کمانش خطی وغیرخطی صفحات دایروی/حلقوی گرافن ارتوتروپیک به کمک ﺗﺌﻮری اﻻﺳﺘﯿﺴﯿﺘﻪ ﻏﯿﺮﻣﻮﺿﻌﯽ
Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
مصطفی
صادقیان
1
(دانشجوی کارشناسی ارشد، دانشکده مکانیک، دانشگاه آزاد اسلامی مشهد)
مهرداد
جبارزاده
2
(استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی مشهد)
Keywords: کمانش, صفحه دایروی/حلقوی, ارتوتروپیک, تئوری غیرموضعی الاستیسیته, روش مربعات دیفرانسیلی,
Abstract :
در این مقاله، تحلیل خطی و غیرخطی کمانش صفحات نسبتا ضخیم دایروی/حلقوی گرافن با خواص ارتوتروپیک بر پایه الاستیک تحت بار مکانیکی مورد بررسی قرار می­گیرد. به کمک ﺗﺌﻮری اﻻﺳﺘﯿﺴﯿﺘﻪ ﻏﯿﺮﻣﻮﺿﻌﯽ، اصل کار مجازی، تئوری مرتبه اول برشی و کرنش­های غیرخطی فون-کارمن، روابط حاکم برحسب جابجایی–ها بدست آمده و از روش مربعات دیفرانسیلی (DQ) همراه با توزیع غیریکنواخت نقاط (چیبشف-گوس-لوباتو) استفاده شده است. برای اعتبار سنجی، نتایج بدست آمده با نتایج کمانش در مراجعدیگر مقایسه شده و اثرات ضریب غیرموضعی، ضخامت، شعاع و پایه الاستیک، بر بارهای بی بعد کمانش مورد بررسی قرار گرفته است و همچنین نتایج تحلیل به روش تئوری غیر موضعی و موضعی با یکدیگر مقایسه شده اند. از نتایج مشاهده می­شود که بار بی­بعد کمانش صفحات گرافن با کاهش انعطاف پذیری از نظر شرط مرزی، با افزایش ضریب غیرموضعی، افزایش بیشتری می­یابد و همچنین با افزایش شعاع صفحه، اختلاف نتایج تحلیل غیر موضعی و موضعی بیشتر می­شود.
[1] Taniguchi N.,On the Basic Concept of Nanotechnolog, Proceedings of the International Conference of Production Engineering, London, 1974, pp.18-23.
[2] Ma M., Tu J.P., Yuan Y.F., Wang X.L., Li K.F., Mao F., Zeng Z.Y., Electrochemical Performance of ZnONanoplates as Anode Materials for Ni/Zn Secondary Batteries, Journal of Power Source, Vol. 179, 2008, pp. 395-400.
[3] J. Yguerabide, E. E. Yguerabide , Resonance Light Scattering Particles as Ultrasensitive Labels for Detection of Analytes in a wide Range of Applications, Journal of Cellular Biochemistry-Supplement, 37, 2001, pp.71-81.
[4] Agesen M., Sorensen C.B., Nanoplates and Their Suitability for Use as Solar Cells, Proceeding of Clean Technology, Boston Secondary Batteries, Journal of Power Source, Vol. 179, 2008, pp. 395-400.
[5] Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A., Electric Field Effect in Atomically Thin Carbon Films, Science, vol. 306, 2004, pp. 666–669.
[6] Xu Z.P., Buehler M.J., Geometry controls conformation of graphene sheets: membranes, ribbons, and scrolls, ACS-Nano, Vol. 4, 2010, pp. 3869–3876.
[7] Chiu H.Y., Hung P., Postma H.W.Ch., Bockrath M., Atomic-Scale Mass Sensing Using Carbon Nanotube Resonators, Nano Letters, Vol.8, 2008, pp. 4342–4346.
[8] Hernandez E., Goze C., Bernier P., Rubio A., Elastic Properties of C and BxCyNz Composite Nanotubes, Physics Review Letters, Vol. 80, 1998, pp. 4502–4505.
