstermiştir. Bununla birlikte, doğruluk açısından sistematik farklılıklar gözlemlenmiştir. CPS4 elemanı referans çözüme kıyasla hafif fazla tahminler üretirken, CPS4R elemanı özellikle gerilme gradiyentlerinin daha belirgin olduğu yüksek geometrik oranlarda referans çözümü tutarlı biçimde düşük tahmin etmiştir. İncelenen formülasyonlar arasında CPS4I elemanı, teorik sonuçlarla en tutarlı ve en doğru uyumu göstermiş; incelenen tüm oran aralığında küçük ve kararlı hata seviyelerini korumuştur. Bu durum, daha gelişmiş bir şekil değiştirme alanı temsili sağlayan ve yerel gerilme tepe değerlerinin daha güvenilir biçimde çözülmesine olanak tanıyan uyumsuz mod iyileştirmesine bağlanmıştır. Elde edilen bulgular, tek eksenli çekme yüküne maruz perforasyonlu yapısal bileşenlerde maksimum gerilme tahminlerinin doğruluğunu sağlamak açısından ABAQUS’te eleman formülasyonu seçiminin kritik önem taşıdığını vurgulamıştır.

Anahtar Kelimeler

• Gerilme yığılması
• Sonlu elemanlar analizi (SEA)
• Düzlem gerilme elemanları
• Eleman formülasyonu doğruluğu
• Tek eksenli çekme
• Sonlu genişlikte delikli plakalar

Kaynakça

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