Implicit Relaxation Applied to Postbuckling Analysis of Cylindrical Shells

Summary

The paper deals with a viscous approach, where an artificial damping is used in order to arrive at points of equilibrium in the pre- or postbuckling range of shell structures.

The artificial damping is based on a creep type procedure with the time playing a purely ficticious role. The required numerical stability is obtained by using an implicit operator in time and a variable viscosity and time step. The viscosity and the time step are combined as a variable damping parameter which depends on the unbalanced forces of the structure.

The procedure allows to find states of static equilibrium with the load applied all at once. Incrementation is not necessary unless the path has to be traced in small steps. With a perturbation different branches of the nonlinear solution can be obtained.

Examples are given for elastic thin walled cylindrical shells in the postbuckling range. The used finite elements are based on a functional with displacements, axial forces and bending moments as nodal variables.