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Volumn 44, Issue 22-23, 2007, Pages 7486-7499

Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem

Author keywords

Displacement formulation; Elasticity; Lam 's solution; Length scale; Potential energy; Strain gradient theory; Thick walled cylinder; Variational method

Indexed keywords

MICROSTRUCTURE; POTENTIAL ENERGY; PROBLEM SOLVING; STRAIN; VARIATIONAL TECHNIQUES;

EID: 34548833808     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.04.022     Document Type: Article
Times cited : (245)

References (35)
  • 1
    • 0026473605 scopus 로고
    • On the structure of the mode III crack-tip in gradient elasticity
    • Altan B.S., and Aifantis E.C. On the structure of the mode III crack-tip in gradient elasticity. Scripta Met. 26 (1992) 319-324
    • (1992) Scripta Met. , vol.26 , pp. 319-324
    • Altan, B.S.1    Aifantis, E.C.2
  • 2
    • 0000616248 scopus 로고    scopus 로고
    • On some aspects in the special theory of gradient elasticity
    • Altan B.S., and Aifantis E.C. On some aspects in the special theory of gradient elasticity. J. Mech. Behav. Mater. 8 3 (1997) 231-282
    • (1997) J. Mech. Behav. Mater. , vol.8 , Issue.3 , pp. 231-282
    • Altan, B.S.1    Aifantis, E.C.2
  • 5
    • 0000823809 scopus 로고
    • La théorie du second gradient et la capillarité
    • Casal P. La théorie du second gradient et la capillarité. C.R. Acad. Sci. Paris A 274 (1972) 1571-1574
    • (1972) C.R. Acad. Sci. Paris A , vol.274 , pp. 1571-1574
    • Casal, P.1
  • 6
    • 0029357270 scopus 로고
    • Second-gradient constitutive theory for granular material with random packing structure
    • Chang C.S., and Gao J. Second-gradient constitutive theory for granular material with random packing structure. Int. J. Solids Struct. 32 (1995) 2279-2293
    • (1995) Int. J. Solids Struct. , vol.32 , pp. 2279-2293
    • Chang, C.S.1    Gao, J.2
  • 7
    • 0020821706 scopus 로고
    • On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves
    • Eringen A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54 (1983) 4703-4710
    • (1983) J. Appl. Phys. , vol.54 , pp. 4703-4710
    • Eringen, A.C.1
  • 8
    • 0032005044 scopus 로고    scopus 로고
    • Gradient elasticity with surface energy: mode-I crack problem
    • Exadaktylos G.E. Gradient elasticity with surface energy: mode-I crack problem. Int. J. Solids Struct. 35 (1998) 421-456
    • (1998) Int. J. Solids Struct. , vol.35 , pp. 421-456
    • Exadaktylos, G.E.1
  • 9
    • 0038800206 scopus 로고    scopus 로고
    • Some basic half-plane problems of the cohesive elasticity theory with surface energy
    • Exadaktylos G.E. Some basic half-plane problems of the cohesive elasticity theory with surface energy. Acta Mech. 133 (1999) 175-198
    • (1999) Acta Mech. , vol.133 , pp. 175-198
    • Exadaktylos, G.E.1
  • 10
    • 0032083716 scopus 로고    scopus 로고
    • Surface instability in gradient elasticity with surface energy
    • Exadaktylos G.E., and Vardoulakis I. Surface instability in gradient elasticity with surface energy. Int. J. Solids Struct. 35 (1998) 2251-2281
    • (1998) Int. J. Solids Struct. , vol.35 , pp. 2251-2281
    • Exadaktylos, G.E.1    Vardoulakis, I.2
  • 11
    • 0034901777 scopus 로고    scopus 로고
    • Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics
    • Exadaktylos G.E., and Vardoulakis I. Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics. Tectonophysics 335 (2001) 81-109
    • (2001) Tectonophysics , vol.335 , pp. 81-109
    • Exadaktylos, G.E.1    Vardoulakis, I.2
  • 12
    • 0141572204 scopus 로고    scopus 로고
    • Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory
    • Gao X.-L. Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory. Int. J. Solids Struct. 40 (2003) 6445-6455
    • (2003) Int. J. Solids Struct. , vol.40 , pp. 6445-6455
    • Gao, X.-L.1
  • 13
    • 0034746524 scopus 로고    scopus 로고
    • Variational solution for a cracked mosaic model of woven fabric composites
    • Gao X.-L., and Mall S. Variational solution for a cracked mosaic model of woven fabric composites. Int. J. Solids Struct. 38 (2001) 855-874
    • (2001) Int. J. Solids Struct. , vol.38 , pp. 855-874
    • Gao, X.-L.1    Mall, S.2
  • 14
    • 34548861938 scopus 로고    scopus 로고
    • Gao, X.-L. and Park, S.K., 2006. Supplemental notes on derivations (81 pages, available upon request).
  • 15
    • 0033908668 scopus 로고    scopus 로고
    • Hybrid method for stress analysis of finite three-dimensional elastic components
    • Gao X.-L., and Rowlands R.E. Hybrid method for stress analysis of finite three-dimensional elastic components. Int. J. Solids Struct. 37 (2000) 2727-2751
    • (2000) Int. J. Solids Struct. , vol.37 , pp. 2727-2751
    • Gao, X.-L.1    Rowlands, R.E.2
  • 16
    • 0003118069 scopus 로고
