ABSTRACT
This chapter describes a decomposition principle by augmented Lagrangians which can be used to simplify the solution of some variational problems having a special structure. Associated with this decomposition principle are some iterative methods which appear to be related, in some particular cases, to alternating direction iterative methods. The decomposition principle and alternating direction iterative methods are applied to the solution of two particular problems in finite elasticity: the calculation of large displacements for a class of flexible, inextensible pipe lines; and the mechanical behavior of incompressible two-dimensional Mooney-Rivlin materials. The chapter discusses the results obtained for the numerical simulation of mechanical situations involving a stream acting on a pipe or involving a time-dependent behavior. It also tests the numerical capabilities of the alternating direction iterative methods to solve nonlinear problems in the field of multidimensional finite elasticity.
