Jump to ContentJump to Main Navigation
Analytic Element MethodComplex Interactions of Boundaries and Interfaces$
Users without a subscription are not able to see the full content.

David R. Steward

Print publication date: 2020

Print ISBN-13: 9780198856788

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198856788.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 28 November 2021

Analytic Elements from Complex Functions

Analytic Elements from Complex Functions

(p.103) 3 Analytic Elements from Complex Functions
Analytic Element Method

David R. Steward

Oxford University Press

The mathematical functions associated with analytic elements may be formulated using a complex function $\Omega$ of a complex variable ${\zcomplex}$. Complex formulation of analytic elements is introduced in Section 3.1 for exact solutions obtained by embedding point elements that generate divergence, circulation, or velocity within a uniform vector field. Influence functions for analytic elements with circular geometry are obtained using Taylor and Laurent series expansions in Section 3.2, and conformal mapping extends this formulation to analytic elements with the geometry of ellipses (Section 3.3). The Courant's Sewing Theorem is employed in Section 3.4 to develop solutions for interface conditions across straight line segments, and the Joukowsky transformation extends methods to circular arcs and wings (Section 3.5), which satisfy a Kutta condition of non-singular vector field at their trailing edges. Vector fields with spatially distributed divergence and curl are formulated using the complex variable ${\zcomplex}$ with its complex conjugate $\overline{\zcomplex}$ in Section 3.6, and the complex conjugate is further employed in the Kolosov formulas (Section 3.7) to solve force deformation problems for analytic elements with traction or displacement specified boundary conditions.

Keywords:   Analytic Element Method, AEM, complex variables, complex function, analytic, holomorphic, point elements, line elements, Joukowsky, complex conjugate, Kolosov, Muskhelishvili

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .