In the analysis of slender elastic structures two main advantages are achieved through the mixed (stress and displacement) format with respect to the more commonly used displacement one: (i) the smaller error in the extrapolations usually employed in the solution strategies of nonlinear problems and (ii) the lower polynomial dependence of the problem equations on the finite element degrees of freedom when solid finite elements are used. The smaller extrapolation error produces a lower number of iterations and larger step length in path-following analysis and a greater accuracy in Koiter asymptotic method.

Stress interpolation is sometimes not simple nor computationally convenient and it turns out to be particularly inefficient in isogeometric analysis.

Recent developments in material science have proposed new classes of composite materials that exhibit, beside others, excellent mechanical properties. In particular  Carbon nanotubes (CNTs), are able to exhibit excellent mechanical, have attracted many researchers, in which the concept of functionally graded materials (FGMs) was combined with carbon nanotubes reinforcements. In the context of standard composite materials so called Variable Angle Tow composites are of interest in many industrial applications. In these context highly optimized structures may exhibit a poor post-buckling behaviour that may destroy the excellent intrinsic performances of the base material. In this work the Koiter method is employed for the optimal design of smart structure also to prevent the imperfection sensitivity of slender structures.