تحلیل کمانش نانو ورق هدفمند تک جهته مستطیلی با در نظر گرفتن اثر سطح

نوع مقاله : مقاله پژوهشی

نویسندگان

1 مهندسی مکانیک/دانشگاه اراک/اراک/ایران

2 دانشگاه اراک - دانشکده فنی و مهندسی - گروه مهندسی مکانیک

چکیده
در مقاله حاضر، کمانش نانو ورق‌های تابعی مدرج مستطیلی با در نظر گرفتن اثر سطح بررسی شده است. به منظور تعریف خواص مواد از مدل موری-تاناکا بهره برده شده است که بر اساس این مدل خواص به طور پیوسته در راستای ضخامت تغییر می‌کند. میدان جابجایی با استفاده از تئوری‌های تغییر شکل برشی اصلاح‌شده بدست آمده‌اند که در این تئوری‌ها بر خلاف تئوری کلاسیک ورق‌ها اثر اینرسی دورانی و تغییر شکل‌های برشی عرضی در نظر گرفته شده است. جهت در نظر گرفتن اثرات مذکور از توابع مختلف مانند توابع نمایی، مثلثاتی، هایپربولیکی و پارابولیکی در راستای ضخامت بهره گرفته شده است. برای در نظر گرفتن اثرات غیر محلی و اثرات سطح به ترتیب از تئوری‌های الاستیسیته‌ی غیر محلی و تئوری الاستیسیته‌ی سطح استفاده شده است. معادلات حاکم بر حرکت با استفاده از اصل همیلتون بدست آمده‌اند و از روش حل گلرکین جهت حل این معادلات استفاده شده است. برای بررسی صحت نتایج به دست آمده، نتایج حاصل از این تحقیق با نتایج منتشر شده در مقالات معتبر مقایسه شده است. درانتها اثر پارامتر‌های مرتبط با اثر سطوح مانند تنش باقیمانده سطح، ثوابت الاستیسیته‌ی سطح و همچنین پارامتر‌هایی مانند نسبت ضخامت به طول، نسبت عرض به طول، اندیس توانی، پارامتر غیر محلی بر روی بار بحرانی کمانش سیستم بررسی می گردد.

کلیدواژه‌ها


عنوان مقاله English

Buckling Analysis of a Functionally Graded unidirectional rectangular nanoPlate considering the surface effect

نویسندگان English

Korosh Khorshidi 1
Mohsen Ghasemi 2
Mahdi Bahrami 2
1 Department of mechanical engineering/Arak University/Arak/Iran
2 Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran
چکیده English

In this paper, buckling analysis of functionally graded rectangular Nano-plates considering the surface effect is investigated. Also, to define the material properties the Mori-Tanaka scheme is used which according to this scheme the material properties change continuously along the thickness direction. Displacement field is obtained using modified shear deformation theories. In these theories, against classical plate theory, the effects of rotary inertia and transverse shear deformations are considered and various functions such as exponential, trigonometric, hyperbolic and parabolic functions are used to considering these effects along the thickness direction. To considering nonlocal and surface effects the nonlocal elasticity theory and surface elasticity theory are employed respectively. The governing equations of motion are obtained by Hamilton’s principle and the Galerkin method is used to solve these equations. To show the accuracy of the present formulations, the presented results in this thesis are compared with those reported in the literature. Finally, the effects of various parameters which is related to the surface parameters such as residual surface stress, surface elasticity constant and also other parameters such as thickness ratio, aspect ratio, material index and nonlocal parameter of functionally graded nano-plate are investigated.

