The aim of this chapter is the development of an efficient and accurate higher-order formulation to solve the weak form of the governing equations that rule the mechanical behavior of doubly-curved shell structures made of composite materials, whose reference domain can be defined by arbitrary shapes. To this aim, a mapping procedure based on Non-Uniform Rational Basis Spline (NURBS) is introduced. It should be specified that the theoretical shell model is based on the Equivalent Single Layer (ESL) approach. In addition, the Generalized Integral Quadrature technique, that is a numerical tool which can guarantee high levels of accuracy with a low computational effort in the structural analysis of the considered shell elements, is introduced. The proposed technique is able to solve numerically the integrals by means of weighted sums of the values that a smooth function assumes in some discrete points placed within the reference domain.
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