Finite element solutions for nonhomogeneous nonlocal elastic problems

Mechanics Research Communications

Volumn 36, Issue 7, 2009, Pages 755-761

  Pisano, Aurora A ^a   Sofi, Alba ^a   Fuschi, Paolo ^a  

^a UNIVERSITY MEDITERRANEA OF REGGIO CALABRIA   (Italy)

Author keywords

2D mechanical problems; Nonhomogeneous nonlocal elasticity; Nonlocal finite elements

Indexed keywords

2D MECHANICAL PROBLEMS; ELASTIC MODELS; ELASTIC PROBLEMS; FINITE ELEMENT PROCEDURE; FINITE ELEMENT SOLUTION; NON-HOMOGENEOUS; NON-LOCAL FINITE ELEMENT METHOD; NONHOMOGENEOUS NONLOCAL ELASTICITY; NONLOCAL; NONLOCAL FINITE ELEMENTS; NONLOCAL OPERATOR; NUMERICAL PROCEDURES;

ELASTICITY;

FINITE ELEMENT METHOD;

EID: 68149103279     PISSN: 00936413     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechrescom.2009.06.003     Document Type: Article

References (26)

1. Adali S. Variational principles for multi-walled carbon nanotubes undergoing buckling based o nonlocal elasticity theory. Physics Letters A 372 (2008) 5701-5705
2. Aifantis E.C. Update on a class of gradient theories. Mechanica Materialia 35 (2003) 259-280
3. Aifantis E.C. Exploring the applicability of gradient elasticity to certain micro/nano reliability problems. Microsystem Technologies 15 (2009) 109-115
4. Chen Y., Lee J.D., and Eskandarian A. Atomistic viewpoint of the applicability of microcontinuum theories. International Journal of Solids and Structures 41 (2004) 2085-2097
5. Ece M.C., and Aydogdu M. Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes. Acta Mechanica 190 (2007) 185-195
6. Edelen D.G.B. Nonlocal field theory. In: Eringen A.C. (Ed). Continuum Physics vol. 4 (1976), Academic Press, New York 75-204
7. Emmrich E., and Weckner O. Analysis and numerical approximation of an integro-differential equation modeling non-local effects in linear elasticity. Mathematics and Mechanics of Solids 12 (2007) 363-384
8. Eringen A.C., and Kim B.S. Stress concentration at the tip of a crack. Mechanics Research Communications 1 (1974) 233-237
9. Eringen A.C. Nonlocal Continuum Field Theories (2001), Springer, New York
10. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiments. Acta Metallurgica Materialia 42 (1994) 475-487
11. Heireche H., Tounsi A., Benzair A., Maachon M., and Adda Beida E.A. Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity. Physica E 40 (2008) 2791-2799
12. Kunin I.A. Elastic Media with Microstructure vol. I (1982), Springer-Verlag, Berlin
13. Kröner E. Elasticity theory of materials with long range cohesive forces. International Journal of Solids and Structures 3 (1967) 731-742
14. Lazar M., Maugin G.A., and Aifantis E.C. On a theory of nonlocal elasticity of bi-Helmholtz type and some applications. International Journal of Solids and Structures 43 (2006) 1404-1421
15. Mathematica5, 2003. Wolfram Research Inc.
16. Peddieson J., Buchanan G.R., and McNitt R.P. Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science 41 (2003) 305-312
17. Pisano A.A., and Fuschi P. Closed form solution for a nonlocal elastic bar in tension. International Journal of Solids and Structures 41 (2003) 13-23
18. Polizzotto C. Nonlocal elasticity and related variational principles. International Journal of Solids and Structures 38 (2001) 7359-7380
19. Polizzotto C. Unified thermodynamic framework for nonlocal/gradient continuum theories. European Journal of Mechanics A/Solids 22 (2003) 651-668
20. Polizzotto C., Fuschi P., and Pisano A.A. A nonhomogeneous nonlocal elasticity model. European Journal of Mechanics A/Solids 25 (2006) 308-333
21. Rogula D. Introduction to nonlocal theory of material media. Nonlocal Theory of Material Media (1982), Springer-Verlag, Berlin 125-222
22. Silling S.A. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of Mechanics and Physics of Solids 48 (2000) 175-209
23. Silling S.A., Zimmermann M., and Abeyaratne R. Deformation of a peridynamic bar. Journal of Elasticity 73 (2003) 173-190
24. Sofi, A., Pisano, A.A., Fuschi, P., 2008. A 2D FE approach for nonlocal elastic problems. In: CD-Rom Proceedings if the eighth World Congress on Computational Mechanics, WCCM8, Venice, Italy.
25. Zhang Y.Q., Lin G.R., and Xie X.Y. Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity. Physics Review B 781 (2005) L95404
26. Zhou Z.G., and Wang B. Investigation of the interaction of two collinear cracks in anisotropic elasticity materials by means of the nonlocal theory. International Journal of Engineering Science 43 (2005) 1107-1120