Keywords: buckling, plates, three-node element.

Three-node plate/shell elements are essential for modelling any complex geometry. Depending on the boundary conditions, load applications and material properties, plate structures may behave according to the classical plate theory - thin plates [1], the first order shear deformation theory - moderately thick plates [2,3], or higher order shear deformation theory - thick plates [4]. Therefore, a general simplified element is required that would respond to all of the above categories. However, the present paper addresses a general element suitable for the thin to moderately thick plate configurations. Triangular elements developed based on the first order shear deformation and conventional full integration schemes show locking effects for high span-to-thickness ratios. Corrective measures have been obtained in various forms to diminish the locking effects.

Strain-displacement relations following the theory of Reissner [2] and Mindlin [3] can be expressed as

where and are curvature and shear strain vectors, respectively.

To improve the state of affairs in thin range the following is suggested for the transverse shear strains:

A full integration scheme is used. The full assembled matrices are linked with IMSL to solve eigen-value and eigen-vector problems.

The following example problem is considered to study critical buckling temperature and mode shapes: All edge clamped skew plates (skew angle = 45 degree), =1, =10 and 100, =204GPa, =0.3, and . For the sake of convenience the following is defined: .

The shell element SHELL43 - Plastic Shell of ANSYS [5] and the shell element CTRIA3 of NASTRAN [6] are considered to compare the present results.

A three-node plate element with full integration scheme has been developed using shear deformation theory of Reissner/Mindlin suitable for moderately thick and thin configurations. The shear locking effects are nullified using shear correction terms in the transverse shear strain components. Critical thermal temperature and mode shapes are studied. The element shows well performance in moderately thick and thin range. The present solution agrees more close to NASTRAN than ANSYS in thin and thick range.

1

P.L. Gould, "Analysis of Shells and Plates, Chapter 8 in Bending of Plates", Springer-Verlag, New York, USA, 1988.

2

E. Reissner, "The effect of transverse shear deformation on the bending of elastic plates," J. Math. Phy, 22, 69-76,1945.

3

R.D. Mindlin, "Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates", J. Appl. Mech ; 18, 31-38,1951.

4

J.N. Reddy and N.D. Phan, "Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory," Journal of Sound and Vibration, 98, 157-170,1985. doi:10.1016/0022-460X(85)90383-9

5

ANSYS Version 5.6, Canonsburg, PA, 1999.

6

MSC/NASTRAN Version 70.7, Macneal-Schwendler Corporation, CA, 2000.

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