Cantilever under Distributed Load Using Skew Systems (Plane Stress)

Objective

To verify the plane stress element subjected to distributed loading and when employing skew coordinate systems.

Physical Problem

A cantilever beam of rectangular cross-section is subjected to a triangular distributed load, see Fig. A.14.

Finite Element Model

Ten 8-node finite elements are employed. The upper face of the elements is acted upon by a linearly varying pressure load. The model is inclined in the global coordinate system.

Solution Results

Using beam theory the theoretical solution for the end displacement is:

The axial stress is evaluated in the element closest to the fixed end at the top surface stress point.

User Hints

• The exact displacement solution according to beam theory for a linearly varying distributed load contains the 5th power of the coordinate. Several 8-node (parabolic) elements are therefore used to obtain a good approximation to the analytical solution.