Static Analysis Of Viscoelastic Beams Through Finite Element Method

Year 2008, Volume: 21 Issue: 2, 85 - 100, 31.12.2008

Hakan Erol , H.selim Sengel M. Tacettin Sarıoğlu

https://izlik.org/JA26UH32TP

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.

Keywords

Viscoelastic Beam , Finite Element , Timoshenko Beam , Laplace Transform

References

• [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.