A review on stress-driven nonlocal elasticity theory

Document Type : Review Paper

Authors

1 Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

4 Department of Mechanical Engineering, University of Hormozgan, Bandar Abbas, Iran

Abstract

The behavior of materials at the nanoscale cannot be studied by classical theories. Accordingly, new theories have been developed to predict the behavior of materials at the nanoscale; some of them are nonlocal elasticity, strain gradient theory, couple stress theory, and surface effect theory. In most articles, the authors use a differential form of nonlocal elasticity theory. Recently, many authors have used the integral form of this theory and obtained interesting results. Therefore, in the present research, the articles related to the integral form of non-local theory have been examined for small-scale tubes, beams, shells, and plates.

Keywords

[1]           A. Hadi, A. Rastgoo, N. Haghighipour, A. Bolhassani, Numerical modelling of a spheroid living cell membrane under hydrostatic pressure, Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, No. 8, pp. 083501, 2018.
[2]           A. Kordzadeh, A. R. Saadatabadi, A. Hadi, Investigation on penetration of saffron components through lipid bilayer bound to spike protein of SARS-CoV-2 using steered molecular dynamics simulation, Heliyon, Vol. 6, No. 12, pp. e05681, 2020.
[3]           A. Hadi, A. Rastgoo, A. Bolhassani, N. Haghighipour, Effects of stretching on molecular transfer from cell membrane by forming pores, Soft Materials, Vol. 17, No. 4, pp. 391-399, 2019.
[4]           M. M. Adeli, A. Hadi, M. Hosseini, H. H. Gorgani, Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory, The European Physical Journal Plus, Vol. 132, No. 9, pp. 393, 2017/09/18, 2017.
[5]           E. C. Aifantis, Strain gradient interpretation of size effects,  in: Z. P. Bažant, Y. D. S. Rajapakse, Fracture Scaling, Eds., pp. 299-314, Dordrecht: Springer Netherlands, 1999.
[6]           M. S. H. Al-Furjan, M. Habibi, F. Ebrahimi, G. Chen, M. Safarpour, H. Safarpour, A coupled thermomechanics approach for frequency information of electrically composite microshell using heat-transfer continuum problem, The European Physical Journal Plus, Vol. 135, No. 10, pp. 837, 2020/10/16, 2020.
[7]           R. Ansari, R. Hassani, E. Hasrati, H. Rouhi, Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approach, Acta Mechanica, 2021/06/26, 2021.
[8]           A. Barati, A. Hadi, M. Z. Nejad, R. Noroozi, On vibration of bi-directional functionally graded nanobeams under magnetic field, Mechanics Based Design of Structures and Machines, pp. 1-18, 2020.
[9]           O. Civalek, M. H. Jalaei, Buckling of carbon nanotube (CNT)-reinforced composite skew plates by the discrete singular convolution method, Acta Mechanica, Vol. 231, No. 6, pp. 2565-2587, 2020/06/01, 2020.
[10]         F. Ebrahimi, A. Dabbagh, T. Rabczuk, On wave dispersion characteristics of magnetostrictive sandwich nanoplates in thermal environments, European Journal of Mechanics - A/Solids, Vol. 85, pp. 104130, 2021/01/01/, 2021.
[11]         F. Ebrahimi, A. Dabbagh, A. Rastgoo, Static stability analysis of multi-scale hybrid agglomerated nanocomposite shells, Mechanics Based Design of Structures and Machines, pp. 1-17, 2020.
[12]         F. Ebrahimi, S. H. S. Hosseini, Parametrically excited nonlinear dynamics and instability of double-walled nanobeams under thermo-magneto-mechanical loads, Microsystem Technologies, Vol. 26, No. 4, pp. 1121-1132, 2020/04/01, 2020.
[13]         M. Emadi, M. Z. Nejad, S. Ziaee, A. Hadi, Buckling analysis of arbitrary two-directional functionally graded nano-plate based on nonlocal elasticity theory using generalized differential quadrature method, Steel and Composite Structures, Vol. 39, No. 5, pp. 565-581, 2021.
[14]         A. C. Eringen, D. G. B. Edelen, On nonlocal elasticity, International Journal of Engineering Science, Vol. 10, No. 3, pp. 233-248, 1972/03/01/, 1972.
