메뉴 건너뛰기




Volumn 82, Issue 3, 2012, Pages 363-376

A nonlinear microbeam model based on strain gradient elasticity theory with surface energy

Author keywords

Geometric nonlinearity; Microbeam; Strain gradient elasticity; Surface energy

Indexed keywords

BEAM MODEL; BEAM THICKNESS; BERNOULLI-EULER BEAM; GALERKIN; GEOMETRIC NON-LINEARITY; GOVERNING EQUATIONS OF MOTION; HAMILTON'S PRINCIPLE; MATERIAL LENGTH SCALE; MICRO BEAMS; MICRO-SCALES; MODEL-BASED OPC; NON-LINEAR VIBRATIONS; NONLINEAR MICROBEAM; NONLINEAR VIBRATION ANALYSIS; NUMERICAL INVESTIGATIONS; SIMPLY SUPPORTED; SIZE EFFECTS; STRAIN GRADIENT EFFECTS; STRAIN GRADIENT ELASTICITY; SURFACE ENERGIES; VON-KARMAN STRAIN;

EID: 84856620433     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-011-0561-9     Document Type: Article
Times cited : (53)

References (38)
  • 1
    • 0347758352 scopus 로고    scopus 로고
    • Glucose Biosensor Based on the Microcantilever
    • DOI 10.1021/ac035048k
    • J. Pei F. Tian T. Thundat 2004 Glucose biosensor based on the microcantilever Anal. Chem. 76 292 297 10.1021/ac035048k (Pubitemid 38090764)
    • (2004) Analytical Chemistry , vol.76 , Issue.2 , pp. 292-297
    • Pei, J.1    Tian, F.2    Thundat, T.3
  • 2
    • 70350055026 scopus 로고    scopus 로고
    • A constitutive model for thin sheet metal in micro-forming considering first order size effects
    • 10.1016/j.matdes.2009.07.037
    • W. Yun D. Peilong X. Zhenying Y. Hua W. Jiangping W. Jingjing 2010 A constitutive model for thin sheet metal in micro-forming considering first order size effects Mater. Des. 31 1010 1014 10.1016/j.matdes.2009.07.037
    • (2010) Mater. Des. , vol.31 , pp. 1010-1014
    • Yun, W.1    Peilong, D.2    Zhenying, X.3    Hua, Y.4    Jiangping, W.5    Jingjing, W.6
  • 3
    • 77956179551 scopus 로고    scopus 로고
    • The size effect on micro deformation behavior in micro-scale plastic deformation
    • 10.1016/j.matdes.2010.06.011
    • W.L. Chan M.W. Fu J. Lu 2011 The size effect on micro deformation behavior in micro-scale plastic deformation Mater. Des. 32 198 206 10.1016/j.matdes.2010.06.011
    • (2011) Mater. Des. , vol.32 , pp. 198-206
    • Chan, W.L.1    Fu, M.W.2    Lu, J.3
  • 4
    • 45849093345 scopus 로고    scopus 로고
    • Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates
    • 05600342 10.1007/s00419-007-0166-5
    • S. Papargyri-Beskou D.E. Beskos 2008 Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates Arch. Appl. Mech. 78 625 635 05600342 10.1007/s00419-007-0166-5
    • (2008) Arch. Appl. Mech. , vol.78 , pp. 625-635
    • Papargyri-Beskou, S.1    Beskos, D.E.2
  • 5
    • 55749091952 scopus 로고    scopus 로고
    • A microstructure-dependent Timoshenko beam model based on a modified couple stress theory
    • 2472995 1171.74367 10.1016/j.jmps.2008.09.007
    • H.M. Ma X.L. Gao J.N. Reddy 2008 A microstructure-dependent Timoshenko beam model based on a modified couple stress theory J. Mech. Phys. Solids 56 3379 3391 2472995 1171.74367 10.1016/j.jmps.2008.09.007
    • (2008) J. Mech. Phys. Solids , vol.56 , pp. 3379-3391
    • Ma, H.M.1    Gao, X.L.2    Reddy, J.N.3
  • 6
    • 0001954361 scopus 로고
    • Couple stresses in the theory of elasticity
    • 0119.39504
    • W.T. Koiter 1964 Couple stresses in the theory of elasticity Proc. K. Ned. Akad. Wet. (B) 67 17 44 0119.39504
    • (1964) Proc. K. Ned. Akad. Wet. (B) , vol.67 , pp. 17-44
    • Koiter, W.T.1
