A B‐spline finite element for the dynamic analysis of sandwich shells of revolution

Presents a new B‐spline finite element for the dynamic analysis of unsymmetrical sandwich shells of revolution. The formulation takes account of the membrane and bending effects in isotropic or orthotropic elastic facings, and membrane, bending and transverse shearing effects in an isotropic or othotropic elastic core. Both geometry and local displacements are interpolated by a set of B‐spline functions. The main aspects added by the sandwich structure of the element are the transverse shearing and membrane‐bending coupling effects in the core. These are well represented by a set of new variables which are the mean end relative in‐plane displacements of the facing middle surfaces. Together with the transverse displacement, these variables constitute the degrees of freedom (dofs) of this new B‐spline sandwich element. The finite elements are grouped into super‐elements with C¹ continuity to obtain the whole finite element model. For each super‐element a total of five dofs per node is then obtained except for its end nodes where the derivatives of these dofs with respect to the meridional co‐ordinate are added. This choice reduces to a minimum the total number of dofs in comparison to existing sandwich elements. Evaluates the efficiency and accuracy of the proposed element through several benchmark examples. Compares the results with the analytical and numerical solutions found in the literature. A very satisfactory behaviour of the element was observed in all test cases.