    • Experimental methods for study of Cosserat elastic solids and other generalized elastic continua
    • Mühlhaus H. (Ed), Wiley, New York
    • Lakes R. Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: Mühlhaus H. (Ed). Continuum Models for Materials with Micro-structure (1995), Wiley, New York 1-22
    • (1995) Continuum Models for Materials with Micro-structure , pp. 1-22
    • Lakes, R.1
  • 18
    • 12344301256 scopus 로고    scopus 로고
    • On the gradient strain elasticity theory of plates
    • Lazopoulos K.A. On the gradient strain elasticity theory of plates. Euro. J. Mech. A/Solids 23 (2004) 843-852
    • (2004) Euro. J. Mech. A/Solids , vol.23 , pp. 843-852
    • Lazopoulos, K.A.1
  • 19
    • 17144377182 scopus 로고    scopus 로고
    • Conservation laws of linear elasticity in stress formulations
    • Li S., Gupta A., and Markenscoff X. Conservation laws of linear elasticity in stress formulations. Proc. R. Soc. A 461 (2005) 99-116
    • (2005) Proc. R. Soc. A , vol.461 , pp. 99-116
    • Li, S.1    Gupta, A.2    Markenscoff, X.3
  • 20
    • 2342529880 scopus 로고    scopus 로고
    • Solution to line loading of a semi-infinite solid in gradient elasticity
    • Li S., Miskioglu I., and Altan B.S. Solution to line loading of a semi-infinite solid in gradient elasticity. Int. J. Solids Struct. 41 (2004) 3395-3410
    • (2004) Int. J. Solids Struct. , vol.41 , pp. 3395-3410
    • Li, S.1    Miskioglu, I.2    Altan, B.S.3
  • 22
    • 0040366845 scopus 로고
    • Micro-structure in linear elasticity
    • Mindlin R.D. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16 (1964) 51-78
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , pp. 51-78
    • Mindlin, R.D.1
  • 23
    • 0000095439 scopus 로고
    • Second gradient of strain and surface-tension in linear elasticity
    • Mindlin R.D. Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Struct. 1 (1965) 417-438
    • (1965) Int. J. Solids Struct. , vol.1 , pp. 417-438
    • Mindlin, R.D.1
  • 24
    • 0001357580 scopus 로고
    • On first strain-gradient theories in linear elasticity
    • Mindlin R.D., and Eshel N.N. On first strain-gradient theories in linear elasticity. Int. J. Solids Struct. 4 (1968) 109-124
    • (1968) Int. J. Solids Struct. , vol.4 , pp. 109-124
    • Mindlin, R.D.1    Eshel, N.N.2
  • 25
    • 33750597812 scopus 로고    scopus 로고
    • Bernoulli-Euler beam model based on a modified couple stress theory
    • Park S.K., and Gao X.-L. Bernoulli-Euler beam model based on a modified couple stress theory. J. Micromech. Microengr. 16 (2006) 2355-2359
    • (2006) J. Micromech. Microengr. , vol.16 , pp. 2355-2359
    • Park, S.K.1    Gao, X.-L.2
  • 26
    • 34548864562 scopus 로고    scopus 로고
    • Park, S.K., Gao, X.-L., 2007. Variational formulation of a modified couple stress theory and its application to a simple shear problem, Z. angew. Math. Phys. (in press).
  • 27
    • 33846993942 scopus 로고
    • Factorization of operators of second order linear homogeneous ordinary differential equations
    • Sandell D.C., and Stein F.M. Factorization of operators of second order linear homogeneous ordinary differential equations. The Two-Year College Math. J. 8 3 (1977) 132-141
    • (1977) The Two-Year College Math. J. , vol.8 , Issue.3 , pp. 132-141
    • Sandell, D.C.1    Stein, F.M.2
  • 28
    • 0022880338 scopus 로고
    • Proof of a conjecture in elastic membrane theory
    • Steigmann D.J. Proof of a conjecture in elastic membrane theory. ASME J. Appl. Mech. 53 (1986) 955-956
    • (1986) ASME J. Appl. Mech. , vol.53 , pp. 955-956
    • Steigmann, D.J.1
  • 29
    • 0026698362 scopus 로고
    • Equilibrium of prestressed networks
    • Steigmann D.J. Equilibrium of prestressed networks. IMA J. Appl. Math. 48 (1992) 195-215
    • (1992) IMA J. Appl. Math. , vol.48 , pp. 195-215
    • Steigmann, D.J.1
  • 31
    • 33744534266 scopus 로고    scopus 로고
    • An example of double forces taken from structural analysis
    • Vardoulakis I., and Giannakopoulos A.E. An example of double forces taken from structural analysis. Int. J. Solids Struct. 43 (2006) 4047-4062
    • (2006) Int. J. Solids Struct. , vol.43 , pp. 4047-4062
    • Vardoulakis, I.1    Giannakopoulos, A.E.2
  • 34
    • 84968520684 scopus 로고
    • Factorization of differential operators
    • Zettl A. Factorization of differential operators. Proc. Am. Math. Soc. 27 (1971) 425-426
    • (1971) Proc. Am. Math. Soc. , vol.27 , pp. 425-426
    • Zettl, A.1
  • 35
    • 13544263609 scopus 로고    scopus 로고
    • Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems
    • Zhang X., and Sharma P. Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems. Int. J. Solids Struct. 42 (2005) 3833-3851
    • (2005) Int. J. Solids Struct. , vol.42 , pp. 3833-3851
    • Zhang, X.1    Sharma, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.