Computational Mechanics and Design Group

Department of Civil & Structural Engineering

The bipenalty method for arbitrary multipoint constraints


In finite element (FE) analysis, traditional penalty methods impose constraints by adding virtual stiffness to the FE system. In dynamics, this can decrease the critical time step of the system when conditionally stable time integration schemes are used by introducing spurious modes with high eigenfrequencies. Recent studies have shown that using mass penalties alongside traditional stiffness penalties can mitigate this effect for systems with a one single-point constraint. In the present work, we extend this finding to include systems with an arbitrary set of multipoint constraints. By analysing the generalised eigenvalue problem, we show that the values of spurious eigenfrequencies may be controlled by the choice of stiffness and mass penalty parameters. The method is demonstrated using numerical examples, including a one-dimensional contact-impact formulation and a two-dimensional crack propagation analysis. The results show that constraint imposition using the bipenalty method can be employed such that the critical time step of an analysis is unaffected, whereas also displaying superiority over the mass penalty method in terms of accuracy and versatility. © 2012 John Wiley & Sons, Ltd.

Publication details

Publication type: 
Journal article
Awarded by: 
Journal / conference name: 
International Journal for Numerical Methods in Engineering
Awarded date: 
Start page: 
End page: 

Research project(s)

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...