Elastic Limit of Functionally Graded Curved Panel Under Thermal Load

Abstract

In this study, the elastic behavior of a functional graded cylindrically curved panel subjected to thermal load in the radial direction is analytically investigated. It is assumed that the elasticity module of the curved panel changes in the radial direction depending on the exponential parameter. It is considered that the panel is in plane strain state. The material properties of the panel are considered together with the effect of the change in the exponential parameter and the general mixture law; all the characteristics of the panel (except for the Poisson ratio) has made a detailed study taking into account the changes in the radial direction. The elastic limit is determined according to the von Mises yield criterion. To yield in the positive and negative temperature; the panel inner surface, outer surface or both surfaces at the same time is observed to start. Numerical results are presented in graphical form for aluminum / steel functionally graded panel.

Keywords

• von Mises Criterion,Functionally Graded Material (FGM),Curved Panel

ISIL YÜK ALTINDA FONKSİYONEL DERECELENDİRİLMİŞ EĞRİ EKSENLİ PANELİN ELASTİK SINIRI

Abstract

Bu çalışmada, radyal doğrultuda ısıl yüke maruz kalan fonksiyonel derecelendirilmiş silindirik eğri eksenli panelin elastik davranışı analitik olarak incelenmiştir. Eğri eksenli panelin elastisite modülünün radyal doğrultuda üstel parametreye bağlı olarak değiştiği varsayılmıştır. Panelin düzlem şekil değiştirme durumunda olduğu göz önüne alınmıştır. Panelin malzeme özellikleri üstel parametredeki değişimin etkisi ve genel karışım kanunu ile birlikte ele alındığında; panelin bütün özellikleri (Poisson oranı hariç) radyal doğrultuda değiştiği hesaba alınarak detaylı bir çalışma yapılmıştır. Elastik sınırlar von Mises akma kriterine göre belirlenmiştir. Pozitif ve negatif sıcaklıkta akmanın; panelin iç yüzeyinde, dış yüzeyinde veya aynı anda her iki yüzeyde başladığı gözlemlenmiştir. Sayısal sonuçlar alüminyum/çelik fonksiyonel derecelendirilmiş panel için grafikler halinde sunulmuştur.

Keywords

• von Mises Kriteri,Fonksiyonel Derecelendirilmiş Malzeme (FDM),Eğri Eksenli Panel

References

1. Arslan, E., Mack, W., ve Gamer, U. (2013). Elastic limits of a radially heated thick-walled cylindrically curved panel. Forschung im Ingenieurwesen, 77(1-2), 13-23. doi.org/10.1007/s10010-013-0162-6
2. Arslan, E., ve Eraslan, A. N. (2010). Analytical solution to the bending of a nonlinearly hardening wide curved bar. Acta Mechanica, 210(1-2), 71-84. doi.org/10.1007/s00707-009-0195-y
3. Arslan, E., ve Haskul, M. (2015). Generalized plane strain solution of a thick-walled cylindrical panel subjected to radial heating. Acta Mechanica, 226(4), 1213-1225. doi.org/10.1007/s00707-014-1248-4
4. Arslan, E., ve Mack, W. (2014). Elastic-plastic states of a radially heated thick-walled cylindrically curved panel. Forschung im Ingenieurwesen, 78(1-2), 1-11. doi.org/10.1007/s10010-014-0170-1
5. Dadras, P. (2001). Plane strain elastic–plastic bending of a strain-hardening curved beam. International journal of mechanical sciences, 43(1), 39-56. doi.org/10.1016/S0020-7403(99)00102-2
6. Duc, N. D., ve Van Tung, H. (2010). Nonlinear response of pressure-loaded functionally graded cylindrical panels with temperature effects. Composite Structures, 92(7), 1664-1672. doi.org/10.1016/j.compstruct.2009.11.033
7. Eraslan, A. N., ve Arslan, E. (2008). A concise analytical treatment of elastic‐plastic bending of a strain hardening curved beam. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 88(8), 600-616. doi.org/10.1002/zaam.20060037
8. Haskul, M., Arslan, E., ve Mack, W. (2017). Radial heating of a thick‐walled cylindrically curved FGM‐panel. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 97(3), 309-321. doi.org/10.1002/zamm.201500310

9. Horgan, C. O., ve Chan, A. M. (1999). The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. Journal of Elasticity, 55(1), 43-59. doi.org/10.1023/A:1007625401963
10. Kiani, Y., Shakeri, M., ve Eslami, M. R. (2012). Thermoelastic free vibration and dynamic behaviour of an FGM doubly curved panel via the analytical hybrid Laplace–Fourier transformation. Acta Mechanica, 223(6), 1199-1218. doi.org/10.1007/s00707-012-0629-9
11. Librescu, L., Nemeth, M. P., Starnes Jr, J. H., ve Lin, W. (2000). Nonlinear response of flat and curved panels subjected to thermomechanical loads. Journal of thermal stresses, 23(6), 549-582. doi.org/10.1080/01495730050143134
12. Peng, X. L., ve Li, X. F. (2010). Thermal stress in rotating functionally graded hollow circular disks. Composite Structures, 92(8), 1896-1904. doi.org/10.1016/j.compstruct.2010.01.008
13. Shaffer, B. W., ve House Jr, R. N. (1957). Displacements in a wide curved bar subjected to pure elastic-plastic bending. J. Appl. Mech. Trans. ASME, 24, 447-452.
14. Shaffer, B. W., ve House, R. N. (1954). The elastic-plastic stress distribution within a wide curved bar subjected to pure bending. New York Unıv Bronx School of Engineering and Science.
15. Timoshenko S.P ve Goodier J.N., (1970). "Theory of Elasticity" McGraw-Hill Book Company.
16. Woo, J., ve Meguid, S. A. (2001). Nonlinear analysis of functionally graded plates and shallow shells. International Journal of Solids and structures, 38(42-43), 7409-7421. doi.org/10.1016/S0020-7683(01)00048-8