Hybrid-Mixed Shell Finite Elements and Implicit Dynamic Schemes for Shell Post-buckling

Two topics are addressed: (i)hybrid-mixed formulations for geometrically exact shell models, and (ii)post-buckling analysis of shells by implicit dynamics schemes. As for the hybrid-mixed elements, seven formulations are compared. The one with the assumed-natural-strain interpolation of membrane strains shows very little sensitivity to mesh distortion for curved shells. Another one, which is based on the Hu-Washizu three-field functional, allows for very large solution increments. Hence, a new element is proposed that combines positive features of both mentioned formulations. As for the post-buckling analysis of shells, we use implicit dynamics. In particular, five time-stepping schemes are tested for shell stability problems that include mode jumping. These are trapezoidal rule, schemes with numerical dissipation in the high-frequency range, and energy-momentum conserving method. Numerical examples show that the dissipative schemes are suitable for simulation of complex phenomena that appear in shell stability.