| Among the various applications of explicit finite element methods, car crash simulations may be the most common example. In general, approximately 75% of the computational cost of a crash simulation is consumed by the contact algorithm. It is therefore understandable that early contact algorithms were developed with high priority given to computational efficiency. As computational resources continue to grow at increasing rates, the burden of speed is lightened and more resources become available for the sake of increased accuracy.; At the same time, crashworithness engineering has progressed such that design goals are to mitigate not only the primary impact but also the secondary impacts of a crash. The time interval of interest has thus become longer and includes more impact events, thus greater accuracy is required of the simulation methods.; This dissertation investigates contact algorithms that satisfy the requisite balance laws in addition to the associated constraints for application to problems modeled by explicit finite element methods. Namely, proven explicit integrators from the field of differential algebraic equations, Shake and Rattle, are modified for application to elastodynamic contact problems. The central question motivating this dissertation is: do these integrators posses any advantages over existing contact algorithms? Impact simulations are performed to highlight the performance of Shake and Rattle. Furthermore, enhancements to the algorithms are proposed and evaluated. |
