Processing of Equality Constraints for Implicit in LS-DYNA v. 970

LSTC is committed to building an implicit capability into LS-DYNA that is as capable as the flagship explicit capability. Over the years LSTC has added many different types of constraint handling capabilities in explicit that now have to be handled by implicit. The vast majority of these constraints are equality constraints imposed on the linear or nonlinear solution required at each time step. We will describe a new approach for handling equality constraints that has allowed us to robustly process them without placing unnecessary restrictions on how the user poses the constraints. Our new approach effectively and efficiently processes the constraints for the linear, nonlinear, and eigenvalue problems that have to be solved by the users of Implicit LS-DYNA. We compute a transformation based on the Jacobian matrix of the constraint equations and apply that transformation to form a reduced stiffness and, if necessary, reduced mass matrices. The transformation is also used to transforms vectors from the unconstrained space to the constrained space and back again. The only restriction placed on the structure of the constraint matrix is that it is full rank. We will also highlight the various constraints now supported for implicit solution in LS-DYNA v. 970 and demonstrate the solution of some problems illustrating these constraint features.