Computational Mechanics and Design Group

Department of Civil & Structural Engineering

Dynamic constraint modelling


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.




(2013). The bipenalty method for arbitrary multipoint constraints. International Journal for Numerical Methods in Engineering, 93 (5), pp. 465-482, Abstract: In finite element (FE) analysis, traditional penalty methods impose constraints by adding virtual...
(2011). A new bipenalty formulation for ensuring time step stability in time domain computational dynamics. International Journal for Numerical Methods in Engineering, 90 (3), pp. 269-286.
(2011). Controlling the critical time step with the bi-penalty method. In ECCOMAS Thematic Conference - COMPDYN 2011: 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering: An IACM Special Interest Conference, Programme.
(2010). The bipenalty method for explicit time integration. In Engineering Computational Technology.