Linear analysis of shells based on discontinuous Galerkin formulation

A discontinuous Galerkin (DG) method for linear shell problems is formulated to investigate the performance of the method in numerical analysis of shells. In the past the DG methods have been successfully applied in fluid mechanics and analysis of simpler structures, such as beams and plates, but it has not been explored in application to shells. The main difficulty with the numerical analysis of shell problem has been the proper separation of the stiff membrane response from considerably weaker bending response. If this separation is inadequate, deformation of shell structures is grossly underestimated and the model is said to lock (membrane and/or shear locking). Although there are a few successful elements capable of solving a large class of shell problems, a sufficiently general and accurate finite element formulation of shells is still elusive. The aim of this thesis is to examine if the DG method can provide general and accurate solutions of shell problems.; In this thesis it has been shown that the DG method does provide an additional mechanism to eliminate the locking in shells. It has also been shown that such mechanism can be combined with other techniques, introduced in the past, to eliminate locking in continuous finite element formulations of shells.; The principal drawback of the originally developed DG methods is the fact that, as compared with the continuous finite element formulation based on the same mesh and the same approximating functions, they generally lead to a significantly larger system of equations. To overcome this drawback, a version of discontinuous Galerkin method for elliptic problems rendering the same set of unknowns in the final system of equations as in continuous displacement based Galerkin method is developed in this work. In addition, the final equations are obtained by the assembly of element matrices whose structure is identical to that of the continuous displacement approach. This makes the present formulation easily implementable within the existing commercial computer codes. This approach is named the embedded discontinuous Galerkin method and while it is developed here in the framework of three-dimensional elasticity, it is used in the computations of linear shell problems. Its role in improving solution for shells is studied by means of numerical examples.