Abstract EN:

In this thesis we deal with the problem of determining the best distribution of the anisotropy for a laminated structure that has to be simultaneously the stiffest and the strongest one. The work has been divided into three main parts. In the first part we presented all the concepts and tools that we have used to develop the research. In the second part we have proposed a tensor invariant formulation, through the polar method, of different polynomial failure criteria for orthotropic sheets. Then, we considered the problem of determining the optimal material orientation to maximise strength by the minimisation of the failure index. The last part of the thesis is dedicated to the development of a new strategy to optimise simultaneously the stiffness and strength of a laminated structure. Our approach is inspired from an already existing hierarchical strategy for the only stiffness maximisation. First of all we defined a new laminate level failure criterion valid for an equivalent homogenised plate. Then, conscious of having two functional, the complementary energy and the laminate failure index, to be minimised at the same time, we proved that the first step of the strategy can be stated as two problems characterised by two functional that are sequentially minimised, preserving only the orthotropy direction. In the first step of the strategy we developed three different algorithms to determine the optimal distribution of material parameters for a given structure. Finally we dealt with the problem of determining the laminate stacking sequence satisfying the optimal distribution of material parameters issued from the first step of the hierarchical strategy.