[15]         M. R. Farajpour, A. R. Shahidi, A. Hadi, A. Farajpour, Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms, Mechanics of Advanced Materials and Structures, Vol. 26, No. 17, pp. 1469-1481, 2019/09/02, 2019.
[16]         A. Hadi, M. Z. Nejad, M. Hosseini, Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science, Vol. 128, pp. 12-23, 2018.
[17]         A. Hadi, M. Z. Nejad, A. Rastgoo, M. Hosseini, Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory, Steel and Composite Structures, Vol. 26, No. 6, pp. 663-672, 2018.
[18]         A. Hadi, M. Z. Nejad, A. Rastgoo, M. Hosseini, Vol. 26, 03/25, 2018. En
[19]         H. Haghshenas Gorgani, M. Mahdavi Adeli, M. Hosseini, Pull-in behavior of functionally graded micro/nano-beams for MEMS and NEMS switches, Microsystem Technologies, Vol. 25, No. 8, pp. 3165-3173, 2019/08/01, 2019.
[20]         Y. Heidari, M. Arefi, M. Irani-Rahaghi, Free Vibration Analysis of Cylindrical Micro/Nano-Shell Reinforced with CNTRC Patches, International Journal of Applied Mechanics, Vol. 0, No. 0, pp. 2150040.
[21]         M. Hosseini, H. H. Gorgani, M. Shishesaz, A. Hadi, Size-Dependent Stress Analysis of Single-Wall Carbon Nanotube Based on Strain Gradient Theory, International Journal of Applied Mechanics, Vol. 09, No. 06, pp. 1750087, 2017/09/01, 2017.
[22]         M. Hosseini, A. Hadi, A. Malekshahi, M. Shishesaz, A review of size-dependent elasticity for nanostructures, Journal of Computational Applied Mechanics, Vol. 49, No. 1, pp. 197-211, 2018. en
[23]         M. Hosseini, M. Shishesaz, A. Hadi, Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness, Thin-Walled Structures, Vol. 134, pp. 508-523, 2019.
[24]         M. Hosseini, M. Shishesaz, K. N. Tahan, A. Hadi, Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials, International Journal of Engineering Science, Vol. 109, pp. 29-53, 2016/12/01/, 2016.
[25]         K. Huang, Y. Yin, B. Qu, Tight-binding theory of graphene mechanical properties, Microsystem Technologies, 2021/05/20, 2021.
[26]         M. M. Khoram, M. Hosseini, A. Hadi, M. Shishehsaz, Bending Analysis of Bidirectional FGM Timoshenko Nanobeam Subjected to Mechanical and Magnetic Forces and Resting on Winkler–Pasternak Foundation, International Journal of Applied Mechanics, Vol. 12, No. 08, pp. 2050093, 2020.
[27]         A. Koochi, M. Abadyan, S. Gholami, Electromagnetic instability analysis of nano-sensor, The European Physical Journal Plus, Vol. 136, No. 1, pp. 44, 2021/01/05, 2021.
[28]         R. Kumar, R. Kumar, Effect of two-temperature parameter on thermoelastic vibration in micro and nano beam resonator, European Journal of Mechanics - A/Solids, Vol. 89, pp. 104310, 2021/08/01/, 2021.
[29]         M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics - A/Solids, Vol. 77, pp. 103793, 2019/09/01/, 2019.
[30]         M. Mousavi Khoram, M. Hosseini, M. Shishesaz, A concise review of nano-plates, Journal of Computational Applied Mechanics, Vol. 50, No. 2, pp. 420-429, 2019.
[31]         I. M. Nazmul, I. Devnath, Closed-form expressions for bending and buckling of functionally graded nanobeams by the Laplace transform, International Journal of Computational Materials Science and Engineering, Vol. 0, No. 0, pp. 2150012.
[32]         M. Z. Nejad, A. Hadi, Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science, Vol. 105, pp. 1-11, 2016/08/01/, 2016.
[33]         M. Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016/06/01/, 2016.
[34]         F. P. Pinnola, S. A. Faghidian, R. Barretta, F. Marotti de Sciarra, Variationally consistent dynamics of nonlocal gradient elastic beams, International Journal of Engineering Science, Vol. 149, pp. 103220, 2020/04/01/, 2020.
