Some Remarks on Finite Elements with an Elliptic Hole

Reinhard Piltner

doi:10.1016/j.finel.2008.04.005

Some Remarks on Finite Elements with an Elliptic Hole

Reinhard Piltner

Mathematical Sciences

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Abstract

Some issues regarding the implementation of finite elements with elliptic holes are discussed. Although the treatment of rigid body modes appears to be different for Trefftz functions satisfying boundary conditions on circular holes from those functions ensuring the satisfaction of boundary conditions on elliptic holes, the programming can be done similarly. For the investigation of the numerical performance of hole elements using a larger number of Trefftz functions, a 24-node hole element is compared to 8-node and 16-node elements. Details of the implementation issues are given.

Original language	American English
Journal	Finite Elements in Analysis and Design
Volume	44
DOIs	https://doi.org/10.1016/j.finel.2008.04.005
State	Published - Aug 1 2008

Disciplines

Education
Mathematics

Keywords

Complex functions
Elasticity
Hybrid-Trefftz finite elements
Stress concentration

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https://doi.org/10.1016/j.finel.2008.04.005

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abstract = "Some issues regarding the implementation of finite elements with elliptic holes are discussed. Although the treatment of rigid body modes appears to be different for Trefftz functions satisfying boundary conditions on circular holes from those functions ensuring the satisfaction of boundary conditions on elliptic holes, the programming can be done similarly. For the investigation of the numerical performance of hole elements using a larger number of Trefftz functions, a 24-node hole element is compared to 8-node and 16-node elements. Details of the implementation issues are given.",

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AB - Some issues regarding the implementation of finite elements with elliptic holes are discussed. Although the treatment of rigid body modes appears to be different for Trefftz functions satisfying boundary conditions on circular holes from those functions ensuring the satisfaction of boundary conditions on elliptic holes, the programming can be done similarly. For the investigation of the numerical performance of hole elements using a larger number of Trefftz functions, a 24-node hole element is compared to 8-node and 16-node elements. Details of the implementation issues are given.

KW - Complex functions

KW - Elasticity

KW - Hybrid-Trefftz finite elements

KW - Stress concentration

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/153

UR - https://doi.org/10.1016/j.finel.2008.04.005

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DO - 10.1016/j.finel.2008.04.005

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VL - 44

JO - Finite Elements in Analysis and Design

JF - Finite Elements in Analysis and Design

ER -

Some Remarks on Finite Elements with an Elliptic Hole

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Keywords

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