How to cite this paper
Rahi, M., Firoozjaee, A & Dehestani, M. (2018). Implementation of discrete least squares meshless method for nonlocal elastic graphene nanoplates.Engineering Solid Mechanics, 6(3), 209-226.
Refrences
Aghababaei, R., & Reddy, J. N. (2009). Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. Journal of Sound and Vibration, 326(1-2), 277-289.
Alzahrani, E. O., Zenkour, A. M., & Sobhy, M. (2013). Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium. Composite Structures, 105, 163-172.
Analooei, H. R., Azhari, M., & Heidarpour, A. (2013). Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method. Applied Mathematical Modelling, 37(10-11), 6703-6717.
Ansari, R., Rajabiehfard, R., & Arash, B. (2010a). Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets. Computational Materials Science, 49(4), 831-838.
Ansari, R., Sahmani, S., & Arash, B. (2010b). Nonlocal plate model for free vibrations of single-layered graphene sheets. Physics Letters A, 375(1), 53-62.
Arash, B., & Wang, Q. (2011). Vibration of single-and double-layered graphene sheets. Journal of Nanotechnology in Engineering and Medicine, 2(1), 011012.
Babaei, H., & Shahidi, A. R. (2011). Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method. Archive of Applied Mechanics, 81(8), 1051-1062.
Behfar, K., Seifi, P., Naghdabadi, R., & Ghanbari, J. (2006). An analytical approach to determination of bending modulus of a multi-layered graphene sheet. Thin Solid Films, 496(2), 475-480.
Chen, J. H., Jang, C., Xiao, S., Ishigami, M., & Fuhrer, M. S. (2008). Intrinsic and extrinsic performance limits of graphene devices on SiO 2. Nature nanotechnology, 3(4), 206.
Choi, W., Lahiri, I., Seelaboyina, R., & Kang, Y. S. (2010). Synthesis of graphene and its applications: a review. Critical Reviews in Solid State and Materials Sciences, 35(1), 52-71.
Duan, W. H., & Wang, C. M. (2009). Nonlinear bending and stretching of a circular graphene sheet under a central point load. Nanotechnology, 20(7), 075702.
Eringen, A. C. (1972). Nonlocal polar elastic continua. International journal of engineering science, 10(1), 1-16.
Eringen, A. C. (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of applied physics, 54(9), 4703-4710.
Eringen, A. C. (2002). Nonlocal continuum field theories. Springer Science & Business Media.
Eringen, A. C., & Edelen, D. G. B. (1972). On nonlocal elasticity. International Journal of Engineering Science, 10(3), 233-248.
Farajpour, A., Shahidi, A. R., Mohammadi, M., & Mahzoon, M. (2012). Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics. Composite Structures, 94(5), 1605-1615.
Firoozjaee, A. R., & Afshar, M. H. (2009). Discrete least squares meshless method with sampling points for the solution of elliptic partial differential equations. Engineering analysis with boundary elements, 33(1), 83-92.
Fleck, N. A., & Hutchinson, J. W. (1997). Strain gradient plasticity. Advances in Applied Mechanics, 33, 296-361.
Geim, A. K. (2009). Graphene: status and prospects. science, 324(5934), 1530-1534.
Geim, A. K., & Kim, P. (2008). Carbon wonderland. Scientific American, 298(4), 90-97.
Geim, A. K., & Novoselov, K. S. (2007). The rise of graphene. Nature materials, 6(3), 183.
Heyrovska, R. (2008). Atomic structures of graphene, benzene and methane with bond lengths as sums of the single, double and resonance bond radii of carbon. arXiv preprint arXiv:0804.4086.
Jomehzadeh, E., & Saidi, A. R. (2011). Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates. Composite Structures, 93(2), 1015-1020.
Katsnelson, M. I. (2007). Graphene: carbon in two dimensions. Materials today, 10(1-2), 20-27.
Kuzmenko, A. B., Van Heumen, E., Carbone, F., & Van Der Marel, D. (2008). Universal optical conductance of graphite. Physical review letters, 100(11), 117401.
