IMPLICIT TIME INTEGRATION OF A CLASS OF CONSTRAINED HYBRID FORMULATIONS .1. SPECTRAL STABILITY THEORY

Incomplete field formulations have recently been the subject of intens e research because of their potential in coupled analysis of independe ntly modeled substructures, adaptive refinement, domain decomposition and parallel processing. This paper presents a spectral stability theo ry for the differential/algebraic dynamic systems associated with thes e formulations, discusses the design and analysis of suitable time-int egration algorithms, and emphasizes the treatment of the inter-subdoma in linear constraint equations. These constraints are shown to introdu ce a destabilizing effect in the dynamic system that can be analyzed b y investigating the behavior of the time-integration algorithm at infi nite and zero frequencies. Three different approaches for constructing penalty-free unconditionally stable second-order accurate solution pr ocedures for this class of hybrid formulations are presented, analyzed and illustrated with numerical examples. In particular, the advantage s of the Hilber-Hughes-Taylor (HHT) method and its generalized version (Generalized cu) are highlighted. The family of problems discussed in this paper can also be viewed as model problems for the more general case of hybrid formulations with non-linear constraints. For example, it is shown numerically in this paper that the theoretical results pre dicted by the spectral stability theory also apply to non-linear multi body dynamics formulations. Therefore, some of the algorithms outlined in this work are important alternatives to the popular technique cons isting of transforming differential/algebraic equations into ordinary differential equations via the introduction of a stabilization term th at depends on arbitrary constants, and that influences the computed so lution.