EXAMPLE 1. Lateral Buckling of a Circular Annular Plate under Uniform Shearing Forces Applied at its Edges

1.1 Description of the Test A circular annular plate is subjected to a uniform shearing forces applied at its edges. Plate

geometric and material properties are shown in Fig. 1.1a.

Note: Effect of uniform shearing forces applied on plate edges is reproduced in finite element

analysis by applying a drilling moment ZM at the master node located at centroid of the

plate (origin of the coordinate axes). All six DOFs of the nodes located on internal edge

of the plate are connected by rigid body link to master node.

1.2 ComparisonoftheResults

According to Dean [1], for the annular plate with material and geometric properties, illustrated in

Fig. 1.1a, the analytical solution of critical moment crM is defined by the following value:

crM = 230,500 kNm

Finite element solution of crM is computed for a regular mesh 1060 (see Fig. 1.1b), using 4-

node quadrilateral shell FE with drilling DOF, and is reported in Table 1. The obtained results

are compared with target solution reported in Dean [1].

Table 1 Comparison of the Critical Moment crM for a Circular Annular Plate under Uniform Shearing Forces

FE Type Dean [1] MIDAS/Civil SAP2000

Thin Shell 240,015.5 240,015.5

Thick Shell 230,500

230,500.0 230,500.0

Geometric properties: Material properties: Ro = 5.0 m E = 2.1108 kN/m2 Ri = 2.5 m = 0.3 t = 0.1 m

a) General View

Figure 1.1 Circular Annular Plate Subjected to Uniform Sheering Forces (Continued)

b) Finite Element Model

Figure 1.1 Circular Annular Plate Subjected to Uniform Sheering Forces

Mode 1

Mode 3 Figure 1.2 Different Modes of Buckled Shapes

1.3 References

1. Dean, W. R., (1924). The Elastic Stability of an Annular Plate, Proc. Royal Society of London. Series A, Papers of a Mathematical and Physical Character, Vol. 106, No. 737, 268-284