New shape functions for arbitrary discontinuities without additional unknowns

Thomas Peter Fries, Ted Belytschko

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in Buch/BerichtBegutachtung


A method is proposed for arbitrary discontinuities, without the need for a mesh that aligns with the interfaces, and without introducing additional unknowns as in the extended finite element method. The approximation space is built by special shape functions that are able to represent the discontinuity, which is described by the level-set method. The shape functions are constructed by means of the moving least-squares technique. This technique employs special mesh-based weight functions such that the resulting shape functions are discontinuous along the interface. The new shape functions are used only near the interface, and are coupled with standard finite elements, which are employed in the rest of the domain for efficiency. The coupled set of shape functions builds a linear partition of unity that represents the discontinuity. The method is illustrated for linear elastic examples involving strong and weak discontinuities.

TitelMeshfree Methods for Partial Differential Equations III
PublikationsstatusVeröffentlicht - 2007


NameLecture Notes in Computational Science and Engineering
ISSN (Print)14397358

ASJC Scopus subject areas

  • Ingenieurwesen (insg.)
  • Computational Mathematics
  • Modellierung und Simulation
  • Steuerung und Optimierung
  • Diskrete Mathematik und Kombinatorik


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