[9] Li C.Y., Chou T.W., Elastic wave velocities in single-walled carbon nanotubes, Physics Review B, Vol. 73, 2006, pp. 245-407.
[10] Li C., Chou T.W., Single-walled carbon nanotubes as ultrahigh frequency nanomechanical resonators, Physics Review B, Vol. 68, 2003, pp. 073405.
[11]Eringen A.C., Nonlocal Continuum Field Theories, Newyork, Springer-Verlag.
[12] Fleck N.A., Hutchinson J.W., Strain Gradient Plasticity, Advance applied mechanics, Vol. 33, 2002, pp. 295-361.
[13]F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong , Couple Stress Based Strain Gradient Theory for Elasticity, International journal of solid structs, 39, 2002, pp. 2731-2743.
[14]Parnes R., Chiskis A., Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling, Journal ofMechanics and Physics of Solids, Vol. 50, 2002, pp. 855–879.
[15]Pradhan S.C., Murmu T., Small Scale Effect onthe Buckling of Single-Layered GrapheneSheetsunder Biaxial Compression via Nonlocal Continuum Mechanics, Computational Materials Science, Vol. 47, 2009, pp. 268-274.
[16]Samaei A.T., Abbasion S., Mirsayar M.M., Buckling Analysis of a Single-Layer Graphene Sheet Embedded in an Elastic Medium Based on Nonlocal Mindlin Plate Theory, Mechanics Research Communications, Vol. 38, 2011, pp.481-485.
[17]Farajpour A., Danesh M., Mohammadi M., Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, PhysicaE., Vol. 44, 2011, pp.719–727.
[18]Narendar S., Gopalakrishnan S., Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics, Physica E., Vol. 43, 2011, pp. 1185–1191.
[19] Lim C.W., Yang Q., Zhang J.B., Thermal buckling of nanorod based on non-local elasticity theory, International Journal of Non-Linear Mechanics, Vol. 47, 2012, pp. 496-505.
[20] Farajpour A., Shahidi A.R., Mohammadi M., Mohzoon M., Buckling of Orthotropic Micro/Nanoscale Plates under Linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, 2012, pp. 1605-1615.
[21] Prasanna Kumar T.J., Narendar S., Gopalakrishnan S., Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics. Composite Structures, Vol. 100, 2013, pp. 332–342.
[22] Emam S.A., A general nonlocal nonlinear model for buckling of nanobeams, Applied Mathematical Modelling, Vol. 37, 2013, pp. 6929–6939.
[23] Mohammadi M., Farajpour A., Moradi A., Ghayour M., Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites: Part B, Vol. 56 , 2014, pp. 629–637.
[24] Sarrami-Foroushani S., Azhari M., Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects, Physica E., Vol. 57, 2014, pp. 83–95.
[25] Golmakania M.E., Rezatalaba J., Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory, Composite Structures, Vol. 119, 2015, pp. 238–250.
[26] Farajpour A., Mohammadi M., Shahidi A.R., Mahzoon M., Axisymmetric Buckling of the Circular Graphene Sheets with the Nonlocal continuum plate model, Physica E., Vol. 43, 2011, pp. 1820–1825.
[27] KaramoozRavari M.R., Shahidi A.R., Axisymmetric buckling of the circularannularnanoplates using finite difference method, Mechanica, Vol. 48, 2013, pp. 135–144.
[28] Bedroud M., Hosseini-Hashemi S., Nazemnezhad R., Buckling of circular/annular Mindlinnanoplates via nonlocal lasticity,Acta Mechanics, Vol. 224, 2013, pp. 2663-2676.
[29] Nosier A., Fallah F., Non-linear Analysis of Functionally Graded Circular Plates under Asymmetric Transverse Loading, International journal of non-Linear mechanics, Vol. 44 , 2009, pp. 928-942.
[30]Naderi A., Saidi A.R., Exact solution for stability analysis of moderately thick functionally graded, Composite Structures, Vol. 93, 2011, pp. 629–638.
[31]Shu C.,Differential Quadrature and Its Application in Engineering, Berlin, Springer.