The Schwarz Inequality and the Schwarz Formula for A-Analytic Functions

In this paper, we study A-analytic functions. We consider main fundamental theorems of the theory of A-analytic functions and prove analogs of the Schwarz inequality, the Schwars formula, and the Poisson formula for A-analytic functions.

Stress analysis of an unsymmetric composite plate with variance of oval-shaped cutout

The complex variable method is used to obtain a solution for stress distribution around cutout of oval shape (and its variance) in an infinite plate having un-symmetric material properties with respect to mid plane. The mapping function used is for an oval shape but, using a different shape and size, a constant oval shape of different size as well as shapes such as a circle, ellipse, square, rectangle and eye are obtained. The stress functions are explicitly solved by incorporating the condition of single-valuedness of the out-of-plane displacement and the Schwarz formula along the hole boundary. The effects of the geometry, stacking sequence, material properties and loading angle on stresses and moments around a hole are studied. Some of the results are compared with existing literature and found to be in close agreement.