Liu, G. R. (2009). Meshfree methods: moving beyond the finite element method. Taylor & Francis.
Lu, P., Zhang, P. Q., Lee, H. P., Wang, C. M., & Reddy, J. N. (2007, December). Non-local elastic plate theories. In Proceedings of the royal society of london a: Mathematical, physical and engineering sciences (Vol. 463, No. 2088, pp. 3225-3240). The Royal Society.
Malekzadeh, P., Setoodeh, A. R., & Beni, A. A. (2011a). Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates. Composite Structures, 93(7), 1631-1639.
Malekzadeh, P., Setoodeh, A. R., & Beni, A. A. (2011b). Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium. Composite Structures, 93(8), 2083-2089.
Martel, R., Schmidt, T., Shea, H. R., Hertel, T., & Avouris, P. (1998). Single-and multi-wall carbon nanotube field-effect transistors. Applied physics letters, 73(17), 2447-2449.
Murmu, T., & Pradhan, S. C. (2009). Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E: Low-dimensional Systems and Nanostructures, 41(7), 1232-1239.
Murmu, T., & Pradhan, S. C. (2009). Buckling of biaxially compressed orthotropic plates at small scales. Mechanics Research Communications, 36(8), 933-938.
Naderi, A., & Baradaran, G. H. (2013). Element free Galerkin method for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory.
Nowacki, W. (1974). The linear theory of micropolar elasticity. In Micropolar Elasticity (pp. 1-43).
Peddieson, J., Buchanan, G. R., & McNitt, R. P. (2003). Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 41(3-5), 305-312.
Pouresmaeeli, S., Fazelzadeh, S. A., & Ghavanloo, E. (2012). Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium. Composites Part B: Engineering, 43(8), 3384-3390.
Pradhan, S. C., & Phadikar, J. K. (2009). Nonlocal elasticity theory for vibration of nanoplates. Journal of Sound and Vibration, 325(1-2), 206-223.
Pumera, M., Ambrosi, A., Bonanni, A., Chng, E. L. K., & Poh, H. L. (2010). Graphene for electrochemical sensing and biosensing. TrAC Trends in Analytical Chemistry, 29(9), 954-965.
Rao, C. N. R., Biswas, K., Subrahmanyam, K. S., & Govindaraj, A. (2009). Graphene, the new nanocarbon. Journal of Materials Chemistry, 19(17), 2457-2469.
Reddy, J. N. (2010). Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 48(11), 1507-1518.
Sakhaee-Pour, A. (2009). Elastic properties of single-layered graphene sheet. Solid State Communications, 149(1-2), 91-95.
Sakhaee-Pour, A., Ahmadian, M. T., & Vafai, A. (2008). Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors. Solid State Communications, 145(4), 168-172.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). FREQUENCY ANALYSIS OF A GRAPHENE SHEET EMBEDDED IN AN ELASTIC MEDIUM WITH CONSIDERATION OF SMALL SCALE. Materials Physics & Mechanics, 22(2), 125-135.
Shen, H. S. (2011). Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments. Composite Structures, 93(3), 1143-1152.
Shen, L. E., Shen, H. S., & Zhang, C. L. (2010). Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments. Computational Materials Science, 48(3), 680-685.
Sobhy, M. (2014). Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions. Acta Mechanica, 225(9), 2521-2538.
Sobhy, M. (2014). Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium. Physica E: Low-dimensional Systems and Nanostructures, 56, 400-409.
Wang, C. M., Tan, V. B. C., & Zhang, Y. Y. (2006). Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. Journal of Sound and Vibration, 294(4-5), 1060-1072.
Wang, Q., & Varadan, V. K. (2006). Wave characteristics of carbon nanotubes. International Journal of Solids and Structures, 43(2), 254-265.
Yang, F. A. C. M., Chong, A. C. M., Lam, D. C. C., & Tong, P. (2002). Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10), 2731-2743.
Zenkour, A. M., & Sobhy, M. (2013). Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium. Physica E: Low-dimensional Systems and Nanostructures, 53, 251-259.
