Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer

Elman Hazar

Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer

Year 2014, Volume: 2 Issue: 2, 59 - 75, 01.10.2014

Abstract

Within the framework of a piecewise homogenous body model and by the use of a threedimensional linearized theory of stability (TLTS), the local near-surface buckling of a material system consisting of a half-space which is covered by the single layer and halfspace materials is elastic. The equations of TLTS are obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary form perturbations technique. By employing the Laplace and Fourier transform, a method for solving the problem is developed. Numerical results on the critical compressive forces and the critical times are presented.Buckling instability, curved-layer, critical time, local near-surface buckling, stability, viscoelastic layer

Keywords

Buckling instability, curved-layer, critical time, local near-surface buckling, stability, viscoelastic layer.

References

E. A. Aliyev, “Local near-surface buckling of a system consisting of elastic (viscoelastic) substrate, a viscoelastic (elastic) bond layer, and an elastic (viscoelastic) covering layer”, Mechanics of Composite Materials, 43, No 6, 521-534 (2007).
Akbarov S.D., Aliyev E.A, “On the near-surface failure of the layered viscoelasticMaterials’’, Mechanics of Composite Materials, 45, No 5, 477-488(2009).
M.A.Biot, Mechanics of Incremental Deformations, Wiley, New York (1965).
A.N.Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).
N.J.Hoff, “A surway of the theories of creep buckling’’, in proceedings of the Third US National Congress of the Applied Mechanics, ASME, New York (1958).
I.Yu.Babich, A.N. Guz and V.N. Chekov, “The Three-Dimentional Theory of Stability of fibrous and laminated materials’’, Int. Appl. Mech., 37, No.9, 1103– 1141 (2001).
R.A.Schapery, “Approximate method of transform inversion for viscoelastic stress analysis’’, Proc. US. Nat. Cong. Appl. ASME, 4, 1075–1085 (1966).
Yu.N.Rabotnov, Elements of Hereditary Mechanics of Solid Bodies [in Russian], Nauka, Moskow (1977)
A.Cilli, Fracture of the uni-directed fiber-layered composites in compression, PhD. Thesis, The Yildiz Technical University, Turkey, Istanbul, 1998-105p.
A.N.Guz, “Three-Dimensional Theory of Stability of Carbon Nanotube in a Matrix II’’, Int. Appl. Mech., 42, No.1, 19–31 (2006).
A.N.Guz and I.A.Guz, “On Models in the theory of stability of Multiwalled carbon nanotubes in matrix’’, Int. Appl. Mech., 42, No.6, 617–628 (2006).
Ya.A.Zhuk and I.A.Guz, “Influence of prestress on the velocities of waves propagating normally to the layers of nanocomposites’’, Int. Appl. Mech., 42, No.7, 729–743 (2006).
S.D. Akbarov, R. Kosker, K. Simsek, “Stress distribution in an infinite elastic body with a locally curved fiber in a geometrically non-linear statement”, Mechanics of Composite Materials , 41, No 4, 291-302 (2005).
Yu.M. Tarnopolsky, A.V.Rose, “Special feature of desigh of parts fabricated from reinforced plastics.(in Russian), Zinatne, Riga.
Guz A. N., Rushchitsky J.J., Guz I. A. Establishing fundamentals of the mechanics of nanocomposites// Int. Appl. Mechan. – 2007. – 43. No 3. – P.247-271.
Zhuk Yu. A., Guz I. A. Features of plane wave propagation along the layers of a pre-strained nanocomposites. Int. Appl. Mech. 2007; 43 (3): 361-379.
Argatov I. I. Averaging of a finely lamineted elastic medium with roughness or adhesion on the contact surfaces of the layers. J.Appl.Math.Mech.73:734-746.1997

Üç Boyutlu Teory Çerçevesinde Yerel Yüzeye Yakın Tabakalarda Elastik ve Elastik Bağlı Sistemler İçin Kayıp Problemleri

Year 2014, Volume: 2 Issue: 2, 59 - 75, 01.10.2014

Elman Hazar

Abstract

Bu çalışmada üç boyutlu linerleştirilmiş teory kullanılarak (TLTS), bir boyutlu homojen sistem modeli çerçevesinde yerel yüzeye yakın tek katmanlı ve yarı-uzay elastic malzemeler ile kaplanmış bir sisteme bakılmıştır. Perturbasyo tekniği uygulayarak viskoelastik teorisinin üç boyutlu denklemleri ve sınır koşulları yardımı ile TLTS denklemleri elde edilmiştir. Laplace ve Fourier Yöntemlerinden yararlanarak, problem çözmek için yeni bir yöntem geliştirilmiştir

