Refined Buckling Analysis of Rectangular Plates Under Uniaxial and Biaxial Compression
In the traditional buckling analysis of rectangular
plates the classical thin plate theory is generally applied, so
neglecting the plating shear deformation. It seems quite clear that this
method is not totally appropriate for the analysis of thick plates, so
that in the following the two variable refined plate theory proposed
by Shimpi (2006), that permits to take into account the transverse
shear effects, is applied for the buckling analysis of simply supported
isotropic rectangular plates, compressed in one and two orthogonal
directions.
The relevant results are compared with the classical ones and, for
rectangular plates under uniaxial compression, a new direct
expression, similar to the classical Bryan-s formula, is proposed for
the Euler buckling stress.
As the buckling analysis is a widely diffused topic for a variety of
structures, such as ship ones, some applications for plates uniformly
compressed in one and two orthogonal directions are presented and
the relevant theoretical results are compared with those ones obtained
by a FEM analysis, carried out by ANSYS, to show the feasibility of
the presented method.
[1] S. Timoshenko, J. Gere, Theory of Elastic Stability, McGraw-Hill
International Book Company, 17th edition, 1985.
[2] R.P. Shimpi and H.G. Patel, "A two variable refined plate theory for
orthotropic plate analysis", International Journal of Solid and
Structures (43), pp. 6783-6799, 2006.
[3] H. Tai, S. Kim, J. Lee, "Buckling analysis of plates using two
variable refined plate theory", Proceedings of Pacific Structural Steel
Conference 2007, Steel Structures in Natural Hazards, Wairakei,
New Zeland, 13-16 March, 2007.
[4] S. Timoshenko, N. Goodier, Theory of Elasticity, McGraw-Hill
International Book Company, 1951.
[5] O. Hughes, Ship Structural Design: a Rationally-Based Computer-
Aided Optimization Approach, SNAME Edition, 1988.
[6] RINA Rules, 2010.
[7] E. Reissner, "The effect of transverse shear deformation on the
bending of elastic plates", Journal of Applied Mechanics Vol. 12
(Transactions ASME 67), pp. 69-77, 1945;
[8] R.D. Mindlin, "Influence of rotary inertia and shear on flexural
motions of isotropic, elastic plates ", Journal of Applied Mechanics
Vol. 18 (Transactions ASME 73), pp. 31-38, 1951;
[9] M. Levinson, "An accurate simple theory of the statics and dynamics
of elastic plates", Mechanics Research Communications Vol. 7, pp.
343-350, 1980;
[10] J.N. Reddy, "A refined non linear theory of plates with transverse
shear deformation", International Journal of Solid and Structures
Vol. 20, pp.881-896, 1984.
[1] S. Timoshenko, J. Gere, Theory of Elastic Stability, McGraw-Hill
International Book Company, 17th edition, 1985.
[2] R.P. Shimpi and H.G. Patel, "A two variable refined plate theory for
orthotropic plate analysis", International Journal of Solid and
Structures (43), pp. 6783-6799, 2006.
[3] H. Tai, S. Kim, J. Lee, "Buckling analysis of plates using two
variable refined plate theory", Proceedings of Pacific Structural Steel
Conference 2007, Steel Structures in Natural Hazards, Wairakei,
New Zeland, 13-16 March, 2007.
[4] S. Timoshenko, N. Goodier, Theory of Elasticity, McGraw-Hill
International Book Company, 1951.
[5] O. Hughes, Ship Structural Design: a Rationally-Based Computer-
Aided Optimization Approach, SNAME Edition, 1988.
[6] RINA Rules, 2010.
[7] E. Reissner, "The effect of transverse shear deformation on the
bending of elastic plates", Journal of Applied Mechanics Vol. 12
(Transactions ASME 67), pp. 69-77, 1945;
[8] R.D. Mindlin, "Influence of rotary inertia and shear on flexural
motions of isotropic, elastic plates ", Journal of Applied Mechanics
Vol. 18 (Transactions ASME 73), pp. 31-38, 1951;
[9] M. Levinson, "An accurate simple theory of the statics and dynamics
of elastic plates", Mechanics Research Communications Vol. 7, pp.
343-350, 1980;
[10] J.N. Reddy, "A refined non linear theory of plates with transverse
shear deformation", International Journal of Solid and Structures
Vol. 20, pp.881-896, 1984.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:61096", author = "V. Piscopo", title = "Refined Buckling Analysis of Rectangular Plates Under Uniaxial and Biaxial Compression", abstract = "In the traditional buckling analysis of rectangular
plates the classical thin plate theory is generally applied, so
neglecting the plating shear deformation. It seems quite clear that this
method is not totally appropriate for the analysis of thick plates, so
that in the following the two variable refined plate theory proposed
by Shimpi (2006), that permits to take into account the transverse
shear effects, is applied for the buckling analysis of simply supported
isotropic rectangular plates, compressed in one and two orthogonal
directions.
The relevant results are compared with the classical ones and, for
rectangular plates under uniaxial compression, a new direct
expression, similar to the classical Bryan-s formula, is proposed for
the Euler buckling stress.
As the buckling analysis is a widely diffused topic for a variety of
structures, such as ship ones, some applications for plates uniformly
compressed in one and two orthogonal directions are presented and
the relevant theoretical results are compared with those ones obtained
by a FEM analysis, carried out by ANSYS, to show the feasibility of
the presented method.", keywords = "Buckling analysis, Thick plates, Biaxial stresses", volume = "4", number = "10", pages = "1090-8", }