Convex or non-convex? On the nature of the feasible domain of laminates

Abstract

This work investigates two aspects linked to the nature of the feasible domain of anisotropic laminates. In the first part of the paper, proofs are given on the non-convexity of the feasible domain for full anisotropic and for membrane-orthotropic laminates, either in the lamination parameters space or in the polar parameters one. Then, adopting the polar formalism, some particular cases are studied, providing analytical expressions of new narrower bounds, in terms of polar parameters of the membrane stiffness tensor. For a particular case, the exact expression of the membrane stiffness tensor feasible domain is determined. In the second part of the paper, a discussion on the necessary and sufficient condition to get membrane/bending uncoupled and/or homogeneous laminates is presented. It is proved that, when the distinct orientations within the stack are two, quasi-triviality represents a necessary and sufficient condition to achieve uncoupling and/or quasi-homogeneity. This work disproves the common belief of the convexity of the feasible domain in the lamination parameters space and fosters new ideas to face the problem of the determination of the feasible domain of laminates.