General asymptotic formulation for the bifurcation problem of thin walled structures in contact with rigid surfaces

The bifurcation problem of thin walled structures in contact with rigid sur faces is formulated by adopting the multiple scales asymptotic technique. T he general theory developed in this paper is very useful for the bifurcatio n analysis of waviness instabilities in the sheet metal forming. The formul ation is presented in a full Lagrangian formulation. Through this general f ormulation, the bifurcation functional is derived within an error of O(E-4) (E : shell's thickness parameter). This functional can be used in numerica l solutions to sheet metal forming instability problem.