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Journals / Çukurova Üniversitesi Mühendislik Fakültesi dergisi / 2012 / Cilt: 27 - Sayı: 1

Dynamic Analysis of Axisymmetric Problems Made Of Viscoelastic Material

Viskoelastik Malzemeye Sahip Eksenel Dönel Simetrik Problemlerin Dinamik Analizi

Beytullah Temel
Mehmet Fatih Şahin
Ali Kara
Pages
13–22
Publication Date
2016-07-25
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results obtained in this study are found to be in good agreement with those available in the literature

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the dynamic behavior of axisymmetric problems is investigated theoretically in the Laplace domain.
📊
Key Findings & Data:For the dynamic loading cases, the finite element formulation in the Laplace domain is presented using Galerkin approximation.
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Conclusion & Impact:The results obtained in this study are found to be in good agreement with those available in the literature
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Sonlu elemanlar · Dinamik analiz · Viskoelastik malzeme modeli

Abstract

In this study, the dynamic behavior of axisymmetric problems is investigated theoretically in the Laplace domain. For the dynamic loading cases, the finite element formulation in the Laplace domain is presented using Galerkin approximation. The material of the problem is assumed to be homogeneous, isotropic, linear elastic or viscoelastic. In viscoelastic modeling, the Kelvin model is employed. In the viscoelastic material case, according to the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace domain. The solutions obtained are transformed to the time domain using the modified Durbin’s inverse Laplace transform method. For this purpose, a general-purpose finite element analysis computer program is coded in Fortran for dynamic analysis of the plane elasticity problems. Present program results are compared with the results obtained by Newmark method in the time domain. The results obtained in this study are found to be in good agreement with those available in the literature

Özet

Bu çalışmada viskoelastik malzemeye sahip eksenel dönel simetrik problemlerin dinamik davranışı Laplace uzayında teorik olarak incelenmiştir. Dinamik yükleme durumu için sonlu elemanlar formülasyonu, Laplace uzayında Galerkin yaklaşımı ile yapılmıştır. Problemin malzemesi izotropik, lineer elastik veya viskoelastik olarak kabul edilmiştir. Viskoelastik malzeme için Kelvin tipi sönüm modeli seçilmiştir. Viskoelastik malzeme durumunda elastik-viskoelastik analojisi yardımıyla malzeme sabitleri Laplace uzayında kompleks karşıtları ile değiştirilmektedir. Zaman uzayındaki gerçek çözümlere geçmek için Durbin'in modifiye edilmiş ters Laplace dönüşüm yöntemi kullanılmıştır. Bu amaçla düzlem gerilme/şekil değiştirme problemlerinin dinamik analizleri için sonlu elemanlar metoduna dayalı Fortran dilinde bir bilgisayar programı hazırlanmıştır. Bu çalışmada bulunan sonuçlar Newmark -adım adım integrasyon yöntemi- yardımıyla elde edilen çözümler ile de karşılaştırılmıştır. Newmark yönteminde zaman artım miktarları küçüldükçe hassasiyetin de o oranda arttığı, buna karşın Laplace uzayında yapılan çözümlerde ise, zaman artım miktarı ne seçilirse seçilsin, sonuçların değişmediği gösterilmiştir

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Cite This Article

Temel, B., Şahin, M. F., Kara, A. (2016). Dynamic Analysis of Axisymmetric Problems Made Of Viscoelastic Material. Çukurova Üniversitesi Mühendislik Fakültesi dergisi, Cilt: 27 - Sayı: 1, 13–22. https://ajindex.com/articles/715481

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