A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory
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Faris W., Nayfeh A.H.: Mechanical response of a capacitive microsensor under thermal load. Commun. Nonlinear Sci. Numer. Simul. 12, 776–783 (2007)
Kahrobaiyan M.H., Asghari M., Rahaeifard M., Ahmadian M.T.: Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory. Int. J. Eng. Sci. 48, 1985–1994 (2010)
Moser Y., Gijs M.A.M.: Miniaturized flexible temperature sensor. J. Microelectromech. Syst. 16, 1349–1354 (2007)
Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)
McFarland A.W., Colton J.S.: Role of material microstructure in plate stiffness with relevance to microcantilever sensors. J. Micromech. Microeng. 15, 1060–1067 (2005)
Poole W.J., Ashby M.F., Fleck N.A.: Micro-hardness of annealed and work-hardened copper polycrystals. Scr. Mater. 34, 559–564 (1996)
Stölken J.S., Evans A.G.: A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109–5115 (1998)
Koiter W.T.: Couple stresses in the theory of elasticity: I and II. Proc. K. Ned. Akad. Wet. B 67, 17–44 (1964)
Mindlin R.D., Tiersten H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal. 11, 415–448 (1962)
Eringen A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)
Aifantis E.C.: Gradient deformation models at nano, micro, and macro scales. J. Eng. Mater. Technol. 121, 189–202 (1999)
Fleck N.A., Hutchinson J.W.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825–1857 (1993)
Fleck N.A., Hutchinson J.W.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49, 2245–2271 (2001)
Vardoulakis I., Sulem J.: Bifurcation Analysis in Geomechanics. Blackie/Chapman & Hall, London (1995)
Akgöz B., Civalek Ö.: Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Compos. Part B Eng. 55, 263–268 (2013)
Akgöz B., Civalek Ö.: Longitudinal vibration analysis for microbars based on strain gradient elasticity theory. J. Vib. Control 20, 606–616 (2014)
Güven U.: Love–Bishop rod solution based on strain gradient elasticity theory. Comptes Rendus Mécanique 342, 8–16 (2014)
Kahrobaiyan M.H., Asghari M., Ahmadian M.T.: Longitudinal behavior of strain gradient bars. Int. J. Eng. Sci. 66-67, 44–59 (2013)
Kahrobaiyan M.H., Tajalli S.A., Movahhedy M.R., Akbari J., Ahmadian M.T.: Torsion of strain gradient bars. Int. J. Eng. Sci. 49, 856–866 (2011)
Sadeghi H., Baghani M., Naghdabadi R.: Strain gradient elasticity solution for functionally graded micro-cylinders. Int. J. Eng. Sci. 50, 22–30 (2012)
Akgöz B., Civalek Ö.: Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. Int. J. Eng. Sci. 49, 1268–1280 (2011)
Akgöz B., Civalek Ö.: Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory. Arch. Appl. Mech. 82, 423–443 (2012)
Akgöz B., Civalek Ö.: A size-dependent shear deformation beam model based on the strain gradient elasticity theory. Int. J. Eng. Sci. 70, 1–14 (2013)
Akgöz B., Civalek Ö.: Shear deformation beam models for functionally graded microbeams with new shear correction factors. Compos. Struct. 112, 214–225 (2014)
Ansari R., Gholami R., Sahmani S.: Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory. Compos. Struct. 94, 221–228 (2011)
Asghari M., Kahrobaiyan M.H., Nikfar M., Ahmadian M.T.: A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory. Acta Mech. 223, 1233–1249 (2012)
Ghayesh M.H., Amabili M., Farokhi H.: Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory. Int. J. Eng. Sci. 63, 52–60 (2013)
Lei J., He Y., Zhang B., Gan Z., Zeng P.: Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory. Int. J. Eng. Sci. 72, 36–52 (2013)
Kahrobaiyan M.H., Rahaeifard M., Tajalli S.A., Ahmadian M.T.: A strain gradient functionally graded Euler–Bernoulli beam formulation. Int. J. Eng. Sci. 52, 65–76 (2012)
Kong S., Zhou S., Nie Z., Wang K.: Static and dynamic analysis of micro beams based on strain gradient elasticity theory. Int. J. Eng. Sci. 47, 487–498 (2009)
Wang B., Zhao J., Zhou S.: A micro scale Timoshenko beam model based on strain gradient elasticity theory. Eur. J. Mech. A Solids 29, 591–599 (2010)
Zhang B., He Y., Liu D., Gan Z., Shen L.: Non-classical Timoshenko beam element based on the strain gradient elasticity theory. Finite Elem. Anal. Des. 79, 22–39 (2014)
Wang B., Zhou S., Zhao J., Chen X.: A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory. Eur. J. Mech. A Solids 30, 517–524 (2011)
Movassagh A.A., Mahmoodi M.J.: A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory. Eur. J. Mech. A Solids 40, 50–59 (2013)
Li A., Zhou S., Zhou S., Wang B.: A size-dependent model for bi-layered Kirchhoff micro-plate based on strain gradient elasticity theory. Compos. Struct. 113, 272–280 (2014)
Sahmani S., Ansari R.: On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory. Compos. Struct. 95, 430–442 (2013)
Ansari R., Gholami R., Faghih Shojaei M., Mohammadi V., Sahmani S.: Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory. Eur. J. Mech. A Solids 49, 251–267 (2015)
Zeighampour H., Tadi Beni Y.: Cylindrical thin-shell model based on modified strain gradient theory. Int. J. Eng. Sci. 78, 27–47 (2014)
Yang F., Chong A.C.M., Lam D.C.C., Tong P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)
Akgöz B., Civalek Ö.: Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory. Mater. Des. 42, 164–171 (2012)
Akgöz B., Civalek Ö.: Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory. Meccanica 48, 863–873 (2013)
Gao X.-L., Huang J.X., Reddy J.N.: A non-classical third-order shear deformation plate model based on a modified couple stress theory. Acta Mech. 224, 2699–2718 (2013)
Jomehzadeh E., Noori H.R., Saidi A.R.: The size-dependent vibration analysis of micro-plates based on a modified couple stress theory. Phys. E 43, 877–883 (2011)
Ke L.L., Wang Y.S., Yang J., Kitipornchai S.: Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory. J. Sound Vib. 331, 94–106 (2012)
Ma H.M., Gao X.L., Reddy J.N.: A non-classical Mindlin plate model based on a modified couple stress theory. Acta Mech. 220, 217–235 (2011)
Thai H.T., Choi D.H.: Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory. Compos. Struct. 95, 142–153 (2013)
Thai H.T., Kim S.E.: A size-dependent functionally graded Reddy plate model based on a modified couple stress theory. Compos. Part B Eng. 45, 1636–1645 (2013)
Thai H.T., Vo T.P.: A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory. Compos. Struct. 96, 376–383 (2013)
Tsiatas G.C.: A new Kirchhoff plate model based on a modified couple stress theory. Int. J. Solids Struct. 46, 2757–2764 (2009)
Yin L., Qian Q., Wang L., Xia W.: Vibration analysis of microscale plates based on modified couple stress theory. Acta Mech. Solida Sin. 23, 386–393 (2010)
Zhang B., He Y., Liu D., Gan Z., Shen L.: A non-classical Mindlin plate finite element based on a modified couple stress theory. Eur. J. Mech. A Solids 42, 63–80 (2013)