[35]         Y.-M. Ren, H. Qing, Bending and Buckling Analysis of Functionally Graded Euler–Bernoulli Beam Using Stress-Driven Nonlocal Integral Model with Bi-Helmholtz Kernel, International Journal of Applied Mechanics, Vol. 0, No. 0, pp. 2150041.
[36]         G. Romano, R. Luciano, R. Barretta, M. Diaco, Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours, Continuum Mechanics and Thermodynamics, Vol. 30, No. 3, pp. 641-655, 2018/05/01, 2018.
[37]         A. F. Russillo, G. Failla, G. Alotta, F. Marotti de Sciarra, R. Barretta, On the dynamics of nano-frames, International Journal of Engineering Science, Vol. 160, pp. 103433, 2021/03/01/, 2021.
[38]         M. M. Selim, Torsional vibration of irregular single-walled carbon nanotube incorporating compressive initial stress effects, Journal of Mechanics, Vol. 37, pp. 260-269, 2021.
[39]         R. Selvamani, S. Mahesh, F. Ebrahimi, Refined couple stress dynamic modeling of thermoelastic wave propagation reaction of LEMV/CFRP composite cylinder excited by multi relaxation times, Waves in Random and Complex Media, pp. 1-20, 2021.
[40]         A. Shahabodini, R. Ansari, H. Rouhi, A three-dimensional surface elastic model for vibration analysis of functionally graded arbitrary straight-sided quadrilateral nanoplates under thermal environment, Journal of Mechanics, Vol. 37, pp. 72-99, 2020.
[41]         G.-L. She, H.-B. Liu, B. Karami, Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets, Thin-Walled Structures, Vol. 160, pp. 107407, 2021/03/01/, 2021.
[42]         M. Shishesaz, M. Hosseini, Mechanical Behavior of Functionally Graded Nano-Cylinders Under Radial Pressure Based on Strain Gradient Theory, Journal of Mechanics, Vol. 35, No. 4, pp. 441-454, 2018.
[43]         M. Shishesaz, M. Hosseini, K. Naderan Tahan, A. Hadi, Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory, Acta Mechanica, Vol. 228, No. 12, pp. 4141-4168, 2017/12/01, 2017.
[44]         B. Uzun, Ö. Civalek, M. Ö. Yaylı, Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions, Mechanics Based Design of Structures and Machines, pp. 1-20, 2020.
[45]         M. S. Vaccaro, F. Marotti de Sciarra, R. Barretta, On the regularity of curvature fields in stress-driven nonlocal elastic beams, Acta Mechanica, 2021/04/26, 2021.
[46]         P. Wang, P. Yuan, S. Sahmani, B. Safaei, Surface stress size dependency in nonlinear free oscillations of FGM quasi-3D nanoplates having arbitrary shapes with variable thickness using IGA, Thin-Walled Structures, Vol. 166, pp. 108101, 2021/09/01/, 2021.
[47]         E. Zarezadeh, V. Hosseini, A. Hadi, Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory, Mechanics Based Design of Structures and Machines, pp. 1-16, 2019.
[48]         G. Zhu, A. Zine, C. Droz, M. Ichchou, Wave transmission and reflection analysis through complex media based on the second strain gradient theory, European Journal of Mechanics - A/Solids, Vol. 90, pp. 104326, 2021/11/01/, 2021.
[49]         H. T. Zhu, H. M. Zbib, E. C. Aifantis, Strain gradients and continuum modeling of size effect in metal matrix composites, Acta Mechanica, Vol. 121, No. 1, pp. 165-176, 1997/03/01, 1997.
[50]         M. Shishesaz, M. Shariati, A. Yaghootian, A. Alizadeh, Nonlinear Vibration Analysis of Nano-Disks Based on Nonlocal Elasticity Theory Using Homotopy Perturbation Method, International Journal of Applied Mechanics, Vol. 11, No. 02, pp. 1950011, 2019.
[51]         A. Barati, M. M. Adeli, A. Hadi, Static torsion of bi-directional functionally graded microtube based on the couple stress theory under magnetic field, International Journal of Applied Mechanics, Vol. 12, No. 02, pp. 2050021, 2020.
[52]         A. Daneshmehr, A. Rajabpoor, A. Hadi, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, Vol. 95, pp. 23-35, 2015.
