بررسی تأثیر انحنای گوشۀ گشودگی بر تمرکز تنش ناشی از شار حرارتی

علوم کاربردی و محاسباتی در مکانیک

مقاله 6، دوره 28، شماره 1 - شماره پیاپی 15، اسفند 1395، صفحه 63-74   

نوع مقاله: مقاله پژوهشی

شناسه دیجیتال (DOI): 10.22067/fum-mech.v28i1.43711

نویسندگان

محمد جعفری^* ؛ محمدباقر نظری

دانشگاه شاهرود

چکیده

بر پایۀ تئوری ترموالاستیسیته دوبعدی حالت پایدار میدان تنش در اطراف گشودگی های مختلف در یک صفحۀ نامحدود همسان‌گرد مورد بررسی قرار می گیرد. صفحه در بی نهایت تحت جریان حرارتی یکنواخت است و مرز گشودگی مرکزی عایق است. بااستفاده از توابع پتانسیل مختلط و به کارگیری نگاشت همنوا و حلّ معادلات انتگرالی، تأثیر انحنای گوشۀ گشودگی بر توزیع تنش اطراف گشودگی مطالعه می شود. روش حل بر پایۀ بسط روش گودیر و فلورنس است. آنها از روش متغیّر مختلط برای تحلیل تنش ورق نامحدود همسان گوشۀ گرد حاوی گشودگی دایره ای و بیضی شکل استفاده کردند. برای سادگی استفاده از انتگرال کوشی ورق نامحدود شامل گشودگی غیردایروی به ناحیة درون دایره ای به شعاع واحد نگاشته می شود. نتایج حاصل نشان می دهند که انحنای گوشۀ گشودگی تأثیر بسزایی بر توزیع تنش دارد.

کلیدواژه‌ها

نرمی گشودگی؛ تنش حرارتی؛ نگاشت همنوا؛ حلّ تحلیلی؛ شار حرارتی

سایر فایل های مرتبط با مقاله

5-jafari-EA.pdf

مراجع

1 Florence, A.L. and Goodier, J.N., "Thermal stress at spherical cavities and circular holes in uniform heat flow", Journal of Applied Mechanics, Vol. 26, pp. 293-294, (1995).

2 Muskhelishvili, N.I., "Some basic problems of mathematical theory of elasticity", 4th edition, Noordhoff, Netherlands, pp.361-366, (1963).

3 Florence, A.L. and Goodier, J.N., "Thermal stresses due to disturbance of uniform heat flow by an insulated ovaloid hole", Journal of Applied Mechanics, Vol. 27, pp. 635-639, (1960).

4 BapuRao, M.N., "Thermal stresses around an elliptic hole in an infinite thick plate subjected to a uniform heat flow", Nuclear Engineering and Design, Vol. 35, pp. 299-307, (1975).

5 Lee, C.W., "Thermal stresses in a thick plate", International Journal of Solids and Structures, Vol. 6, pp. 605-615, (1970).

6 Takeuti, Y. and Sumi, N., "Thermal stresses in rectangular plate with a circular hole based on an improve complex variable approach", Mechanics Research Communication, Vol. 3, pp. 133-138, (1976).

7 Nisitani, H., Saimoto, A., Noguchi, H. and Chert, D.H., "Method of analysis of two-dimensional stationary thermo-elastic problem by a body force method-1st Report, The Basic Theory", Transactions of the Japan Society of Mechanical Engineers, Vol. 57, No. 542, pp. 2561-2567, (1991).

8 Kattis, M.A., "Thermoelastic plane problems with curvilinear boundaries", Acta Mechanica, Vol. 87, pp. 93-103, (1991).

9 Hasebe, N., Tamai, K. and Nakamura, T., "Analysis of a kinked crack under uniform heat flow", Journal of engineering mechanics (ASCE Transaction), Vol. 112, pp. 31–42, (1986).

10 Bhullar, S.K., "Thermal stresses in a hexagonal region with an elliptic hole", Nonlinear Dynamics and Systems Theory, Vol. 6, pp. 245–256, (2006).

11 Aseeri, S.A.,"Goursat functions for a problem of an isotropic plate with a curvilinear hole", International Journal of Open Problems in Computer Science, Vol. 1, No. 3, pp. 266-285, (2008).

12 Bhullar, S.K. and Wegner, J.L., "Thermal stresses in a plate with hyper-elliptical hole", Journal of Engineering and Technology Research, Vol. 8, pp. 152-170, (2009).

13 Wu, C.H., "Plane anisotropic thermoelasticity", Journal of Applied Mechanics, Vol. 51, pp. 724-726, (1984).

14 Hwu, C., "Thermal stresses in an anisotropic plate disturbed by an insulated elliptic hole or crack", Journal of Applied Mechanics, Vol. 57, pp. 916-922, (1990).

15 Yoshikawa, K. and Hasebe, N. ,"Green's function of the displacement boundary value problem for a heat source in an infinite plane with an arbitrary shaped rigid inclusion", Archive of Applied Mechanics, Vol. 69, pp. 227- 239, (1999).

16 Chao, C.K. and Gao, B., "Mixed boundary-value problems of two-dimensional anisotropic thermoelasticity with elliptic boundaries", International Journal of Solids and Structures, Vol. 38, pp. 5975-5994, (2001).

17 Hasebe, N., "Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole", Archive of Applied Mechanics, Vol. 80, pp. 1353-1370, (2010).

18 Hasebe, N., Bucher ,C.H. and Heuer, R.,"Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack", International Journal of Solids and Structures, Vol. 47, pp. 138–147, (2010).

19 Wang, C.H. and Chao, C.K., "On perturbation solutions for nearly circular inclusion problems in plane thermoelasticity", Journal of Applied Mechanics, Vol. 69, pp. 36-44, (2002).

20 Hasebe, N., Wang, X.F., Saito, T. and Sheng, W., "Interaction between a rigid inclusion and a line crack under uniform heat flux", International Journal of Solids and Structures, Vol. 44, pp. 2426–2441, (2007).

21 Chen, Y.Z., "General solution for arc crack problem in thermoelastic medium", International Journal of Engineering Science, Vol. 40, pp. 2223–2234, (2002).

22 Vinh, P.C., Hasebe, N., Wang, X.F. and Saito, T., "Interaction between a cracked hole and a line crack under uniform heat flux", International Journal of Fracture, Vol. 131, pp.367–384, (2005)

23 Gao, C.F., Zhao, Y.T. and Wang, M.-Zh., "An exact and explicit treatment of an elliptic hole problem in thermopiezoelectric media", International Journal of Solids and Structures, Vol. 39, pp. 2665–2685, (2002).

24 Li, R. and Kardomateas, G. A., "Thermo-elastic crack branching in general anisotropic media", International Journal of Solids and Structures, Vol. 42, pp. 1091–1109, (2005).

25 Seddeek M. A., Abdou M. A. , El-Sayed W. G. and El-Saedy F. M., "Complex Potential Functions and Integro-Differential Equation in Elastic Media Problem in Presence of Heat", American Journal of Fluid Dynamics, Vol. 2, pp. 31-41, (2012).