Numerical results show that the Hybrid-Game helps an EA to accelerate optimization process. From the practical point of view, applying a SCB on the suction and pressure sides significantly reduces transonic total drag and improves lift-to-drag (L/D) value when compared to the baseline design.

The numerical accuracy of the presented sensitivity analysis has been tested by perturbing a mesh. The capability of the presented sensitivity analysis for the detection of pollution error has also been tested.

A new adaptive remeshing strategy based on the sensitivity analysis of the point wise error estimation has been developed and tested. This strategy produces very cheap meshes for the accurate evaluation of stresses at specific points.

• — the use of the classical error energy norm and an optimality criterion based on the equal distribution of the density of error,

• — the use of alternative error norms based on measurements of the point wise error contained in the main magnitudes that control the equilibrium problem and/or the material constitutive equations such as the stresses (e.g. the Von Mises stress).

The feasibility of using all the described strategies is demonstrated through the solution of a benchmark example. This example is also used for comparison between the described refinement criteria.

With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial direction. This reduction provides a composite performance equivalent to what is found in a delaminated material.

To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.

Once having described the different approaches used, and the parameters on which they depend, this paper describes a new formulation capable of obtaining the compression strength of composites taking into account the fiber buckling phenomenon. This formulation uses the serial/parallel mixing theory developed by Rastellini et al. (Comput. Struct. 86(9):879–896, 2008) to simulate the composite, and takes advantage of knowing the mechanical performance of the composite constituents to simulate the fiber buckling phenomenon. This is done with an homogenization procedure. It consists in introducing the interaction between fibers and matrix into their respective constitutive equations. The interaction between fiber and matrix takes into account fiber initial misalignments, its volumetric participation and the mechanical properties of both constituents.

The new formulation proposed is implemented in a finite element code, taking into account that fibers can have different misalignment levels, and that the composite behaves differently if it is under tensile or compression forces. The mechanical performance of the formulation proposed is studied with several finite element simulations of compressed composites. Finally, the correctness of the formulation is proved by comparing the numerical results with the experimental tests provided by Barbero and Tomblin (Int. J. Solids Struct. 33(29):4379–4393, 1996), Tomblin et al. (Int. J. Solids Struct. 34(13):1667–1679, 1997).