Zhang, Y., Lei, Z. X., Zhang, L. W., Liew, K. M., & Yu, J. L. (2015). Nonlocal continuum model for vibration of single-layered graphene sheets based on the element-free kp-Ritz method. Engineering Analysis with Boundary Elements, 56, 90-97.
Alzahrani, E. O., Zenkour, A. M., & Sobhy, M. (2013). Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium. Composite Structures, 105, 163-172.
Analooei, H. R., Azhari, M., & Heidarpour, A. (2013). Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method. Applied Mathematical Modelling, 37(10-11), 6703-6717.
Ansari, R., Rajabiehfard, R., & Arash, B. (2010a). Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets. Computational Materials Science, 49(4), 831-838.
Ansari, R., Sahmani, S., & Arash, B. (2010b). Nonlocal plate model for free vibrations of single-layered graphene sheets. Physics Letters A, 375(1), 53-62.
Arash, B., & Wang, Q. (2011). Vibration of single-and double-layered graphene sheets. Journal of Nanotechnology in Engineering and Medicine, 2(1), 011012.
Babaei, H., & Shahidi, A. R. (2011). Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method. Archive of Applied Mechanics, 81(8), 1051-1062.
Behfar, K., Seifi, P., Naghdabadi, R., & Ghanbari, J. (2006). An analytical approach to determination of bending modulus of a multi-layered graphene sheet. Thin Solid Films, 496(2), 475-480.
Chen, J. H., Jang, C., Xiao, S., Ishigami, M., & Fuhrer, M. S. (2008). Intrinsic and extrinsic performance limits of graphene devices on SiO 2. Nature nanotechnology, 3(4), 206.
Choi, W., Lahiri, I., Seelaboyina, R., & Kang, Y. S. (2010). Synthesis of graphene and its applications: a review. Critical Reviews in Solid State and Materials Sciences, 35(1), 52-71.
Duan, W. H., & Wang, C. M. (2009). Nonlinear bending and stretching of a circular graphene sheet under a central point load. Nanotechnology, 20(7), 075702.
Eringen, A. C. (1972). Nonlocal polar elastic continua. International journal of engineering science, 10(1), 1-16.
Eringen, A. C. (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of applied physics, 54(9), 4703-4710.
Eringen, A. C. (2002). Nonlocal continuum field theories. Springer Science & Business Media.
Eringen, A. C., & Edelen, D. G. B. (1972). On nonlocal elasticity. International Journal of Engineering Science, 10(3), 233-248.
Farajpour, A., Shahidi, A. R., Mohammadi, M., & Mahzoon, M. (2012). Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics. Composite Structures, 94(5), 1605-1615.
Firoozjaee, A. R., & Afshar, M. H. (2009). Discrete least squares meshless method with sampling points for the solution of elliptic partial differential equations. Engineering analysis with boundary elements, 33(1), 83-92.
Fleck, N. A., & Hutchinson, J. W. (1997). Strain gradient plasticity. Advances in Applied Mechanics, 33, 296-361.
Geim, A. K. (2009). Graphene: status and prospects. science, 324(5934), 1530-1534.
Geim, A. K., & Kim, P. (2008). Carbon wonderland. Scientific American, 298(4), 90-97.
Geim, A. K., & Novoselov, K. S. (2007). The rise of graphene. Nature materials, 6(3), 183.
Heyrovska, R. (2008). Atomic structures of graphene, benzene and methane with bond lengths as sums of the single, double and resonance bond radii of carbon. arXiv preprint arXiv:0804.4086.
Jomehzadeh, E., & Saidi, A. R. (2011). Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates. Composite Structures, 93(2), 1015-1020.
Katsnelson, M. I. (2007). Graphene: carbon in two dimensions. Materials today, 10(1-2), 20-27.
Kuzmenko, A. B., Van Heumen, E., Carbone, F., & Van Der Marel, D. (2008). Universal optical conductance of graphite. Physical review letters, 100(11), 117401.
Liu, G. R. (2009). Meshfree methods: moving beyond the finite element method. Taylor & Francis.
