تحلیل تنش در صفحه مستطیلی از جنس ماده الکترومگنتوالاستیک با رفتار تابعی حاوی چندین ترک

نوع مقاله : مقاله علمی پژوهشی

نویسندگان

1 استادیار دانشکده فنی مهندسی مکانیک،واحد کرج، دانشگاه آزاد اسلامی

2 استادیار دانشکده مکانیک، دانشگاه آزاد اسلامی، واحد هشتگرد

3 دانشگاه آزاد کرج

چکیده

در این مطالعه، تحلیل تنش در صفحه مستطیلی از جنس ماده الکترومگنتوالاستیک تابعی تضعیف شده توسط چندین ترک، تحت بار نقطه ای خارج صفحه ای مکانیکی و درون صفحه‌ای الکترومغناطیسی انجام شده است. در این مطالعه فرض شده که رفتار محیط الاستیک خطی است و سطوح ترکها هموار می‌باشد. از روش نابجایی، تبدیل فوریه محدود و روش جداسازی متغیرها برای بدست آوردن معادلات انتگرالی تکین از نوع کوشی استفاده شده است. برای صحت سنجی نتایج، تاثیرات ثوابت ماده، طول ترکها، محل اعمال بار نقطه ای و نحوه چیدمان ترکها بر روی ضرایب شدت میدانی، مثالهایی آورده شده است.

کلیدواژه‌ها

موضوعات


[1] Gao, C.F., Tong, P., and Zhang, T.Y., “Fracture Mechanics for a Mode III Crack in a Magnetoelectroelastic”, International Journal of Solids and Structures, Vol. 41, pp. 6613–6629, (2004).
 [2] Wang, B.L., and Mai, Y.W., “Fracture of Piezoelectromagnetic Materials”, Mechanics Research Communications, Vol. 31, pp. 65–73, (2004).
 
[3] Zhong, X.C., and Li, X.F., “Magnetoelectroelastic Analysis for an Opening Crack in a Piezoelectromagnetic Solid”, European Journal of Mechanics, A/Solids, Vol. 26, pp. 405–417, (2007).
 
[4] Zhang, X.S., “A Finite Rectangular Sheet with a Pair of Edge Cracks Excited by a Normal Anti-plane Shear Wave”, Engineering Fracture Mechanics, Vol. 35, pp. 1037-1042, (1990).
 
[5] Ma, S.W., and Zhang, L.X., “A New Solution of an Eccentric Crack off the Center Line of a Rectangular Sheet for Mode-III”, Engineering Fracture Mechanics, Vol. 40, pp. 1-7, (1991).
 
[6] Lee, K.Y., and Kwon, S.M., “Analysis of Stress and Electric Fields in a Rectangular Piezoelectric Body with a Center Crack under Anti-plane Shear Loading”, International Journal of Solids and Structures, Vol. 37, pp. 4859-4869, (2000).
 
[7] Kwon, S.M., and Lee, K.Y., “Transient Response of a Rectangular Piezoelectric Medium with a Center Crack”, European Journal of Mechanics, A/Solids, Vol. 20, pp. 457-468, (2001).
 
[8] Li, X.F., and Lee, K.Y., “Electroelastic Behavior of a Rectangular Piezoelectric Ceramic with an Anti-plane Shear Crack at Arbitrary Position”, European Journal of Mechanics, A/Solids, Vol. 23, pp. 645-658, (2004).
 
[9] Zhou, Z.G., Wu, L.Z., and Wang, B., “The Behavior of a Crack in Functionally Graded Piezoelectric/Piezomagnetic Materials under Anti-plane Shear Loading”, Archive of Applied Mechanics, Vol. 74, pp. 526–535, (2005).
 
[10] Qin, Q.H., Kang, Y.L., and Hu., K.Q., “A Moving Crack in a Rectangular Magnetoelectroelastic Body”, Engineering Fracture Mechanics, Vol. 74, pp. 751-770, (2007).
 
