Geometrically nonlinear dynamic analysis of laminated shells using Bézier functions (Q1370825)

This article develops a refined method for a finite element analysis of multilayer composite shells in static and dynamic, linear and nonlinear cases. The formulation starts from a three-dimensional continuum mechanics where finite deformations are function of coordinates of the middle surface of the shell. The middle surface is described with Bézier functions developed to an order greater than 2, in terms of edge point coordinates. The three-dimensional displacements are exact Green strain-displacements relations, but the transverse strains are supposed to be only linear. Bézier surface patches give admissible displacements of order 5 for the in-plane displacements, and of order 7 for the normal ones, representing the middle surface displacements and the rotations. Integration with respect to the thickness is achieved through the different layers. Finally, the total potential energies are expressed by matrices of 180 degrees of freedom. The computation is carried out by use of existing programs and by application of Newton-Raphson procedures, with a convergence criterion \((0,1\%)\), neglecting or not the nonlinear terms. Different applications are presented, in particular to linear and nonlinear free vibrations of elliptic cylinders with different eccentricities (from \(-0.2\) to \(+0.2\)), or to shallow shell panels made of 24 cross-plied orthotropic layers, submitted to impulsive loads. The authors establish a good agreement with the results due to \textit{C. T. Tsai} and \textit{A. N. Palazotto} [ibid., 26, No. 3/4, 379-388 (1991; Zbl 0850.73073)]. The rather small differences do not precise which are the best.