Convergence Investigation for the Exponential Matrix and Mathematical Layers in the Static Analysis of Multilayered Composite Structures

The exact three-dimensional analysis of a large group of geometries is accomplished here using the same formulation written in orthogonal mixed curvilinear coordinates. This solution is valid for plates, cylindrical shells, cylinders and spherical shells. It does not need specialized equations for each proposed geometry. It makes use of a formulation that is valid for spherical shells and automatically degenerates in the simpler geometries. Second order differential equations are reduced of an order redoubling the number of variables, and then they are solved via the exponential matrix method. Coefficients of equations vary through the thickness when shells are considered. M mathematical layers must be introduced into each physical layer to approximate the curvature. The correlation between M and the order of expansion N for the exponential matrix is analyzed in this paper in order to find their opportune combined values to obtain the exact results. As their effects may depend on different parameters, several geometries, lamination sequences, thickness ratios and imposed half-wave numbers are taken into consideration