[11] Zhong, X.C., and Zhang, K.S., “Dynamic Analysis of a Penny-shaped Dielectric Crack in a Magnetoelectroelastic Solid under Impacts”, European Journal of Mechanics, A/Solids, Vol. 29, pp. 242–252, (2010).
 
[12] Zhang, P.W., “Dynamic Fracture of a Rectangular Limited-permeable Crack in Magneto-Electro-elastic Media under a Time-harmonic Elastic P-Wave”, International Journal of Solids and Structures, Vol. 48, pp. 553-566, (2011).
 
[13] Faal, R.T., Daliri, M., and Milani, A.S., “Anti-plane Stress Analysis of Orthotropic Rectangular Planes Weakened by Multiple Defects”, International Journal of Solids and Structures, Vol. 48, pp. 661–672, (2011).
 
[14] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., “Stress Analysis of a Functionally Graded Magneto-electro-elastic Strip with Multiple Moving Cracks”, Mathematics and Mechanics of Solids, Vol. 30, pp. 1-20, (2015).
 
[15] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., “Analytical Solution of Multiple Moving Cracks in Functionally Graded Piezoelectric Strip”, Applied Mathematics and Mechanics, Vol. 36, pp. 777–792, (2015).
 
[16] Ayatollahi, M., Monfared, M.M., and Nourazar, M., “Analysis of Multiple Moving Mode-III Cracks in a Functionally Graded Magnetoelectroelastic Half-plane” Journal of Intelligent Material Systems and Structures, Vol. 28, pp. 2823–2834, (2017).
 
[17] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., “Analysis of Cracked Piezoelectric Layer with Imperfect Non-homogeneous Orthotropic Coating”, International Journal of Mechanical Sciences, Vol. 93, pp. 93–101, (2015).
 
[18] Faal, R.T., and Dehghan, A.A., “Mode III Stress Intensity Factors for Cracked FGM Rectangular Plane”, Engineering Fracture Mechanics, Vol. 140, pp. 17-30, (2015).
 
[19] Bleustein, J.L., “A New Surface Wave in Piezoelectric Materials”, Applied Physics Letters, Vol. 13, pp. 412-413, (1968).
 
[20] Zhou, Z.G., and Wang, B., “Two Parallel Symmetry Permeable Cracks in Functionally Graded Piezoelectric/Piezomagnetic Materials under Anti-plane Shear Loading”, International Journal of Solids and Structures, Vol. 41, pp. 4407–4422, (2004).
 
[21] Deeg, W.F., “The Analysis of Dislocation, Crack and Inclusion Problems in Piezoelectric Solids”, Ph.D. Thesis, Stanford University, San Francisco, USA, (1980).
 
[22] Pak, Y.E., “Crack Extension Force in a Piezoelectric Material”, Journal of Applied Mechanics, Vol. 57, pp. 647-653, (1990).
 
[23] Li, S., Gao, W., and Cross, L.E., “Stress and Electric Displacement Distribution Near Griffith's Type III Crack Tips in Piezoceramics”, Materials Letters, Vol. 10, pp. 219-222, (1990).
 
[24] Sosa, H.A., “Three-dimensional Eigenfunction Analysis of a Crack in a Piezoelectric Material”, International Journal of Solids and Structures, Vol. 36, pp. 1-15, (1990).
 
[25] Gao, H., Zhang, T.Y., and Tong, P., “Local and Global Energy Release Rates for an Electrically Yielded Crack in a Piezoelectric Ceramic”, Journal of Mechanics and Physics Solids, Vol. 45, pp. 491-510, (1997).
 
[26] Hills, D.A., Kelly, P.A., Dai, D.N., and Korsunsky, A.M., “Solution of Crack Problems: the Distributed Dislocation Technique”, Kluwer: Academic Publishers, (1996)
 
[27] Erdogan, F., Gupta, G. D., and Cook, T. S., “Numerical Solution of Singular Integral Equations, Method of Analysis and Solution of Crack Problems”, Edited by G. C. Sih, Noordhoof, Leyden, Holland, (1973).