Free formulation elements with drilling freedoms for stability analysis of shells

The paper describes a class of shell elements based on the free formulation by Bergan and Nygard. The elements include the “drilling” freedom that gives a significantly improved membrane action as compared to traditional elements. The elements may undertake arbitrarily large displacements and rotations and material nonlinearities are accounted for. The “hyperplane displacement control” method is applied for solution of the static instability problems including singularities. A linearized eigenvalue analysis may be carried out at any stage during the incremental solution in order to find the limit point or bifurcation paths. The examples given cover verification-type problems like snap-through analysis of shells and buckling of plates. Further, an extensive buckling analysis of a corrugated aluminum shear panel is described. The examples verify that the shell elements and the solution algorithms are accurate, reliable and efficient.