Curved Beam Under Out-of-Plane Load, Iso-Beam Elements

Objective

To verify the three-dimensional action of curved iso-beam elements including torsion.

Physical Problem

Fig. A.11 shows the curved beam to be analyzed. The beam is relatively slender and fixed at one end. The other end is loaded by a concentrated force in the out-of-plane direction.

Finite Element Model

Six 3-node iso-beam elements are used to approximate the 90-degree circular bend.

Solution Results

The theoretical tip displacement in the direction of the force, torsional moment Mtor and bending moment Mb are ([1], p. 412): 

User Hints

•  Torsional effects are very important in this example. The iso-beam element contains special displacement assumptions for torsional behavior and the element performs very well.
•  The constant curvature of the circular bend is only approximated by the 3-node (parabolic) isoparametric beam elements. Since six elements are used for the bend the solution still agrees very well with the exact solution. 

Referance