  • 7
    • 0033901519 scopus 로고    scopus 로고
    • Effect of couple-stresses on the elastic bending of beams
    • DOI 10.1016/S0020-7683(98)00283-2
    • A. Anthoine 2000 Effect of couple-stresses on the elastic bending of beams Int. J. Solids Struct. 37 1003 1018 0978.74044 10.1016/S0020-7683(98) 00283-2 (Pubitemid 30509380)
    • (2000) International Journal of Solids and Structures , vol.37 , Issue.7 , pp. 1003-1018
    • Anthoine, A.1
  • 8
    • 33750597812 scopus 로고    scopus 로고
    • Bernoulli-Euler beam model based on a modified couple stress theory
    • DOI 10.1088/0960-1317/16/11/015, PII S0960131706219259, 015
    • S.K. Park X.L. Gao 2006 Bernoulli-Euler beam model based on a modified couple stress theory J. Micromech. Microeng. 6 2355 2359 10.1088/0960-1317/16/ 11/015 (Pubitemid 44679456)
    • (2006) Journal of Micromechanics and Microengineering , vol.16 , Issue.11 , pp. 2355-2359
    • Park, S.K.1    Gao, X.-L.2
  • 9
    • 41749123679 scopus 로고    scopus 로고
    • The size-dependent natural frequency of Bernoulli-Euler micro-beams
    • 1213.74189 10.1016/j.ijengsci.2007.10.002
    • S.L. Kong S.J. Zhou Z.F. Nie K. Wang 2008 The size-dependent natural frequency of Bernoulli-Euler micro-beams Int. J. Eng. Sci. 46 427 437 1213.74189 10.1016/j.ijengsci.2007.10.002
    • (2008) Int. J. Eng. Sci. , vol.46 , pp. 427-437
    • Kong, S.L.1    Zhou, S.J.2    Nie, Z.F.3    Wang, K.4
  • 10
    • 0037150391 scopus 로고    scopus 로고
    • Couple stress based strain gradient theory for elasticity
    • DOI 10.1016/S0020-7683(02)00152-X, PII S002076830200152X
    • F. Yang A.C.M. Chong D.C.C. Lam 2002 Couple stress based strain gradient theory for elasticity Int. J. Solids Struct. 39 2731 2743 1037.74006 10.1016/S0020-7683(02)00152-X (Pubitemid 34617098)
    • (2002) International Journal of Solids and Structures , vol.39 , Issue.10 , pp. 2731-2743
    • Yang, F.1    Chong, A.C.M.2    Lam, D.C.C.3    Tong, P.4
  • 11
    • 79958834680 scopus 로고    scopus 로고
    • Investigation of the size effects in Timoshenko beams based on the couple stress theory
    • doi: 10.1007/s00419-010-0452-5
    • Asghari, M.; Kahrobaiyan, M.H.; Rahaeifard, M.; Ahmadian, M.T.: Investigation of the size effects in Timoshenko beams based on the couple stress theory. Archive Appl. Mech. (2010) doi: 10.1007/s00419-010-0452-5
    • (2010) Archive Appl. Mech.
    • Asghari, M.1    Kahrobaiyan, M.H.2    Rahaeifard, M.3    Ahmadian, M.T.4
  • 12
    • 76549113272 scopus 로고    scopus 로고
    • On the size-dependent behavior of functionally graded microbeams
    • 10.1016/j.matdes.2009.12.006
    • M. Asghari M.T. Ahmadian M.H. Kahrobaiyan M. Rahaeifard 2010 On the size-dependent behavior of functionally graded microbeams Mater. Des. 31 2324 2329 10.1016/j.matdes.2009.12.006
    • (2010) Mater. Des. , vol.31 , pp. 2324-2329
    • Asghari, M.1    Ahmadian, M.T.2    Kahrobaiyan, M.H.3    Rahaeifard, M.4
  • 13
    • 78649883379 scopus 로고    scopus 로고
    • The modified couple stress functionally graded Timoshenko beam formulation
    • 10.1016/j.matdes.2010.08.046
    • M. Asghari M. Rahaeifard M.H. Kahrobaiyan M.T. Ahmadian 2011 The modified couple stress functionally graded Timoshenko beam formulation Mater. Des. 32 1435 1443 10.1016/j.matdes.2010.08.046
    • (2011) Mater. Des. , vol.32 , pp. 1435-1443
    • Asghari, M.1    Rahaeifard, M.2    Kahrobaiyan, M.H.3    Ahmadian, M.T.4
  • 14
