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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce a PDE-based node-to-element contact formulation as analternative to classical, purely geometrical formulations. It is challenging todevise solutions to nonsmooth contact problem with continuous gap using finiteelement discretizations. We herein achieve this objective by constructing anapproximate distance function (ADF) to the boundaries of solid objects, and indoing so, also obtain universal uniqueness of contact detection. Unilateralconstraints are implemented using a mixed model combining the screened Poissonequation and a force element, which has the topology of a continuum elementcontaining an additional incident node. An ADF is obtained by solving thescreened Poisson equation with constant essential boundary conditions and avariable transformation. The ADF does not explicitly depend on the number ofobjects and a single solution of the partial differential equation for thisfield uniquely defines the contact conditions for all incident points in themesh. Having an ADF field to any obstacle circumvents the multiple targetsurfaces and avoids the specific data structures present in traditionalcontact-impact algorithms. We also relax the interpretation of the Lagrangemultipliers as contact forces, and the Courant--Beltrami function is used witha mixed formulation producing the required differentiable result. Wedemonstrate the advantages of the new approach in two- and three-dimensionalproblems that are solved using Newton iterations. Simultaneous constraints foreach incident point are considered.

Continuous gap contact formulation based on the screened Poisson equation