References
193
References
1. Sheremetev, M.P., Pelekh, B.L.: To the construction of a refined theory of plates. Eng. J. 4(3),
34–46 (1964)
2. Hanuska, A.: Contribution to the Reissnerian algorithm in the theory of bending of elastic
plates. Aplik. Matemat. 12(6), 449–467 (1967)
3. Krysko, A.V., Kirichenko, V.F.: Refined theory of orthotropic thermosensitive gently sloping
shells in the framework of Pelekh-Sheremetev hypotheses. In: III International Symposium on
’Nonclassical problems of the theory of thin-walled structural elements of the physicochemical
mechanics of composite materials’, Ivano-Frankovsk, Ukraine, pp. 142–148 (1995)
4. Levinson, M.: A new rectangular beam theory. J. Sound Vibr. 74, 81–87 (1981)
5. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51,
745–752 (1984)
6. Fu, Y., Zhang, J.: Electromechanical dynamic buckling phenomenon in symmetric electric
fields actuated microbeams considering material damping. Acta Mech. 212, 29–42 (2010)
7. Moghimi, Z.M., Ahmadian, M.T.: Static pull-in analysis of electrostatically actuated
microbeams using homotopy perturbation method. Appl. Math. Model. 34, 1032–1046 (2010)
8. Jia, X.L., Yang, J., Kitipornchai, S.: Pull-in instability of geometrically nonlinear microswitches under electrostatic and Casimir forces. Acta Mech. 218, 161–174 (2011)
9. Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory
and experiments. Acta Metall. Mater. 42, 475–487 (1994)
10. Nix, W.D.: Mechanical properties of thin films. Metall. Trans. A 20, 2217–2245 (1989)
11. Mazza, E., Abel, S., Dual, J.: Experimental determination of mechanical properties of Ni and
Ni-Fe microbars. Micros. Technol. 2(4), 197–202 (1996)
12. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain
gradient elasticity. J. Mech. Phys. Soli 51, 1477–1508 (2003)
13. Ma, Q., Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10(4),
853–863 (1995)
14. Scheible, D.V., Erbe, A., Blick, R.H.: Evidence of a nanomechanical resonator being driven
into chaotic response via the Ruelle-Takens route. Appl. Phys. Lett. 81, 1884–1886 (2002)
15. Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech.
Anal. 11, 415–448 (1962)
16. Toupin, R.A.: Elastic materials with couple-stresses. Arch. Ration. Mech. Anal. 11, 385–414
(1962)
17. Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)
18. Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)
19. Gurtin, M.E., Weissmuller, J., Larche, F.: The general theory of curved deformable inter-faces
in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998)
20. Yang, F., Chong, M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for
elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)
21. Fleck, N.A., Hutchinson, J.W.: Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (eds.)
Advances in Applied Mechanics, vol. 33, pp. 295–366. Academic Press, New York (1997)
22. Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H., Rahaeifard, M.: On the size-dependent
behavior of functionally graded micro-beams. Mater. Des. 31, 2324–2329 (2010)
23. Asghari, M., Kahrobaiyan, M.H., Ahmadian, M.T.: A nonlinear Timoshenko beam formulation
based on the modified couple stress theory. Int. J. Eng. Sci. 48, 1749–1766 (2010)
24. Lazopoulos, K.A., Lazopoulos, A.K.: Bending and buckling of thin strain gradient elastic
beams. Eur. J. Mech. A-Sol. 29, 837–843 (2010)
25. 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)
26. Ma, H.M., Gao, X.L., Reddy, J.N.: A nonclassical Reddy-Levinson beam model based on a
modified couple stress theory. Int. J. Multiscale Comput. Eng. 8, 167–180 (2010)
27. Kirchhoff, G.: Vorlesungen Über Mathematische Physik. Mechanik, Leipzig (1876)
193
References
1. Sheremetev, M.P., Pelekh, B.L.: To the construction of a refined theory of plates. Eng. J. 4(3),
34–46 (1964)
2. Hanuska, A.: Contribution to the Reissnerian algorithm in the theory of bending of elastic
plates. Aplik. Matemat. 12(6), 449–467 (1967)
3. Krysko, A.V., Kirichenko, V.F.: Refined theory of orthotropic thermosensitive gently sloping
shells in the framework of Pelekh-Sheremetev hypotheses. In: III International Symposium on
’Nonclassical problems of the theory of thin-walled structural elements of the physicochemical
mechanics of composite materials’, Ivano-Frankovsk, Ukraine, pp. 142–148 (1995)
4. Levinson, M.: A new rectangular beam theory. J. Sound Vibr. 74, 81–87 (1981)
5. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51,
745–752 (1984)
6. Fu, Y., Zhang, J.: Electromechanical dynamic buckling phenomenon in symmetric electric
fields actuated microbeams considering material damping. Acta Mech. 212, 29–42 (2010)
7. Moghimi, Z.M., Ahmadian, M.T.: Static pull-in analysis of electrostatically actuated
microbeams using homotopy perturbation method. Appl. Math. Model. 34, 1032–1046 (2010)
8. Jia, X.L., Yang, J., Kitipornchai, S.: Pull-in instability of geometrically nonlinear microswitches under electrostatic and Casimir forces. Acta Mech. 218, 161–174 (2011)
9. Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory
and experiments. Acta Metall. Mater. 42, 475–487 (1994)
10. Nix, W.D.: Mechanical properties of thin films. Metall. Trans. A 20, 2217–2245 (1989)
11. Mazza, E., Abel, S., Dual, J.: Experimental determination of mechanical properties of Ni and
Ni-Fe microbars. Micros. Technol. 2(4), 197–202 (1996)
12. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain
gradient elasticity. J. Mech. Phys. Soli 51, 1477–1508 (2003)
13. Ma, Q., Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10(4),
853–863 (1995)
14. Scheible, D.V., Erbe, A., Blick, R.H.: Evidence of a nanomechanical resonator being driven
into chaotic response via the Ruelle-Takens route. Appl. Phys. Lett. 81, 1884–1886 (2002)
15. Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech.
Anal. 11, 415–448 (1962)
16. Toupin, R.A.: Elastic materials with couple-stresses. Arch. Ration. Mech. Anal. 11, 385–414
(1962)
17. Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)
18. Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)
19. Gurtin, M.E., Weissmuller, J., Larche, F.: The general theory of curved deformable inter-faces
in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998)
20. Yang, F., Chong, M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for
elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)
21. Fleck, N.A., Hutchinson, J.W.: Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (eds.)
Advances in Applied Mechanics, vol. 33, pp. 295–366. Academic Press, New York (1997)
22. Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H., Rahaeifard, M.: On the size-dependent
behavior of functionally graded micro-beams. Mater. Des. 31, 2324–2329 (2010)
23. Asghari, M., Kahrobaiyan, M.H., Ahmadian, M.T.: A nonlinear Timoshenko beam formulation
based on the modified couple stress theory. Int. J. Eng. Sci. 48, 1749–1766 (2010)
24. Lazopoulos, K.A., Lazopoulos, A.K.: Bending and buckling of thin strain gradient elastic
beams. Eur. J. Mech. A-Sol. 29, 837–843 (2010)
25. 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)
26. Ma, H.M., Gao, X.L., Reddy, J.N.: A nonclassical Reddy-Levinson beam model based on a
modified couple stress theory. Int. J. Multiscale Comput. Eng. 8, 167–180 (2010)
27. Kirchhoff, G.: Vorlesungen Über Mathematische Physik. Mechanik, Leipzig (1876)