Lu, P., Zhang, P. Q., Lee, H. P., Wang, C. M., & Reddy, J. N. (2007, December). Non-local elastic plate theories. In Proceedings of the royal society of london a: Mathematical, physical and engineering sciences (Vol. 463, No. 2088, pp. 3225-3240). The Royal Society.
Malekzadeh, P., Setoodeh, A. R., & Beni, A. A. (2011a). Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates. Composite Structures, 93(7), 1631-1639.
Malekzadeh, P., Setoodeh, A. R., & Beni, A. A. (2011b). Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium. Composite Structures, 93(8), 2083-2089.
Martel, R., Schmidt, T., Shea, H. R., Hertel, T., & Avouris, P. (1998). Single-and multi-wall carbon nanotube field-effect transistors. Applied physics letters, 73(17), 2447-2449.
Murmu, T., & Pradhan, S. C. (2009). Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E: Low-dimensional Systems and Nanostructures, 41(7), 1232-1239.
Murmu, T., & Pradhan, S. C. (2009). Buckling of biaxially compressed orthotropic plates at small scales. Mechanics Research Communications, 36(8), 933-938.
Naderi, A., & Baradaran, G. H. (2013). Element free Galerkin method for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory.
Nowacki, W. (1974). The linear theory of micropolar elasticity. In Micropolar Elasticity (pp. 1-43).
Peddieson, J., Buchanan, G. R., & McNitt, R. P. (2003). Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 41(3-5), 305-312.
Pouresmaeeli, S., Fazelzadeh, S. A., & Ghavanloo, E. (2012). Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium. Composites Part B: Engineering, 43(8), 3384-3390.
Pradhan, S. C., & Phadikar, J. K. (2009). Nonlocal elasticity theory for vibration of nanoplates. Journal of Sound and Vibration, 325(1-2), 206-223.
Pumera, M., Ambrosi, A., Bonanni, A., Chng, E. L. K., & Poh, H. L. (2010). Graphene for electrochemical sensing and biosensing. TrAC Trends in Analytical Chemistry, 29(9), 954-965.
Rao, C. N. R., Biswas, K., Subrahmanyam, K. S., & Govindaraj, A. (2009). Graphene, the new nanocarbon. Journal of Materials Chemistry, 19(17), 2457-2469.
Reddy, J. N. (2010). Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 48(11), 1507-1518.
Sakhaee-Pour, A. (2009). Elastic properties of single-layered graphene sheet. Solid State Communications, 149(1-2), 91-95.
Sakhaee-Pour, A., Ahmadian, M. T., & Vafai, A. (2008). Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors. Solid State Communications, 145(4), 168-172.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). FREQUENCY ANALYSIS OF A GRAPHENE SHEET EMBEDDED IN AN ELASTIC MEDIUM WITH CONSIDERATION OF SMALL SCALE. Materials Physics & Mechanics, 22(2), 125-135.
Shen, H. S. (2011). Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments. Composite Structures, 93(3), 1143-1152.
Shen, L. E., Shen, H. S., & Zhang, C. L. (2010). Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments. Computational Materials Science, 48(3), 680-685.
Sobhy, M. (2014). Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions. Acta Mechanica, 225(9), 2521-2538.
Sobhy, M. (2014). Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium. Physica E: Low-dimensional Systems and Nanostructures, 56, 400-409.
Wang, C. M., Tan, V. B. C., & Zhang, Y. Y. (2006). Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. Journal of Sound and Vibration, 294(4-5), 1060-1072.
Wang, Q., & Varadan, V. K. (2006). Wave characteristics of carbon nanotubes. International Journal of Solids and Structures, 43(2), 254-265.
Yang, F. A. C. M., Chong, A. C. M., Lam, D. C. C., & Tong, P. (2002). Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10), 2731-2743.
Zenkour, A. M., & Sobhy, M. (2013). Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium. Physica E: Low-dimensional Systems and Nanostructures, 53, 251-259.
Zhang, Y., Lei, Z. X., Zhang, L. W., Liew, K. M., & Yu, J. L. (2015). Nonlocal continuum model for vibration of single-layered graphene sheets based on the element-free kp-Ritz method. Engineering Analysis with Boundary Elements, 56, 90-97.