کلیدواژه‌ها English

Surface effect
Buckling
Functionally graded Nano-plate
Surface elasticity theory
Nonlocal elasticity theory
[1] Khorshidi K, Taheri M, Ghasemi M. Sensitivity Analysis of Vibrating Laminated Composite Rec-tangular Plates in Interaction with Inviscid Fluid Using EFAST Method. Mechanics of Advanced Composite Structures.2020;7:219-31.
[2] Rojas EF, Faroughi S, Abdelkefi A, Park YH. Investigations on the performance of piezoelectric-flexoelectric energy harvesters. Applied Energy. 2021;288:116611.
[3] Rojas EF, Faroughi S, Abdelkefi A, Park YH. Nonlinear size dependent modeling and performance analysis of flexoelectric energy harvesters. Microsystem Technologies. 2019;25:3899-921.
[4] Rahmani A, Faroughi S, Friswell MI, Babaei A. Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects. Mechanics of Advanced Materials and Structures.2022;29:4813-38.
[5] Faroughi S, Sari MS, Abdelkefi A. Nonlocal Timoshenko representation and analysis of multi-layered functionally graded nanobeams. Microsystem Technologies. 2021;27:893-911.
[6] Alijani F, Bakhtiari-Nejad F, Amabili M. Nonlinear vibrations of FGM rectangular plates in thermal environments. Nonlinear Dynamics. 2011;66:251-70.
[7] Khorshidi K, Fallah A. Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory. International journal of mechanical sciences. 2016;113:94-104.
[8] Khorshidi K, Ghasemi M, Fallah A. Buckling analysis of functionally graded rectangular microplate in thermal environment based on exponential shear deformation theory using the modified couple stress theory. Journal of Solid and Fluid Mechanics. 2018;8:179-96. (In Persian)
[9] Khorshidi K, Bakhsheshy A. Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid. Acta Mechanica. 2015;226:3401-23.
[10] Kirchhoff G. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die reine und angewandte Mathematik (Crelles Journal). 1850;1850:51-88.
[11] Mindlin RD. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. 1951.
[12] Reddy JN. A simple higher-order theory for laminated composite plates. 1984.
[13] Sayyad AS, Ghugal YM. Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory. Applied and Computational mechanics. 2012;6.
[14] Ghugal YM, Sayyad AS. Free vibration of thick orthotropic plates using trigonometric shear deformation theory. Latin American Journal of Solids and Structures. 2011;8:229-43.
[15] Soldatos KP. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica.1992;94:195-220.
[16] Panc V. Theories of elastic plates: Springer Science & Business Media, 1975.
[17] Javaheri R, Eslami MR. Thermal buckling of functionally graded plates based on higher order theory. Journal of thermal stresses. 2002;25:603-25.
[18] Javaheri R, Eslami M. Buckling of functionally graded plates under in‐plane compressive loading. ZAMM‐ Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics. 2002;82:277-83.
[19] Hosseini-Hashemi S, Khorshidi K, Amabili M. Exact solution for linear buckling of rectangular Mindlin plates. Journal of sound and vibration. 2008;315:318-42.
[20] Zhang LW, Zhu P, Liew KM. Thermal buckling of functionally graded plates using a local Kriging meshless method. Composite Structures. 2014;108:472-92.
[21] Thai H-T, Kim S-E. Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation. International Journal of Mechanical Sciences. 2013;75:34-44.
[22] El Meiche N, Tounsi A, Ziane N, Mechab I. A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. International Journal of Mechanical Sciences. 2011;53:237-47.
[23] Mozafari H, Ayob A. Effect of thickness variation on the mechanical buckling load in plates made of functionally graded materials. Procedia Technology. 2012;1:496-504.
[24] Aifantis EC. Strain gradient interpretation of size effects. Fracture scaling: Springer; 1999. p. 299-314.
[25] Toupin R. Elastic materials with couple-stresses. Archive for rational mechanics and analysis. 1962;11:385-414.
[26] Eringen AC, Edelen DGB. On nonlocal elasticity. International journal of engineering science. 1972;10:233-48.
[27] Eringen AC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of applied physics. 1983;54:4703-10.
[28] Eringen AC. Nonlocal continuum field theories springer, berlin. 2002.
[29] Khorshidi K, Fallah A. Effect of exponential stress resultant on buckling response of functionally graded rectangular plates. Journal of Stress Analysis. 2017;2:27-33.
[30] Gurtin ME, Ian Murdoch A. A continuum theory of elastic material surfaces. Archive for rational mechanics and analysis. 1975;57:291-323.
[31] Gurtin ME, Murdoch AI. Surface stress in solids. International journal of Solids and Structures. 1978;14:431-40.
[32] Lu P, He LH, Lee HP, Lu C. Thin plate theory including surface effects. International journal of Solids and Structures. 2006;43:4631-47.
[33] Ansari R, Sahmani S. Surface stress effects on the free vibration behavior of nanoplates. International journal of engineering science. 2011;49:1204-15.
[34] Assadi A. Size dependent forced vibration of nanoplates with consideration of surface effects. Applied Mathematical Modelling. 2013;37:3575-88.
[35] Wang KF, Wang BL. A finite element model for the bending and vibration of nanoscale plates with surface effect. Finite Elements in Analysis and Design. 2013;74:22-9.
[36] Raghu P, Preethi K, Rajagopal A, Reddy JN. Nonlocal third-order shear deformation theory for analysis of laminated plates considering surface stress effects. Composite Structures. 2016;139:13-29.
[37] Karimi M, Shahidi AR. Nonlocal, refined plate, and surface effects theories used to analyze free vibration of magnetoelectroelastic nanoplates under thermo-mechanical and shear loadings. Applied Physics A. 2017;123:1-17.
[38] Attia MA. On the mechanics of functionally graded nanobeams with the account of surface elasticity. International journal of engineering science. 2017;115:73-101.
[39] Wang KF, Wang BL, Xu MH, Yu AB. Influences of surface and interface energies on the nonlinear vibration of laminated nanoscale plates. Composite Structures. 2018;183:423-33.
[40] Zhu C-S, Fang X-Q, Liu J-X. Surface energy effect on buckling behavior of the functionally graded nanoshell covered with piezoelectric nano-layers under torque. International Journal of Mechanical Sciences.2017;133:662-73.
[41] Lu L, Guo X, Zhao J. On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy. International journal of engineering science. 2018;124:24-40.
[42] Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta metallurgica. 1973;21:571-4.
[43] Reddy BS, Kumar JS, Reddy CE, Reddy K. Buckling analysis of functionally graded material plates using higher order shear deformation theory. Journal of composites. 2013;2013.
[44] Thai H-T, Choi D-H. An efficient and simple refined theory for buckling analysis of functionally graded plates. Applied Mathematical Modelling. 2012;36:1008-22.

  • تاریخ دریافت 26 دی 1401
  • تاریخ بازنگری 16 بهمن 1401
  • تاریخ پذیرش 29 فروردین 1402