[53]         K. Dehshahri, M. Z. Nejad, S. Ziaee, A. Niknejad, A. Hadi, Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates, Advances in nano research, Vol. 8, No. 2, pp. 115-134, 2020.
[54]         M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics-A/Solids, Vol. 77, pp. 103793, 2019.
[55]         M. Moraveji, H. Keshvari, A. Karkhaneh, S. Bonakdar, A. Hadi, N. Haghighipour, The effect of collagen/polycaprolactone fibrous scaffold decorated with graphene nanoplatelet and low-frequency electromagnetic field on neuronal gene expression by stem cells, Advances in nano research, Vol. 10, No. 6, pp. 549-557, 2021.
[56]         M. Najafzadeh, M. M. Adeli, E. Zarezadeh, A. Hadi, Torsional vibration of the porous nanotube with an arbitrary cross-section based on couple stress theory under magnetic field, Mechanics Based Design of Structures and Machines, pp. 1-15, 2020.
[57]         H. Nekounam, R. Dinarvand, R. Khademi, F. Asghari, N. Mahmoodi, H. Arzani, E. Hasanzadeh, A. Hadi, R. Karimi, M. Kamali, Preparation of cationized albumin nanoparticles loaded indirubin by high pressure hemogenizer, bioRxiv, 2021.
[58]         A. Soleimani, K. Dastani, A. Hadi, M. H. Naei, Effect of out-of-plane defects on the postbuckling behavior of graphene sheets based on nonlocal elasticity theory, Steel and Composite Structures, Vol. 30, No. 6, pp. 517-534, 2019.
[59]         M. Z. Nejad, A. Hadi, A. Omidvari, A. Rastgoo, Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory, Structural engineering and mechanics: An international journal, Vol. 67, No. 4, pp. 417-425, 2018.
[60]         R. Barretta, S. A. Faghidian, R. Luciano, C. Medaglia, R. Penna, Stress-driven two-phase integral elasticity for torsion of nano-beams, Composites Part B: Engineering, Vol. 145, pp. 62-69, 2018.
[61]         R. Barretta, M. Diaco, L. Feo, R. Luciano, F. M. de Sciarra, R. Penna, Stress-driven integral elastic theory for torsion of nano-beams, Mechanics Research Communications, Vol. 87, pp. 35-41, 2018.
[62]         R. Barretta, S. A. Faghidian, R. Luciano, Longitudinal vibrations of nano-rods by stress-driven integral elasticity, Mechanics of Advanced Materials and Structures, Vol. 26, No. 15, pp. 1307-1315, 2019.
[63]         A. Apuzzo, R. Barretta, F. Fabbrocino, S. A. Faghidian, R. Luciano, F. Marotti de Sciarra, Axial and torsional free vibrations of elastic nano-beams by stress-driven two-phase elasticity, Journal of Applied and Computational Mechanics, Vol. 5, No. 2, pp. 402-413, 2019.
[64]         P.-L. Bian, H. Qing, C.-F. Gao, One-dimensional stress-driven nonlocal integral model with bi-Helmholtz kernel: Close form solution and consistent size effect, Applied Mathematical Modelling, Vol. 89, pp. 400-412, 2020.
[65]         A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of applied physics, Vol. 54, No. 9, pp. 4703-4710, 1983.
[66]         G. Romano, R. Barretta, Nonlocal elasticity in nanobeams: the stress-driven integral model, International Journal of Engineering Science, Vol. 115, pp. 14-27, 2017.
[67]         G. Romano, R. Barretta, Stress-driven versus strain-driven nonlocal integral model for elastic nano-beams, Composites Part B: Engineering, Vol. 114, pp. 184-188, 2017.
[68]         G. Romano, R. Barretta, M. Diaco, F. M. de Sciarra, Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, International Journal of Mechanical Sciences, Vol. 121, pp. 151-156, 2017.
[69]         A. Apuzzo, R. Barretta, R. Luciano, F. M. de Sciarra, R. Penna, Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model, Composites Part B: Engineering, Vol. 123, pp. 105-111, 2017.
[70]         R. Barretta, S. Fazelzadeh, L. Feo, E. Ghavanloo, R. Luciano, Nonlocal inflected nano-beams: A stress-driven approach of bi-Helmholtz type, Composite Structures, Vol. 200, pp. 239-245, 2018.