    • 78649633224 scopus 로고    scopus 로고
    • Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration
    • 2778756 10.1016/j.ijengsci.2010.04.010
    • W. Xia L. Wang L. Yin 2010 Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration Int. J. Eng. Sci. 48 2044 2053 2778756 10.1016/j.ijengsci.2010.04.010
    • (2010) Int. J. Eng. Sci. , vol.48 , pp. 2044-2053
    • Xia, W.1    Wang, L.2    Yin, L.3
  • 15
    • 78649635287 scopus 로고    scopus 로고
    • A nonlinear Timoshenko beam formulation based on the modified couple stress theory
    • 2778746 10.1016/j.ijengsci.2010.09.025
    • M. Asghari M.H. Kahrobaiyan M.T. Ahmadian 2010 A nonlinear Timoshenko beam formulation based on the modified couple stress theory Int. J. Eng. Sci. 48 1749 1761 2778746 10.1016/j.ijengsci.2010.09.025
    • (2010) Int. J. Eng. Sci. , vol.48 , pp. 1749-1761
    • Asghari, M.1    Kahrobaiyan, M.H.2    Ahmadian, M.T.3
  • 16
    • 80054951548 scopus 로고    scopus 로고
    • Nonlinear free vibration of size-dependent functionally graded microbeams
    • doi: 10.1016/j.ijengsci.2010.12.008
    • Ke, L.L.; Wang, Y.S.; Yang, J.; Kitipornchai, S.: Nonlinear free vibration of size-dependent functionally graded microbeams. Int. J. Engng. Sci. (2011) doi: 10.1016/j.ijengsci.2010.12.008
    • (2011) Int. J. Engng. Sci.
    • Ke, L.L.1    Wang, Y.S.2    Yang, J.3    Kitipornchai, S.4
  • 17
    • 79951512853 scopus 로고    scopus 로고
    • Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory
    • 10.1016/j.compstruct.2010.09.008
    • L.L. Ke Y.S. Wang 2011 Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory Compos. Struct. 93 342 350 10.1016/j.compstruct.2010.09.008
    • (2011) Compos. Struct. , vol.93 , pp. 342-350
    • Ke, L.L.1    Wang, Y.S.2
  • 18
    • 0032206622 scopus 로고    scopus 로고
    • Bending of marble with intrinsic length scales: A gradient theory with surface energy and size effects
    • I. Vardoulakis G. Exadaktylos S.K. Kourkoulis 1998 Bending of marble with intrinsic length scales: a gradient theory with surface energy and size effects J. de Phys. IV 8 399 406
    • (1998) J. de Phys. IV , vol.8 , pp. 399-406
    • Vardoulakis, I.1    Exadaktylos, G.2    Kourkoulis, S.K.3
  • 21
    • 60449092814 scopus 로고    scopus 로고
    • Static and dynamic analysis of microbeams based on strain gradient elasticity theory
    • 2503148 1213.74190 10.1016/j.ijengsci.2008.08.008
    • S.L. Kong S.J. Zhou Z.F. Nie K. Wang 2009 Static and dynamic analysis of microbeams based on strain gradient elasticity theory Int. J. Eng. Sci. 47 487 498 2503148 1213.74190 10.1016/j.ijengsci.2008.08.008
    • (2009) Int. J. Eng. Sci. , vol.47 , pp. 487-498
    • Kong, S.L.1    Zhou, S.J.2    Nie, Z.F.3    Wang, K.4
  • 22
    • 0038721068 scopus 로고    scopus 로고
    • Experiments and theory in strain gradient elasticity
    • 1077.74517 10.1016/S0022-5096(03)00053-X
    • D.C.C. Lam F. Yang A.C.M. Chong 2003 Experiments and theory in strain gradient elasticity J. Mech. Phys. Solids 51 1477 1508 1077.74517 10.1016/S0022-5096(03)00053-X
    • (2003) J. Mech. Phys. Solids , vol.51 , pp. 1477-1508
    • Lam, D.C.C.1    Yang, F.2    Chong, A.C.M.3
  • 23
    • 77955328833 scopus 로고    scopus 로고
    • A micro scale Timoshenko beam model based on strain gradient elasticity theory
    • 10.1016/j.euromechsol.2009.12.005
