A proof of the convexity of the set of lamination parameters

TL;DR

This paper corrects a widely cited proof by demonstrating the convexity of lamination parameters set when the layup angle function is a step function, clarifying the mathematical properties of composite material design.

Contribution

It provides a valid proof of the convexity of lamination parameters set specifically for step function layup angles, rectifying previous inaccuracies.

Findings

Convexity holds for step function layup angles

Previous proof by Grenestedt and Gudmundson was incorrect

Clarifies mathematical properties of lamination parameters

Abstract

In this paper we show that the proof of the convexity of the set of lamination parameters given by J.L. Grenestedt and P. Gudmundson, which is extensively cited in the literature, is not correct. We give a proof of the convexity of this set when the class of functions which gives the layup angle as a function of the through-the-thickness coordinate is the set of step functions.