[71]         M. F. Oskouie, R. Ansari, H. Rouhi, Bending of Euler–Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach, Acta Mechanica Sinica, Vol. 34, No. 5, pp. 871-882, 2018.
[72]         M. Faraji Oskouie, R. Ansari, H. Rouhi, A numerical study on the buckling and vibration of nanobeams based on the strain and stress-driven nonlocal integral models, International Journal of Computational Materials Science and Engineering, Vol. 7, No. 03, pp. 1850016, 2018.
[73]         M. F. Oskouie, R. Ansari, H. Rouhi, Stress-driven nonlocal and strain gradient formulations of Timoshenko nanobeams, The European Physical Journal Plus, Vol. 133, No. 8, pp. 336, 2018.
[74]         R. Barretta, F. Fabbrocino, R. Luciano, F. M. de Sciarra, Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nano-beams, Physica E: Low-dimensional Systems and Nanostructures, Vol. 97, pp. 13-30, 2018.
[75]         R. Barretta, S. A. Faghidian, R. Luciano, C. Medaglia, R. Penna, Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress-driven nonlocal models, Composites Part B: Engineering, Vol. 154, pp. 20-32, 2018.
[76]         R. Barretta, R. Luciano, F. M. de Sciarra, G. Ruta, Stress-driven nonlocal integral model for Timoshenko elastic nano-beams, European Journal of Mechanics-A/Solids, Vol. 72, pp. 275-286, 2018.
[77]         R. Barretta, M. Čanađija, R. Luciano, F. M. de Sciarra, Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams, International Journal of Engineering Science, Vol. 126, pp. 53-67, 2018.
[78]         E. Mahmoudpour, S. Hosseini-Hashemi, S. Faghidian, Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model, Applied Mathematical Modelling, Vol. 57, pp. 302-315, 2018.
[79]         R. Barretta, A. Caporale, S. A. Faghidian, R. Luciano, F. M. de Sciarra, C. M. Medaglia, A stress-driven local-nonlocal mixture model for Timoshenko nano-beams, Composites Part B: Engineering, Vol. 164, pp. 590-598, 2019.
[80]         F. P. Pinnola, M. S. Vaccaro, R. Barretta, F. M. de Sciarra, Random vibrations of stress-driven nonlocal beams with external damping, Meccanica, pp. 1-16, 2020.
[81]         M. Roghani, H. Rouhi, Nonlinear stress-driven nonlocal formulation of Timoshenko beams made of FGMs, Continuum Mechanics and Thermodynamics, pp. 1-13, 2020.
[82]         A. Apuzzo, C. Bartolomeo, R. Luciano, D. Scorza, Novel local/nonlocal formulation of the stress-driven model through closed form solution for higher vibrations modes, Composite Structures, Vol. 252, pp. 112688, 2020.
[83]         R. Barretta, F. Fabbrocino, R. Luciano, F. M. De Sciarra, G. Ruta, Buckling loads of nano-beams in stress-driven nonlocal elasticity, Mechanics of Advanced Materials and Structures, Vol. 27, No. 11, pp. 869-875, 2020.
[84]         H. Darban, F. Fabbrocino, L. Feo, R. Luciano, Size-dependent buckling analysis of nanobeams resting on two-parameter elastic foundation through stress-driven nonlocal elasticity model, Mechanics of Advanced Materials and Structures, pp. 1-9, 2020.
[85]         R. Luciano, A. Caporale, H. Darban, C. Bartolomeo, Variational approaches for bending and buckling of non-local stress-driven Timoshenko nano-beams for smart materials, Mechanics Research Communications, Vol. 103, pp. 103470, 2020.
[86]         R. Luciano, H. Darban, C. Bartolomeo, F. Fabbrocino, D. Scorza, Free flexural vibrations of nanobeams with non-classical boundary conditions using stress-driven nonlocal model, Mechanics Research Communications, pp. 103536, 2020.
[87]         Y. He, H. Qing, C.-F. Gao, Theoretical analysis of free vibration of microbeams under different boundary conditions using stress-driven nonlocal integral model, International Journal of Structural Stability and Dynamics, Vol. 20, No. 03, pp. 2050040, 2020.
