On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length

Year 2016, Volume: 4 Issue: 2, 32 - 41, 01.10.2016

M. Eröz D. Şimşek

Abstract

In this study, the influence of initial stress on a pre-stressed orthotropic plate-strip with finite length resting on a rigid half plane is investigated by utilizing Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. The material of the plate-strip is assumed to be anisotropic. The total energy functional of the considered problem is developed. Also, finite element modeling is developed for the considered boundary-value problem.

Keywords

Anisotropic material, Initial stress, Finite element method, Forced vibration, Time-harmonic load

Sonlu Uzunluğa Sahip Öngerilmeli Anizotrop Şerit-Plağın İki Boyutlu Dinamik Analizi Üzerine

Abstract

Bu çalışmada, rijit zemin üzerinde oturan sonlu uzunluğa sahip öngerilmeli anizotrop bir şeritplakta öngerilmenin etkisi öngerilmeli ortamlardaki elastik dalgaların doğrusallaştırılmış üç boyutlu teorisi kullanılarak incelenmiştir. Şerit-plağın anizotrop malzemeden yapıldığı kabul edilmiştir. Ele alınan problemin toplam potansiyel enerji fonksiyoneli oluşturulmuştur. Ayrıca, ilgili sınır değer probleminin sonlu eleman modellemesi yapılmıştır

Keywords

Anizotrop madde, Öngerilme, Sonlu elemanlar metodu, Zorlanmış titreşim, Harmonik yük

References

• References
• [1] D.M. Barnett, J. Lothe, S.D. Gavazza, M.J.P. Musgrave, Consideration of the existence of interfacial Stoneley waves in bonded anisotropic elastic half-spaces. Proceedings of the Royal Society of London A, 402 (1985) 153-166.
• [2] A.N. Stroh, Steady state problems in anisotropic elasticity. Journal of Mathematical Physics, 41 (1962) 77-103.
• [3] M.A. Dowaikh, R.W. Ogden, On surface waves and deformations in a pre-stressed incompressible elastic solid, IMA Journal of Applied Mathematics, 44 (1990) 261-284.
• [4] M.A. Dowaikh, R.W. Ogden, Interfacial waves and deformations in pre-stressed elastic media, Proceedings of the Royal Society of London A, 433 (1991) 313-328.
• [5] A.N. Guz, Linearized theory of propagation of elastic waves in bodies with initial stresses. International Applied Mechanics, 14 (4) (1978) 339-362.
• [6] S. Yu Babich, A.N. Guz, A.P. Zhuk, Elastic waves in bodies with initial stresses. International Applied Mechanics, 15 (4) (1979) 277-291.
• [7] G.A. Rogerson, Y.B. Fu, An asymptotic analysis of the dispersion relation of a pre-stressed incompressible elastic plate. Acta Mechanica, 111 (1995) 59-77.
• [8] G.A. Rogerson, Some asymptotic expansions of the dispersion relation for an incompressible elastic plate. International Journal of Solids and Structures, 34(22) (1997) 2785-2802.
• [9] G.A. Rogerson, K.J. Sandiford, The effect of finit primary deformations on harmonic waves in layered elastic media. International Journal of Solids and Structures, 37(14) (2000) 2059-2087.
• [10] G.A. Rogerson, On the existence of surface waves and the propagation of plate waves in pre- stressed fibre reinforced composites. Journal of the Mechanics and Physics of Solids, 49(9) (1998) 1581-1612.
• [11] A.E. Green, R.S. Rivlin, R.T. Shield, General theory of small elastic deformations superposed on finite elastic deformations. Proceedings of the Royal Society of London A, 211 (1952) 128-154.
• [12] M.A. Biot, Mechanics of Incremental Deformations. Wiley, New York, 1965.
• [13] C. Truestell , W. Noll, The nonlinear field theories of mechanics. In: Fluegge, Ed., Handbuch der Physik, vol.III/3. Springer, Berlin, New York, 1965.
• [14] A.N. Guz, Elastic Waves in a Body with Initial Stresses, I. General Theory. Naukova Dumka, Kiev, 1986 (In Russian).
• [15] A.N. Guz, Elastic Waves in a Body with Initial Stresses, II. Propagation Laws. Naukova Dumka, Kiev, 1986 (In Russian).
• [16] A.N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses. A.S.K., Kiev, 2004 (In Russian).
• [17] A.N. Guz, Elastic waves in bodies with initial (residual) stresses, Int. Appl. Mech. 38 (1) (2002) 23- 59.
• [18] S.D. Akbarov, Axisymmetric Lamb’s problem for the finite pre-strained half-space covered with the finite pre-stressed layer, International Applied Mechanics, 43 (3) (2007) 132–143.
• [19] S.D. Akbarov, C. Guler, On the stress field in a half-plane covered by the pre-stretched layer under the action of arbitrary linearly located time-harmonic forces, Applied Mathematical Modelling, 31 (2007) 2375–2390.
• [20] Ya.A. Zhuk, I.A. Guz, Influence of prestress on the velocities of plane waves propagating normally to the layers of nanocomposites, , International Applied Mechanics, 42 (7) (2006) 729–743.
• [21] Ya.A. Zhuk, I.A. Guz, Features of propagation of plane waves along to the layers of an initially stressed nanocomposite material. International Applied Mechanics, 43 (4) (2007) 3–26.
• [22] S.D. Akbarov, O. Ozaydın, The effect of initial stresses on harmonic stress fields within the stratified half-plane. European Journal of Mechanics A/Solids, 20 (2001) 385-396.
• [23] S.D. Akbarov, A. Yildiz, M. Eröz, FEM modeling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation. Applied Mathematical Modelling, 35 (2011) 952-964.
• [24] S.D. Akbarov, A. Yildiz, M. Eröz, Forced vibration of the pre-stressed bilayered plate-strip with finite length resting on a rigid foundation. Applied Mathematical Modelling, 35 (2011) 250-256.
• [25] M. Eröz, The stress field problem for a pre-stressed plate-strip with finite length under the action of arbitrary time-harmonic forces, Applied Mathematical Modelling 36(11) (2012) 5283-5292.
• [26] S.G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, Holden Day, San Francisco, 1963.
• [27] O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, fifth ed., vol.1, Butterworth-Heinemann, 2000.