Keywords

Burkulma kararsizliğı, kavisli dalga, kritik zaman , yüzeye yakın burkulma, kararlılık, viskoelastik yerel tabaka

References

E. A. Aliyev, “Local near-surface buckling of a system consisting of elastic (viscoelastic) substrate, a viscoelastic (elastic) bond layer, and an elastic (viscoelastic) covering layer”, Mechanics of Composite Materials, 43, No 6, 521-534 (2007).
Akbarov S.D., Aliyev E.A, “On the near-surface failure of the layered viscoelasticMaterials’’, Mechanics of Composite Materials, 45, No 5, 477-488(2009).
M.A.Biot, Mechanics of Incremental Deformations, Wiley, New York (1965).
A.N.Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).
N.J.Hoff, “A surway of the theories of creep buckling’’, in proceedings of the Third US National Congress of the Applied Mechanics, ASME, New York (1958).
I.Yu.Babich, A.N. Guz and V.N. Chekov, “The Three-Dimentional Theory of Stability of fibrous and laminated materials’’, Int. Appl. Mech., 37, No.9, 1103– 1141 (2001).
R.A.Schapery, “Approximate method of transform inversion for viscoelastic stress analysis’’, Proc. US. Nat. Cong. Appl. ASME, 4, 1075–1085 (1966).
Yu.N.Rabotnov, Elements of Hereditary Mechanics of Solid Bodies [in Russian], Nauka, Moskow (1977)
A.Cilli, Fracture of the uni-directed fiber-layered composites in compression, PhD. Thesis, The Yildiz Technical University, Turkey, Istanbul, 1998-105p.
A.N.Guz, “Three-Dimensional Theory of Stability of Carbon Nanotube in a Matrix II’’, Int. Appl. Mech., 42, No.1, 19–31 (2006).
A.N.Guz and I.A.Guz, “On Models in the theory of stability of Multiwalled carbon nanotubes in matrix’’, Int. Appl. Mech., 42, No.6, 617–628 (2006).
Ya.A.Zhuk and I.A.Guz, “Influence of prestress on the velocities of waves propagating normally to the layers of nanocomposites’’, Int. Appl. Mech., 42, No.7, 729–743 (2006).
S.D. Akbarov, R. Kosker, K. Simsek, “Stress distribution in an infinite elastic body with a locally curved fiber in a geometrically non-linear statement”, Mechanics of Composite Materials , 41, No 4, 291-302 (2005).
Yu.M. Tarnopolsky, A.V.Rose, “Special feature of desigh of parts fabricated from reinforced plastics.(in Russian), Zinatne, Riga.
Guz A. N., Rushchitsky J.J., Guz I. A. Establishing fundamentals of the mechanics of nanocomposites// Int. Appl. Mechan. – 2007. – 43. No 3. – P.247-271.
Zhuk Yu. A., Guz I. A. Features of plane wave propagation along the layers of a pre-strained nanocomposites. Int. Appl. Mech. 2007; 43 (3): 361-379.
Argatov I. I. Averaging of a finely lamineted elastic medium with roughness or adhesion on the contact surfaces of the layers. J.Appl.Math.Mech.73:734-746.1997

There are 17 citations in total.

Details

Other ID	JA76AH79ZE
Journal Section	Research Article
Authors	Elman Hazar This is me
Publication Date	October 1, 2014
Published in Issue	Year 2014 Volume: 2 Issue: 2

Cite

APA	Hazar, E. (2014). Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer. MANAS Journal of Engineering, 2(2), 59-75.
AMA	Hazar E. Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer. MJEN. October 2014;2(2):59-75.
Chicago	Hazar, Elman. “Three–dimensional Stability Loss Problems Of Local Near-Surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer”. MANAS Journal of Engineering 2, no. 2 (October 2014): 59-75.
EndNote	Hazar E (October 1, 2014) Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer. MANAS Journal of Engineering 2 2 59–75.
IEEE	E. Hazar, “Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer”, MJEN, vol. 2, no. 2, pp. 59–75, 2014.
ISNAD	Hazar, Elman. “Three–dimensional Stability Loss Problems Of Local Near-Surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer”. MANAS Journal of Engineering 2/2 (October 2014), 59-75.
JAMA	Hazar E. Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer. MJEN. 2014;2:59–75.
MLA	Hazar, Elman. “Three–dimensional Stability Loss Problems Of Local Near-Surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer”. MANAS Journal of Engineering, vol. 2, no. 2, 2014, pp. 59-75.
Vancouver	Hazar E. Three–dimensional Stability Loss Problems Of Local Near-surface Buckling Of A System Consisting Of An Elastıc Bond Layer And An Elastic Covering Layer. MJEN. 2014;2(2):59-75.