• optimization;
  • classical linear elasticity;
  • composite materials;
  • anisotropy;
  • polar method;
  • laminates;
  • strength criteria

The strength optimisation of orthotropic materials is an open problem. The majority of the studies conducted on strength optimisation of anisotropic materials have been performed with the help of a phenomenological failure criterion that describe the conditions to obtain a limit state identified with the ultimate strength of the material. This paper is a study concerning the bidimensional linear case. Our approach concerns the formulation of a failure criterion through tensors invariants, in order to reduce the optimisation variables to only one: the orientation of material properties of the continuum. Finally, the analytical approach is introduced in order to minimise the failure index and results obtained with the use of three different failure criteria that are compared in order to understand the role of the three formulations with respect to the strength's behaviour. Copyright © 2012 John Wiley & Sons, Ltd.