New shape functions for arbitrary discontinuities without additional unknowns

Thomas Peter Fries, Ted Belytschko

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

Abstract

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.

Originalspracheenglisch
TitelMeshfree Methods for Partial Differential Equations III
Seiten87-103
Seitenumfang17
Band57
DOIs
PublikationsstatusVeröffentlicht - 2007

Publikationsreihe

NameLecture Notes in Computational Science and Engineering
Band57
ISSN (Print)14397358

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Shape Function
Discontinuity
Unknown
Arbitrary
Mesh
Moving Least Squares
Extended Finite Element Method
Partition of Unity
Approximation Space
Level Set Method
Special Functions
Weight Function
Finite Element
Finite element method

Schlagwörter

    ASJC Scopus subject areas

    • !!Engineering(all)
    • !!Computational Mathematics
    • !!Modelling and Simulation
    • !!Control and Optimization
    • !!Discrete Mathematics and Combinatorics

    Dies zitieren

    Fries, T. P., & Belytschko, T. (2007). New shape functions for arbitrary discontinuities without additional unknowns. in Meshfree Methods for Partial Differential Equations III (Band 57, S. 87-103). (Lecture Notes in Computational Science and Engineering; Band 57). https://doi.org/10.1007/978-3-540-46222-4_6

    New shape functions for arbitrary discontinuities without additional unknowns. / Fries, Thomas Peter; Belytschko, Ted.

    Meshfree Methods for Partial Differential Equations III. Band 57 2007. S. 87-103 (Lecture Notes in Computational Science and Engineering; Band 57).

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

    Fries, TP & Belytschko, T 2007, New shape functions for arbitrary discontinuities without additional unknowns. in Meshfree Methods for Partial Differential Equations III. Bd. 57, Lecture Notes in Computational Science and Engineering, Bd. 57, S. 87-103. https://doi.org/10.1007/978-3-540-46222-4_6
    Fries TP, Belytschko T. New shape functions for arbitrary discontinuities without additional unknowns. in Meshfree Methods for Partial Differential Equations III. Band 57. 2007. S. 87-103. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-540-46222-4_6
    Fries, Thomas Peter ; Belytschko, Ted. / New shape functions for arbitrary discontinuities without additional unknowns. Meshfree Methods for Partial Differential Equations III. Band 57 2007. S. 87-103 (Lecture Notes in Computational Science and Engineering).
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