Constraint violation in concurrent range space methods for transient dynamic analysis Academic Article uri icon


  • Despite the fact that many authors have dismissed redundant coordinate formulations as being of order N3, and hence less attractive than recursive formulations, this paper presents recent research that demonstrates that a class of redundant, nonrecursive multibody formulations consistently achieve order N computational cost for systems of rigid and/or flexible bodies. This formulation is based upon the rapidly convergent preconditioned range space formulation for nonlinear multibody dynamics. The method can be traced to its foundation in equality constrained quadratic optimization and incorporates some aspects of subdomain decomposition techniques used in variational boundary value problems. Until recently, however, this approach had not been investigated in the context of multibody simulation, and presents theoretical questions unique to nonlinear dynamics. Nonrecursive methods have additional advantages with respect to recursive order N methods: (1) the formalisms retain the highly desirable order N computational cost; (2) the techniques are amenable to concurrent simulation strategies; (3) the approaches do not depend upon system topology to induce concurrency; (4) the methods can be derived to balance the computational load automatically on concurrent multiprocessors. However, the preconditioned range space formulation can suffer from degradation in accuracy due to constraint violation drift. This effect becomes even more pronounced when one induces concurrency via domain decomposition. A central theme of this paper is the derivation and development of concurrent constraint stabilization methods that retain the order N computational cost of the underlying preconditioned range space formulation. It is demonstrated that variants of the penalty and augmented Lagrangian methods for nonlinear multibody dynamics are well suited for concurrent constraint stabilization. Moreover, this paper presents new theoretical results regarding the rate of convergence of order N constraint stabilization schemes associated with the newly introduced class of methods. © 1994.

published proceedings

  • Computing Systems in Engineering

author list (cited authors)

  • Kurdila, A. J., Menon, R., & Strganac, T. W.

citation count

  • 1

complete list of authors

  • Kurdila, Andrew J||Menon, Ramesh||Strganac, Thomas W

publication date

  • August 1993