On the Normal Stresses in a System Formed of a Covering Layer, Two Locally Curving Layers and Half-Space

Year 2020, Issue: 19, 866 - 872, 31.08.2020

Ramazan Tekercioğlu

Abstract

The layered system consisting of the covering layer, two locally curved layers and half-space is considered. It is assumed that the two layers have local curving. Moreover, the layered system is loaded at infinity by uniformly distributed normal forces which acts in the layers’ lying way. Within these assumptions, the normal stresses caused by the local curving of the layers are studied within the framework of the piecewise-homogeneous body model with the use of the three-dimensional geometrically non-linear exact equations of the theory of elasticity. The numerous numerical results related to the stresses considered and to the problem parameters’ influence are given.

Keywords

Normal Stresses, Locally Curving Layer, Layered Half-Space

Yarı Uzay Üzerinde İki Katlı Yerel Eğrilikli Levha ile Bir Örten Levhadan Oluşan Sistemde Normal Gerilmeler Hakkında

Abstract

Yarı uzay üzerinde iki katlı yerel eğrilikli levha ile bir örten levhadan oluşan sistem dikkate alınmıştır. İki levhanın yerel eğriliğe sahip olduğu varsayılmaktadır. Ayrıca, X2=0 düzlemi boyunca üst üste yerleştirilen levhalardan oluşan sisteme X1-->-+sonsuz (X3-->-+sonsuz)’da yoğunluğu P1 (P3) olan düzgün yayılı normal basınç kuvveti etki etmektedir. Bu kabuller çerçevesinde yerel eğriliğe sahip olan levhaların sebep olduğu normal gerilmeler, elastisite teorisinin üç boyutlu geometrik doğrusal olmayan denklemlerinden yararlanılarak parçalı-homojen cisim modeli çerçevesinde incelenmiştir. Dikkate alınan gerilmeler ve problem parametrelerinin etkisi ile ilgili çeşitli sayısal sonuçlar verilmiştir.

Keywords

Normal gerilmeler, Yerel eğrilikli levha, Tabakalı yarı uzay

References

• Akbarov, S.D., & Guz, A.N. (2000). Mechanics of Curved Composites, Kluwer Academic Publishers, Dordrecht, Boston, London.
• Akbarov, S.D., Tekercioglu, R. (2006). Near-surface buckling instability of a system consisting of a moderately rigid substrate, a viscoelastic bond layer, and an elastic covering layer, Mechanics of Composite Materials, 42(4), 363-372.
• Akbarov, S.D., Tekercioglu, R. (2007). Surface undulation instability of the viscoelastic half-space covered with the stack of layers in bi-axial compression, International Journal of Mechanical Sciences, 49(6), 778-789.
• Altan, H., Bilgic, F., Arslanoglu, Z., Kale, E. , Köroğlu Kale, A. , Altan, A. , & Sahin, O. (2016). Nanomechanical Properties of Different Dental Restorative Materials, Acta Physica Polonica A, 130, 394-396.
• Babich, I.Yu., Guz, A.N, & Chekhov, Vik.N. (2001). The three-dimensional theory of stability of fibrous and laminated materials. Int. Appl. Mech., 37(9), 1103-1141.
• Balint, D.S., & Hutchinson, J.W. (2003). Undulation instability of a compressed elastic film on a nonlinear creeping substrate. Acta Materialia, 51, 3965-3983.
• Bowden, N., Brittain, S., Evans, A.G., Hutchinson, J.W., & Whitesides, G.M. (1998). Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature (London), 39, 146-149.
• Budiansky, B., & Fleck, N.A. (1994). Compressive kinking of fiber composites: a topical review. Appl. Mech. Rev., Pt.2, 47(6), 246-270.
• Çiçek Bezir, N., Evcin, A , . Okçu, H., Kayali, R., Kaleli, M., & Aldemir, D.A. (2017). Effect of Layer Thickness on I-V Characteristics of GaInP Nanofibers Fabricated by Electrospinning on n-Si Substrates, Acta Physica Polonica A, 132, 638-641.
• Çiçek Bezir, N., Evcin , A., Kayali, R., . Özen, M.K., & Esen, K. (2017). Comparison of Five-Layered ZrO2 and Single-Layered Ce, Eu, and Dy-Doped ZrO2 Thin Films Prepared by Sol-Gel Spin Coating Method, Acta Physica Polonica A, 132, 612-616.
• Dow, N.F., & Gruntfest, I.J. (1960, June). Determination of most needed potentially possible improvements in materials for ballistic and space vehicles. General Electric Co., Space Sci. Lab., TISR 60 SD 389.
• Guz, A.N. (1990), Fracture mechanics of composites under compression, Naukova Dumka, Kiev (in Russian).
• Huang, R., & Suo, Z. (2002) .Wrinkling of a compressed elastic film on a viscous layer. Journal of Applied Physics, 91(3), 1135-1142.
• Huck, W.T.S., Bowden, N., Onck, P., Pardoen, T., Hutchinson, J.W., & Whitesides, G.M. (2000). Ordering of spontaneously formed buckles on planar surfaces, Langmuir, 16, 3497-3501.
• Povstenko, Y., Avcı, D., Iskender Eroglu, B. B., & Ozdemir, N. (2017). Control of Thermal Stresses in Axissymmetric Problems of Fractional Thermoelasticity for an Infinite Cylindrical Domain, Thermal Science, 21(1A), 19-28.
• Rosen, B.W. (1965). Mechanics of composite strengthening fiber composite materials, American Society of Metals, 37-75.
• Yang, Y., Feng, Z., & Lin, R. (2017). A Prediction Method of Temperature Distribution and Thermal Stress for the Throttle Turbine Rotor and Its Application, Thermal Science, 21(Suppl. 1), S267-S274.