Overview

Test Case

A cantilever beam of length L, height h, and width w is bent by a force F applied at the free end. Modeling the beam using SHELL281 shell elements having four layers of identical material properties and thickness, determine the shear stress distribution through the beam thickness and the maximum Tsai-Wu failure criterion. The normal and shear failure stresses are σ_xf and σ_xyf respectively.

Figure 109: Cantilever Beam Problem Sketch

Analysis Assumptions and Modeling Notes

Poisson's ratio is set to zero to model the narrow beam assumption. The failure stresses are input in the nonlinear material property table (TB commands). Compression values are allowed to default to negative tension values and arbitrary values are assigned to failure stresses in the Y and Z directions. The target solution for the maximum Tsai-Wu failure criterion (FC3) is obtained from equation 2–92 of the Mechanical APDL Theory Reference). Since σ_y = σ_z = σ_xy = σ_yx = 0, most terms vanish and the equation reduces to:

By substituting relations for σ_xz (from S. Timoshenko, J. N. Goodier, Theory of Elasticity), it can be shown that σ_x and FC3 has a maximum value at the middle plane and:

POST1 is used to find the maximum value of the Tsai-Wu failure criterion (FCMX).

Results Comparison

Poisson's ratio is set to zero to model the narrow beam assumption. The failure stresses are input in the nonlinear material property table (TB commands). Compression values are allowed to default to negative tension values and arbitrary.