[88]         P. Jiang, H. Qing, C. Gao, Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model, Applied Mathematics and Mechanics, Vol. 41, No. 2, pp. 207-232, 2020.
[89]         P. Zhang, H. Qing, Buckling analysis of curved sandwich microbeams made of functionally graded materials via the stress-driven nonlocal integral model, Mechanics of Advanced Materials and Structures, pp. 1-18, 2020.
[90]         P. Zhang, H. Qing, Closed-form solution in bi-Helmholtz kernel based two-phase nonlocal integral models for functionally graded Timoshenko beams, Composite Structures, Vol. 265, pp. 113770, 2021.
[91]         P. Zhang, H. Qing, C.-F. Gao, Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress-driven nonlocal integral model, Composite Structures, pp. 112362, 2020.
[92]         R. Penna, L. Feo, A. Fortunato, R. Luciano, Nonlinear free vibrations analysis of geometrically imperfect FG nano-beams based on stress-driven nonlocal elasticity with initial pretension force, Composite Structures, Vol. 255, pp. 112856, 2021.
[93]         R. Barretta, M. Čanađija, F. Marotti de Sciarra, A. Skoblar, R. Žigulić, Dynamic behavior of nanobeams under axial loads: Integral elasticity modeling and size‐dependent eigenfrequencies assessment, Mathematical Methods in the Applied Sciences, 2021.
[94]         M. S. Vaccaro, F. P. Pinnola, F. M. de Sciarra, M. Canadija, R. Barretta, Stress-driven two-phase integral elasticity for Timoshenko curved beams, Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, pp. 2397791421990514, 2021.
[95]         R. Barretta, S. A. Faghidian, F. M. de Sciarra, Stress-driven nonlocal integral elasticity for axisymmetric nano-plates, International Journal of Engineering Science, Vol. 136, pp. 38-52, 2019.
[96]         A. Farajpour, C. Q. Howard, W. S. Robertson, On size-dependent mechanics of nanoplates, International Journal of Engineering Science, Vol. 156, pp. 103368, 2020.
[97]         M. Shariati, B. Azizi, M. Hosseini, M. Shishesaz, On the calibration of size parameters related to non-classical continuum theories using molecular dynamics simulations, International Journal of Engineering Science, Vol. 168, pp. 103544, 2021.
[98]         M. Shishesaz, M. Shariati, M. Hosseini, Size effect analysis on Vibrational response of Functionally Graded annular nano plate based on Nonlocal stress-driven method, International Journal of Structural Stability and Dynamics, 2021, In press.
[99]         M. Shariati, M. Shishesaz, R. Mosalmani, S. A. S. Roknizadeh, Size Effect on the Axisymmetric Vibrational Response of ‎Functionally Graded Circular Nano-Plate Based on the Nonlocal Stress-Driven Method, Journal of Applied and Computational Mechanics, pp. -, 2021.
[100]      A. F. Russillo, G. Failla, G. Alotta, F. M. de Sciarra, R. Barretta, On the dynamics of nano-frames, International Journal of Engineering Science, Vol. 160, pp. 103433, 2021.
[101]      H. M. Sedighi, M. Malikan, Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment, Physica Scripta, Vol. 95, No. 5, pp. 055218, 2020.
[102]      H. M. Sedighi, H. M. Ouakad, R. Dimitri, F. Tornabene, Stress-driven nonlocal elasticity for the instability analysis of fluid-conveying C-BN hybrid-nanotube in a magneto-thermal environment, Physica Scripta, Vol. 95, No. 6, pp. 065204, 2020.
[103]      H. M. Ouakad, A. Valipour, K. K. Żur, H. M. Sedighi, J. Reddy, On the nonlinear vibration and static deflection problems of actuated hybrid nanotubes based on the stress-driven nonlocal integral elasticity, Mechanics of Materials, Vol. 148, pp. 103532, 2020.
[104]      X. Yang, S. Sahmani, B. Safaei, Postbuckling analysis of hydrostatic pressurized FGM microsized shells including strain gradient and stress-driven nonlocal effects, Engineering with Computers, pp. 1-16, 2020.
Volume 52, Issue 3
September 2021
Pages 535-552
  • Receive Date: 27 September 2021
  • Revise Date: 04 October 2021
  • Accept Date: 02 October 2021
  • First Publish Date: 02 October 2021