L11: Circular Plate with a Hole Static Analysis

A circular plate with a center hole is built-in along the inner edge (i.e. fixed). The plate is subjected to bending by a moment applied along the outer edge. Determine the maximum deflection and slope of the plate. Also determine the moment and stresses near the inner and outer edges.

The circular plate is axisymmetric and only a small sector of the complete plate is needed for the analysis. We will use a 10 degree segment for approximating the circular boundary with a straight edge.

The model has 14 joints and 6 plate elements. The joints are numbered from 1 to 7 and 11 to 17. The joints 8 to 10 are not used. The plate elements are 4-node elements.

The uniform moment of 10 in-lb/in is equivalent to a total moment of 52.3598 in-lb for the 10 degree segment. The moment is applied at joints 7 and 17 as joint loads with magnitude of

My = -26.1799387 (at joints 7 and 17)

Linear static analysis with one (1) load case is performed.

Modulus of Elasticity = 30,000,000 psi

Poisson's Ratio = 0.30

Shear Modulus = 11,538,461 psi

Plate Thickness = 0.25 inches

Radius (inner) = 10 inches

Radius (outer) = 30 inches

The model is defined using cylindrical coordinates with R, Q and Z. The joints 1 to 7 are at Q = -5 degrees and 11 to 17 are at Q = +5 degrees. The joint displacement directions are also defined in cylindrical R, Q and Z directions.

In LARSA, the bending moments are computed at the center of the plate elements.

Tested Features

Sources

Timoshenko, S.,"Strength of Materials, Part II", 3rd Edition, D. Van Nostrand Co., Inc., New York, p. 111.
LARSA 4D