Buckling of plates including effect of shear deformations: a hyperelastic formulation

다국어 초록 (Multilingual Abstract)

Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

참고문헌 (Reference)

1 Fung, Y.C., "Thin-Shell Structures: Theory, Experiment, and Design" Prentice-Hall 1974

2 Reddy, J.N., "Theory and analysis of elastic plates and shells" CRC 2007

3 Ziegler, H., "The influence of inplane deformation on the buckling loads of isotropic elastic plates" 53 (53): 61-72, 1983

4 Matsunaga, H., "The application of a two-dimensional higher-order theory for the analysis of a thick elastic plate" 45 (45): 633-648, 1992

5 Reissner, E., "The Effect of Transverse Shear Deformation on the Bending of Elastic Plates" 12 : A-69-A-77, 1945

6 Taber, L.A., "On a theory for large elastic deformation of shells of revolution including torsion and thick-shell effects" 24 (24): 973-985, 1988

7 Stein, M., "Nonlinear theory for plates and shells including the effects of transverse shearing" 24 (24): 1537-1544, 1986

8 Reddy, J.N., "Non-linear bending of thick rectangular, laminated composite plates" 16 (16): 291-301, 1981

9 Vijayakumar, K., "Modified Kirchhoff's theory of plates including transverse shear deformations" 38 (38): 211-213, 2011

10 Attard, M.M., "Lateral buckling of beams with shear deformations-a hyperelastic formulation" 47 (47): 2825-2840, 2010

11 Mindlin, R.D., "Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic Elastic Plates" 18 : 31-38, 1951

12 Attard, M.M., "Hyperelastic constitutive modeling under finite strain" 41 (41): 5327-5350, 2004

13 Murty, A.V.K., "High-order theory of homogeneous plate flexure" 26 (26): 719-725, 1988

14 Attard, M.M., "Column buckling with shear deformations-a hyperelastic formulation" 45 (45): 4322-4339, 2008

15 Shariat, B.A.S., "Buckling of thick functionally graded plates under mechanical and thermal loads" 78 (78): 433-439, 2007

16 Di Sciuva, M., "Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model" 105 (105): 425-442, 1986

17 Thai, H.T., "Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates" 54 (54): 269-276, 2012

18 Reddy, J.N., "A refined nonlinear theory of plates with transverse shear deformation" 20 (20): 881-896, 1984

19 Mantari, J.L., "A new higher order shear deformation theory for sandwich and composite laminated plates" 43 (43): 1489-1499, 2012

20 Reddy, J.N., "A general non-linear third-order theory of plates with moderate thickness" 25 (25): 677-686, 1990