    • B. Wang J. Zhao S. Zhou 2010 A micro scale Timoshenko beam model based on strain gradient elasticity theory Eur. J. Mech. A/Solids 29 591 599 10.1016/j.euromechsol.2009.12.005
    • (2010) Eur. J. Mech. A/Solids , vol.29 , pp. 591-599
    • Wang, B.1    Zhao, J.2    Zhou, S.3
  • 25
    • 77955470363 scopus 로고    scopus 로고
    • Bending and buckling of thin strain gradient elastic beams
    • 10.1016/j.euromechsol.2010.04.001
    • K.A. Lazopoulos A.K. Lazopoulos 2010 Bending and buckling of thin strain gradient elastic beams Eur. J. Mech. A/Solids 29 837 843 10.1016/j.euromechsol. 2010.04.001
    • (2010) Eur. J. Mech. A/Solids , vol.29 , pp. 837-843
    • Lazopoulos, K.A.1    Lazopoulos, A.K.2
  • 26
    • 0001906239 scopus 로고
    • Cahier du Groupe Francais d'Etudes de Rheologie C.N.R.S. VI, 31-37
    • Casal, P.: La capillarite interne. Cahier du Groupe Francais d'Etudes de Rheologie C.N.R.S. VI, 31-37 (1961)
    • (1961) La Capillarite Interne
    • Casal, P.1
  • 27
    • 0003340614 scopus 로고
    • Capillarite interne en mecanique
    • 0114.15802
    • P. Casal 1963 Capillarite interne en mecanique C.R. Acad. Sci. 256 3820 3822 0114.15802
    • (1963) C.R. Acad. Sci. , vol.256 , pp. 3820-3822
    • Casal, P.1
  • 28
    • 0000823809 scopus 로고
    • La theorie du second gradient et la capillarite
    • 297213 0286.76004
    • P. Casal 1972 La theorie du second gradient et la capillarite C.R. Acad. Sci. 274 1571 1574 297213 0286.76004
    • (1972) C.R. Acad. Sci. , vol.274 , pp. 1571-1574
    • Casal, P.1
  • 29
    • 0030414078 scopus 로고    scopus 로고
    • Gradient elasticity with surface energy: Mode-III crack problem
    • DOI 10.1016/0020-7683(95)00277-4
    • I. Vardoulakis G. Exadaktylos E. Aifantis 1996 Gradient elasticity with surface energy: mode-III crack problem Int. J. Solids Struct. 33 4531 4559 0919.73237 10.1016/0020-7683(95)00277-4 (Pubitemid 126382853)
    • (1996) International Journal of Solids and Structures , vol.33 , Issue.30 , pp. 4531-4559
    • Vardoulakis, I.1    Exadaktylos, G.2    Aifantis, E.3
  • 31
    • 0034901777 scopus 로고    scopus 로고
    • Microstructure in linear elasticity and scale effects: A reconsideration of basic rock mechanics and rock fracture mechanics
    • DOI 10.1016/S0040-1951(01)00047-6, PII S0040195101000476
    • G.E. Exadaktylos I. Vardoulakis 2001 Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics Tectonophysics 335 81 109 10.1016/S0040-1951(01)00047-6 (Pubitemid 32719335)
    • (2001) Tectonophysics , vol.335 , Issue.1-2 , pp. 81-109
    • Exadaktylos, G.E.1    Vardoulakis, I.2
  • 32
    • 0040366845 scopus 로고
    • Microstructure in linear elasticity
    • 160356 0119.40302 10.1007/BF00248490
    • R.D. Mindlin 1964 Microstructure in linear elasticity Arch. Ration. Mech. Anal. 16 51 78 160356 0119.40302 10.1007/BF00248490
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , pp. 51-78
    • Mindlin, R.D.1
  • 34
    • 0036809397 scopus 로고    scopus 로고
    • Static and dynamic analysis of a gradient-elastic bar in tension
    • DOI 10.1007/s00419-002-0231-z
    • K. Tsepoura S. Papargyri-Beskou D. Polyzos D.E. Beskos 2002 Static and dynamic analysis of gradient elastic bars in tension Arch. Appl. Mech. 72 483 497 1053.74028 10.1007/s00419-002-0231-z (Pubitemid 35354516)
    • (2002) Archive of Applied Mechanics , vol.72 , Issue.6-7 , pp. 483-497
    • Tsepoura, K.G.1    Papargyri-Beskou, S.2    Polyzos, D.3    Beskos, D.E.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.