English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Rigid unilateral contacts in multibody problems lead to non-smooth dynamics: this requires the development of new types of time integrators that draw on the solution of a variational inequality at each time step. In most settings, this variational inequality is a complementarity problem. In the context of non-smooth multibody dynamics, projected fixed-point, spectral and Nesterov methods have been successfully used to solve those complementarity problems, especially for granular problems or real-time simulations [2] [3], but large scale and ill-conditioned problems still advocate for solvers with better convergence. The promising class of interior-point method has been applied only recently to multibody dynamics [4]. Their implementation is more complicate, but this comes at the benefit of high precision and good convergence, moreover they can be applied to problems with both deformable and rigid bodies [5]. We present an algorithm based on a dual-primal interior point method. The solution is advanced along the central path using the Mehotra predictor-corrector scheme, in a small number of sub steps that leverage on a parallel direct solver for computing the updates from highly sparse saddle-point problems. Although the original method addresses unilateral constraints only, it is possible to restate it in order to fit also equality constraints, as might happen when introducing joints between colliding parts. The algorithm is implemented in C++ language in our open-source simulator. Results show that the method regularly converges to small residuals even in cases (for instance, odd mass ratios) that degraded the convergence of other methods.

SOLVING UNILATERAL CONTACT PROBLEMS IN MULTIBODY DYNAMICS USING A PRIMAL-DUAL INTERIOR POINT METHOD