Finite Element Method with Applications in Engineering

6.5 ONE-DIMENSIONAL TORSION OF A CIRCULAR SHAFT

The one-dimensional torsional elements can be used to analyse an assemblage of circular shafts. Procedure is explained in the following steps.

Step 1: Select element type

A two-node torsion element is shown in Figure 6.17(a). The T₁ and T₂ are the torques at nodes 1 and 2, respectively, whereas ø₁ and ø₂ are angular rotations at nodes 1 and 2, respectively, of the element. The sign convention is shown in the Figure 6.17(a).

 

 

Figure 6.17a One-dimensional torsion element

 

Step 2: Select approximation function

Let the rotation about x-axis at a section located at distance x units from node 1 ...