A new Kirchhoff plate model based on a modified couple stress theory

International Journal of Solids and Structures

Volumn 46, Issue 13, 2009, Pages 2757-2764

  Tsiatas, G C ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Couple stress elasticity; Gradient elasticity; Kirchhoff plate; Meshless methods; Method of fundamental solutions

Indexed keywords

COUPLE STRESS ELASTICITY; GRADIENT ELASTICITY; KIRCHHOFF PLATE; MESHLESS METHODS; METHOD OF FUNDAMENTAL SOLUTIONS;

BOUNDARY CONDITIONS; ELASTOHYDRODYNAMICS;

ELASTICITY;

EID: 65349137070     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2009.03.004     Document Type: Article

References (30)

1. 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
2. Askes H., and Aifantis E.C. Numerical modeling of size effects with gradient elasticity - Formulation, meshless discretization and example. Int. J. Fracture 117 (2002) 347-358
3. Bezine G. Boundary integral equations for plate flexure with arbitrary boundary conditions. Mech. Res. Commun. 5 (1978) 197-206
4. Dym C.L., and Shames J.H. Solid mechanics. A variational approach (1973), McGraw-Hill, New York
5. 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
6. Gao X.-L., and Park S.K. Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem. Int. J. Solids Struct. 44 (2007) 7486-7499
7. Karageorghis A., and Fairweather G. The method of fundamental solutions for the numerical solution of the biharmonic equation. J. Comput. Phys. 69 (1987) 434-459
8. Karageorghis A., and Fairweather G. The Almansi method of fundamental solutions for solving biharmonic problems. Int. J. Numer. Meth. Eng. 26 (1988) 1665-1682
9. Karageorghis A., and Fairweather G. The simple layer potential method of fundamental solutions for certain biharmonic problems. Int. J. Numer. Meth. Fluids 9 (1989) 1221-1234
10. Katsikadelis, J.T., 1982. The analysis of plates on elastic foundation by the boundary integral equation method. Ph. D. Thesis, Polytechnic Institute of New York.
11. Katsikadelis J.T. Boundary Elements: Theory and Applications (2002), Elsevier, Amsterdam-London
12. Katsikadelis J.T., and Armenakas A.E. New boundary equation solution to the plate problem. J. Appl. Mech.-T. ASME 56 (1989) 364-374
13. Kong S., Zhou S., Nie Z., and Wang K. The size-dependent natural frequency of Bernoulli-Euler micro-beams. Int. J. Eng. Sci. 46 (2008) 427-437
14. Koiter, W.T., 1964. Couple stresses in the theory of elasticity, I and II. In: Proc. K. Ned. Akad. Wet. (B) 67, pp. 17-44.
15. Lam D.C.C., Yang F., Chong A.C.M., Wang J., and Tong P. Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51 (2003) 1477-1508
16. Lazopoulos K.A. On the gradient strain elasticity theory of plates. Euro. J. Mech. A/Solids 23 (2004) 843-852
17. Li X., and Zhu J. The method of fundamental solutions for nonlinear elliptic problems. Eng. Anal. Bound. Elem. 33 (2009) 322-329
18. Ma H.M., Gao X.-L., and Reddy J.N. A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. J. Mech. Phys. Solids 56 (2008) 3379-3391
19. Mindlin R.D. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16 (1964) 51-78
20. Papargyri-Beskou S., and Beskos D.E. Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates. Arch. Appl. Mech. 78 (2008) 625-635
21. Park S.K., and Gao X.-L. Bernoulli-Euler beam model based on a modified couple stress theory. J. Micromech. Microeng. 16 (2006) 2355-2359
22. Park S.K., and Gao X.-L. Variational formulation of a modified couple stress theory and its application to a simple shear problem. Z. Angew. Math. Phys. 59 (2008) 904-917
23. Reddy J.N. Theory and Analysis of Elastic Plates (1999), Taylor and Francis, Philadelphia
24. Stern M. A general boundary integral formulation for the numerical solution of plate bending problems. Int. J. Solids Struct. 15 (1979) 769-782
25. Timoshenko S.P., and Woinowsky-Krieger S. Theory of Plates and Shells (1959), McGraw-Hill, New York
26. Timoshenko S.P., and Goodier J.N. Theory of Elasticity (1970), McGraw-Hill, New York
27. Tsepoura K., Papargyri-Beskou S., Polyzos D., and Beskos D.E. Static and dynamic analysis of gradient elastic bars in tension. Arch. Appl. Mech. 72 (2002) 483-497
28. Vardoulakis I., and Sulem J. Bifurcation Analysis in Geomechanics (1995), Blackie/Chapman and Hall, London
29. Yang F., Chong A.C.M., Lam D.C.C., and Tong P. Couple stress based strain gradient theory of elasticity. Int. J. Solids Struct. 39 (2002) 2731-2743
30. Zeb A., Ingham D.B., and Lesnic D. The method of fundamental solutions for a biharmonic inverse boundary determination problem. Comp. Mech. 42 (2008) 371-379