In this project, we develop new penalty methods for use in fast transient dynamic problems, simulated with time-domain integrators. A problem that has plagued the community for many decades is that the usual stiffness-type penalties tend to decrease the critical time step of conditionally stable time integrators such as the central difference scheme. We resolve this by the simultaneous use of stiffness-type penalties and inertia-type penalties - termed the “bipenalty method” - which allows for high accuracy in constraint imposition across a wide variety of problem types without the need to decrease the time step of an analysis.
Fundamental considerations relate to the stability and accuracy of the method, the derivation of mathematical proofs for suitable ratios of the two types of penalties, and the development of robust algorithms for the selection of penalty parameters. Practical applications include the imposition of support conditions, the simulation of crack propagation with interface elements, and the modelling of contact-impact.