Non-linear shell dynamics based on a mixed variational formulation

摘要

A simple, but efficient procedure for the investigation of the geometrically non-linear dynamic behaviour of thin elastic shells which can be described sufficiently accurate by the Donnell-Marguerre-Mushtari-Vlasov theory is proposed and tested. It is based on a mixed variational formulation generalizing D'Alembert's principle. The discretization with respect to the space is performed by Euler's method and that with respect to the time by means of the central difference quotient. Due to the regular and simple structure of the governing algebraic equations wave propagation phenomena can be studied adequately. The introduction of an (artificial) damping allows the approximation of pure static problems and includes as well the branching of equilibrium. Some illustrative examples are presented.