Stress distribution in orthotropic plates with coupled elastic properties

Summary

If the roots of the characteristic equation of the governing differential equation for the stress function of an orthotropic plate under generalized plane stress conditions are equal classical solutions of anisotropic elasticity theory do not hold anymore. The general form of the stress function for such orthotropic materials is discussed and the exact solution is given for the plate with an elliptic opening loaded in tension.

Comparison of the stress distribution for the material with distinct characteristic roots indicated that in produces much higher stress concentrations than the model with equal roots. For the latter case solution of any boundary value problem may be obtained very easily through an existing solution for the isotropic material.

Given also that there are several problems involving stress concentrations in orthotropic plates as yet unsolved, the analysis presented here might be of considerable help in the, designing of the structure of composite laminates.