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

Yıl 2016, Cilt: 4 Sayı: 2, 32 - 41, 01.10.2016

Öz

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.

Kaynakça

  • 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.

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

Yıl 2016, Cilt: 4 Sayı: 2, 32 - 41, 01.10.2016

Öz

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

Kaynakça

  • 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.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA59YD22CT
Bölüm Araştırma Makalesi
Yazarlar

M. Eröz Bu kişi benim

D. Şimşek Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Eröz, M., & Şimşek, D. (2016). On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length. MANAS Journal of Engineering, 4(2), 32-41.
AMA Eröz M, Şimşek D. On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length. MJEN. Ekim 2016;4(2):32-41.
Chicago Eröz, M., ve D. Şimşek. “On Two Dimensional Dynamical Analysis Of A Pre-Stressed Anisotropict Plate-Strip With Finite Length”. MANAS Journal of Engineering 4, sy. 2 (Ekim 2016): 32-41.
EndNote Eröz M, Şimşek D (01 Ekim 2016) On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length. MANAS Journal of Engineering 4 2 32–41.
IEEE M. Eröz ve D. Şimşek, “On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length”, MJEN, c. 4, sy. 2, ss. 32–41, 2016.
ISNAD Eröz, M. - Şimşek, D. “On Two Dimensional Dynamical Analysis Of A Pre-Stressed Anisotropict Plate-Strip With Finite Length”. MANAS Journal of Engineering 4/2 (Ekim 2016), 32-41.
JAMA Eröz M, Şimşek D. On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length. MJEN. 2016;4:32–41.
MLA Eröz, M. ve D. Şimşek. “On Two Dimensional Dynamical Analysis Of A Pre-Stressed Anisotropict Plate-Strip With Finite Length”. MANAS Journal of Engineering, c. 4, sy. 2, 2016, ss. 32-41.
Vancouver Eröz M, Şimşek D. On Two Dimensional Dynamical Analysis Of A Pre-stressed Anisotropict Plate-strip With Finite Length. MJEN. 2016;4(2):32-41.

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