Journals / Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi / 2008 / Cilt: 21 Sayı: 2

Static Analysis Of Viscoelastic Beams Through Finite Element Method

Pages
85–100
Publication Date
2008-12-31
DOI
—
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AI Summary & Key Takeaways

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

Following these analyses, results are obtained by using everse Laplace Transformation method developed by Honig and Hirdes.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study focuses on straight beams by taking viscoelastic behavior of material.
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Key Findings & Data:Time-dependent behavior of the material is stated with the help of Prony series.
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Conclusion & Impact:Following these analyses, results are obtained by using everse Laplace Transformation method developed by Honig and Hirdes.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Viscoelastic Beam · Finite Element · Timoshenko Beam

Abstract

This study focuses on straight beams by taking viscoelastic behavior of material. Time-dependent behavior of the material is stated with the help of Prony series. A constant poisson ratio has been used. Constitution equations for beam are combined in one function with Hamilton Principle, and Laplace transformation is used to free it from time parameter. Finite element formulation is formed with linear shape functions. While integral operation of equations with a shear effect is executed with reduced integration method, integral operations of others are executed with full integration method. Following these analyses, results are obtained by using everse Laplace Transformation method developed by Honig and Hirdes.

Özet

This study focuses on straight beams by taking viscoelastic behavior of material. Time-dependent behavior of the material is stated with the help of Prony series. A constant poisson ratio has been used. Constitution equations for beam are combined in one function with Hamilton Principle, and Laplace transformation is used to free it from time parameter. Finite element formulation is formed with linear shape functions. While integral operation of equations with a shear effect is executed with reduced integration method, integral operations of others are executed with full integration method. Following these analyses, results are obtained by using everse Laplace Transformation method developed by Honig and Hirdes.

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Cite This Article

EROL, H., SENGEL, H., SARIOĞLU, M. T. (2008). Static Analysis Of Viscoelastic Beams Through Finite Element Method. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, Cilt: 21 Sayı: 2, 85–100. https://ajindex.com/articles/905180

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References (12)

  1. W. Flügge, “Viscoelasticity”, 2nd ed., Springer, Berlin, 1975
  2. A. C. Eringen, “Mecanics of Continua”, Robert E. Krieger Publishing Company, New York, 1980, pp. 592
  3. J.N. Reddy, “An Introduction To The Finite Element Method”, Second Edition, McGraw Hill International Editions, 1993, pp.3-13
  4. A.R. Zak, “Structural Analysis Of Realistic Solid Propellant Materials”, Journal of Spacecrafi Rockets, Vol. 5, 1986, pp. 270-275
  5. B. Uyan, “Çözümlü Problemlerle Diferansiyel Denklemler, Fourier Serileri, Laplace Transformasyonu”, Đstanbul 1980 (In Turkish)
  6. E. Hinton, Owen, D.R.J., “An Introduction To Finite Element Computations”, Pineridge Press Swansea UK., 1979, pp. 140-147
  7. H. Erol, “Viskoelastik Kirislerin Sonlu Elemanlar Metodu ile Çözümü”, Master Thesis, Eskisehir, 1999 (In Turkish)
  8. H.T. Chen, Chen, T.M., Chen, C.k., “Hybrid Laplace Transform/Finite Element For One- Dimensional Transient Heat Conduction Problems”, Computer Method In Applied Mechanics And Engineering, Vol.63, 1987, pp.83-95
  9. G. Honig, Hirdes, U., “A Method For The Numerical Inversion Of Laplace Transform”, Journal of Computational And Applied Mathematics, Vol. 10, 1984, pp.113-132
  10. C.L. Dym, Shames I.H., “Solid Mechanics A Variational Approach”, McGraw-Hill, New York, 1973
  11. Y. Aköz, Kadıoğlu, F., “The Mixed Finite Element Method For The Quasi-Static And Dynamic Analysis Of Viscoelastic Timoshenko Beams”, International Journal for Numerical Methods In Engineering, Vol. 44, 1999, pp. 1909-1932
  12. Tzer-Ming Chen, “The Hybrid Laplace Transform/Finite Element Method Applied To The Quasi-Static And Dynamic Anaiysis Of Viscoelastic Timoshenko Beams”, International Journal For Numerical Methods In Engineering, Vol.38, 1995, pp.509-522 [13] W.N. Findley, J.S. Lai, K. Onaran, “Creep And Relaxation of Nonlinear Viscoelastic Materials”, North-Holland, New York, 1976.