Higher-order structural theories for the static analysis of doubly-curved laminated composite panels reinforced by curvilinear fibers

• Static analysis of doubly-curved composite panels reinforced by curvilinear fibers.
• Through-the-thickness recovery procedure for strains, stresses and displacements.
• Geometric description via differential geometry of doubly-curved laminated structures.
• General higher-order layer-wise and equivalent single layer theories.
• Generalized Differential Quadrature method applied in curvilinear principal coordinates.

The main aim of this paper is the evaluation of the through-the-thickness profiles of strain, stress and displacement components of several doubly-curved panels reinforced by curvilinear fibers. The placement of the reinforcing phase along curved paths allows to obtain mechanical properties which change point by point and affects the static behavior of shell structures. Some numerical applications based on both higher-order Equivalent Single Layer (ESL) and Layer-Wise (LW) theories are shown in order to underline the curvilinear fiber influence on the static analysis. The structural model, which is based on the so-called Carrera Unified Formulation (CUF), is completely general and can deal easily with variable stiffness shells. An appropriate recovery procedure based on the three-dimensional elasticity equations in principal curvilinear coordinates is presented to compute strains and stresses. The equation system which governs the static problem under consideration is solved numerically through the Generalized Differential Quadrature (GDQ) method. The same numerical technique is employed to evaluate the geometrical parameters needed for the characterization of the shell reference surface, according to the differential geometry.