标题： 优化各向异性层合板的负泊松比行为 显示英文标题

标题： Optimizing the auxetic behavior of anisotropic laminates

摘要： 具有至少某些方向上负泊松比的各向异性层合板称为 auxetic。 在本文中，我们考虑优化正交各向异性层合板的 auxetic 性能的条件，即：对于由给定材料组成的层合板，(i) 如何获得最低，即最高的负泊松比，以及 (ii) 如何最大化 auxetic 区域，即泊松比为负的方向集合。 结果表明，在这两种情况下，最优解出现在可行域的边界上，并且特别是可以通过使用相同层的角铺设序列来获得。 采用无量纲模量的极坐标方法来表示层合板的各向异性行为，这一方面可以降低问题的维度，另一方面可以通过无量纲不变量来有效表示各向异性。 显示英文摘要

摘要： Anisotropic laminates with a negative Poisson's ratio for at least some directions are called auxetic. In this paper, we consider the conditions for optimizing the auxeticity of an orthotropic laminate, namely: for a laminate composed by a given material, (i) how to obtain the lowest, i.e. the highest negative, Poisson's ratio and (ii) how to maximize the auxetic zone, i.e. the set of directions where the Poisson's ratio is negative. It is shown that in both the cases the optimal solution is found on the boundary of the feasible domain and in particular that it can be obtained using angle-ply sequences of identical layers. The polar method with dimensionless moduli is employed for representing the anisotropic behavior of the laminate, which allows, on the one hand, to reduce the dimensionality of the problem and, on the other hand, to have an effective mathematical representation of anisotropy by dimensionless invariants.