A note on the computation of the extrema of Young’s modulus for hexagonal materials: An approach by planar tensor invariants

Abstract

A simple method to obtain the highest and lowest Young's modulus for a material of the hexagonal class is presented. It is based upon the use of tensor invariants of plane anisotropic elasticity; in fact, the cylindrical symmetry of the elastic tensor allows for transforming the 3D original problem into a planar one, with a considerable simplification.

Anisotropy and Shape Optimal Design of Shells by the Polar–Isogeometric Approach

“…The polar formalism has successfully been applied to several different optimization problems concerning laminated structures, [6][7][8][9][10][11][12][13][14][15][16][42][43][44][45][46][47][48] as well as to some theoretical problems, [40,41,[49][50][51][52][53][54][55][56][57].…”

“…, p = {p i } i∈Iγ ∈ R 3×n and (52), (53) hold}. (56) As well as the polar parameters moduli R K 0 and R 1 , the orthotropy angle is assumed to be parameterized as a B-spline function of given knot vectors and degrees which can be chosen arbitrarily of the ones of R K 0 and R 1 .…”