Nonlocal Finite Element Model with Eight Degrees of Freedom and Sinusoidal Shear Deformation Theory for Bending and Buckling Analysis of Functionally Graded Nanobeams
Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical EngineeringMehdi Dehghan 1 , Mojtaba Esmailian 2 *
1 - Department of Mechanical Engineering, Malek-Ashtar University
2 - Faculty of Mechanical, Malek Ashtar University of Technology, Iran
Keywords: Nanobeam, Nonlocal finite element, Sinusoidal Shear Deformation Theory, Static analysis, DOE,
Abstract :
In the present study, an efficient nonlocal finite element model is used to investigate the buckling and bending behavior of functionally graded (FG) nanobeams. A two-node element with eight degrees of freedom is formulated according to the sinusoidal higher-order shear deformation theory. This theory assumes an accurate sinusoidal distribution of transverse shear stress in the thickness direction to provide stress-free boundary conditions without requiring shear correction factors on the top and bottom surfaces of the nanobeams. To apply size effects, the nonlocal Eringen elasticity theory is used. The material properties of FG nanobeams vary in the thickness direction as a continuous power function. Numerical results indicate the acceptable accuracy of the nonlocal finite element model. Additionally, the effects of various parameters, such as FG material power law index, length-to-thickness aspect ratio, and nonlocal parameter, on the critical buckling load and deflection of FG nanobeams are investigated.
[1] Eringen, A. C., 1972, "Nonlocal polar elastic continua," International journal of engineering science, 10 (1), pp. 1-16.
[2] Eringen, A. C., 1983, "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves," Journal of applied physics, 54 (9), pp. 4703-4710.
[3] Mindlin, R. D., Microstructure in linear elasticity. Columbia University New York, 1963.
[4] Papargyri-Beskou, S., Tsepoura, K., Polyzos, D., and Beskos, D., 2003, "Bending and stability analysis of gradient elastic beams," International Journal of solids and structures, 40 (2), pp. 385-400.
[5] Yang, F., Chong, A., Lam, D. C. C., and Tong, P., 2002, "Couple stress based strain gradient theory for elasticity," International journal of solids and structures, 39 (10), pp. 2731-2743.
[6] Askes, H. and Aifantis, E. C., 2009, "Gradient elasticity and flexural wave dispersion in carbon nanotubes," Physical Review B, 80 (19), p. 195412.
[7] Ghayesh, M. H. and Farajpour, A., 2019, "A review on the mechanics of functionally graded nanoscale and microscale structures," International Journal of Engineering Science, 137 pp. 8-36.
[8] Thai, H.-T. and Vo, T. P., 2012, "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams," International Journal of Engineering Science, 54 pp. 58-66.
[9] Thai, H.-T., 2012, "A nonlocal beam theory for bending, buckling, and vibration of nanobeams," International Journal of Engineering Science, 52 pp. 56-64.
[10] Pham, Q.-H., Malekzadeh, P., Tran, V. K., and Nguyen-Thoi, T., 2023/04/01 2023, "Free vibration analysis of functionally graded porous curved nanobeams on elastic foundation in hygro-thermo-magnetic environment," Frontiers of Structural and Civil Engineering, 17 (4), pp. 584-605.
[11] Pham, Q.-H. and Nguyen, P.-C., 2022, "Effects of size-dependence on static and free vibration of FGP nanobeams using finite element method based on nonlocal strain gradient theory," Steel and Composite Structures, An International Journal, 45 (3), pp. 331-348.
[12] Uzun, B., Civalek, Ö., and Yaylı, M. Ö., 2023, "Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions," Mechanics Based Design of Structures and Machines, 51 (1), pp. 481-500.
[13] Chaht, F. L., Kaci, A., Houari, M. S. A., Tounsi, A., Bég, O. A., and Mahmoud, S., 2015, "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect," Steel and Composite Structures, 18 (2), pp. 425-442.