A hybrid-Trefftz formulation for plane elasticity with selective enrichment of the approximations

• Published in: International journal for numerical methods in biomedical engineering Vol. 27; no. 5; pp. 785 - 804
• Main Authors: de Souza, Charlton Okama, Proença, Sergio Persival Baroncini
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01-05-2011; Wiley
• Subjects: Approximation; approximation enrichment; Boundary element method; Clouds; Enrichment; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); generalized finite element method; hybrid-Trefftz formulation; Mathematical analysis; Mathematical models; non-conventional approach; Numerical analysis; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Enrichment; Stress analysis; Trefftz method; Clouds; Modeling; Finite element method; Plane elasticity; Meshless method; hybrid-Trefftz formulation; generalized finite element method; non-conventional approach; Boundary element method; approximation enrichment; eXtended Finite Element Method
• ISSN: 2040-7939; 2040-7947; 2040-7947
• DOI: 10.1002/cnm.1334

This work is related to the so‐called non‐conventional finite element formulations. Essentially, a methodology for the enrichment of the initial approximation which is typical of the meshless methods and based on the clouds concept is introduced in the hybrid‐Trefftz formulation for plane elasticity. The formulation presented allows for the approximation and direct enrichment of two independent fields: stresses in the domains and displacements on the boundaries of the elements. Defined by a set of elements and interior boundaries sharing a common node, the cloud notion is employed to select the enrichment support for the approximation fields. The numerical analysis performed reveals an excellent performance of the resulting formulation, characterized by the good approximation ability and a reduced computational effort. Copyright © 2009 John Wiley & Sons, Ltd.