Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems

Aykut Erkal, Debra Laefer, Semih Tezcan

Research output: Contribution to journalArticle

Abstract

This paper promotes the further development and adoption of infinite elements for unbounded problems. This is done by demonstrating the ease of application and computational efficiency of infinite elements. Specifically, this paper introduces a comprehensive set of coordinate and field variable mapping functions for one-dimensional and two-dimensional infinite elements and the computational steps for the solution of the affiliated combined finite-infinite element models. Performance is then benchmarked against various parametric models for deflections and stresses in two examples of solid, unbounded problems: (1) a circular, uniformly-distributed load, and (2) a point load on a semiinfinite, axisymmetrical medium. The results are compared with those from the respective closed-form solution. As an example, when the vertical deflections in Example 2 are compared with the closed form solution, the 45% error level generated with fixed boundaries and 14% generated with spring-supported boundaries is reduced to only 1% with infinite elements, even with a coarse mesh. Furthermore, this increased accuracy is achieved with lower computational costs.

Original languageEnglish (US)
Article number04014085
JournalJournal of Computing in Civil Engineering
Volume29
Issue number6
DOIs
StatePublished - Nov 1 2015

Fingerprint

Boundary conditions
Computational efficiency
Costs

Keywords

  • Boussinesq problem
  • Far field domain
  • Finite element method
  • Infinite elements
  • Unbounded problem

ASJC Scopus subject areas

  • Computer Science Applications
  • Civil and Structural Engineering

Cite this

Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems. / Erkal, Aykut; Laefer, Debra; Tezcan, Semih.

In: Journal of Computing in Civil Engineering, Vol. 29, No. 6, 04014085, 01.11.2015.

Research output: Contribution to journalArticle

@article{eaa71722d8e446d6a0698b3dbe6c8cf5,
title = "Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems",
abstract = "This paper promotes the further development and adoption of infinite elements for unbounded problems. This is done by demonstrating the ease of application and computational efficiency of infinite elements. Specifically, this paper introduces a comprehensive set of coordinate and field variable mapping functions for one-dimensional and two-dimensional infinite elements and the computational steps for the solution of the affiliated combined finite-infinite element models. Performance is then benchmarked against various parametric models for deflections and stresses in two examples of solid, unbounded problems: (1) a circular, uniformly-distributed load, and (2) a point load on a semiinfinite, axisymmetrical medium. The results are compared with those from the respective closed-form solution. As an example, when the vertical deflections in Example 2 are compared with the closed form solution, the 45{\%} error level generated with fixed boundaries and 14{\%} generated with spring-supported boundaries is reduced to only 1{\%} with infinite elements, even with a coarse mesh. Furthermore, this increased accuracy is achieved with lower computational costs.",
keywords = "Boussinesq problem, Far field domain, Finite element method, Infinite elements, Unbounded problem",
author = "Aykut Erkal and Debra Laefer and Semih Tezcan",
year = "2015",
month = "11",
day = "1",
doi = "10.1061/(ASCE)CP.1943-5487.0000391",
language = "English (US)",
volume = "29",
journal = "Journal of Computing in Civil Engineering",
issn = "0887-3801",
publisher = "American Society of Civil Engineers (ASCE)",
number = "6",

}

TY - JOUR

T1 - Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems

AU - Erkal, Aykut

AU - Laefer, Debra

AU - Tezcan, Semih

PY - 2015/11/1

Y1 - 2015/11/1

N2 - This paper promotes the further development and adoption of infinite elements for unbounded problems. This is done by demonstrating the ease of application and computational efficiency of infinite elements. Specifically, this paper introduces a comprehensive set of coordinate and field variable mapping functions for one-dimensional and two-dimensional infinite elements and the computational steps for the solution of the affiliated combined finite-infinite element models. Performance is then benchmarked against various parametric models for deflections and stresses in two examples of solid, unbounded problems: (1) a circular, uniformly-distributed load, and (2) a point load on a semiinfinite, axisymmetrical medium. The results are compared with those from the respective closed-form solution. As an example, when the vertical deflections in Example 2 are compared with the closed form solution, the 45% error level generated with fixed boundaries and 14% generated with spring-supported boundaries is reduced to only 1% with infinite elements, even with a coarse mesh. Furthermore, this increased accuracy is achieved with lower computational costs.

AB - This paper promotes the further development and adoption of infinite elements for unbounded problems. This is done by demonstrating the ease of application and computational efficiency of infinite elements. Specifically, this paper introduces a comprehensive set of coordinate and field variable mapping functions for one-dimensional and two-dimensional infinite elements and the computational steps for the solution of the affiliated combined finite-infinite element models. Performance is then benchmarked against various parametric models for deflections and stresses in two examples of solid, unbounded problems: (1) a circular, uniformly-distributed load, and (2) a point load on a semiinfinite, axisymmetrical medium. The results are compared with those from the respective closed-form solution. As an example, when the vertical deflections in Example 2 are compared with the closed form solution, the 45% error level generated with fixed boundaries and 14% generated with spring-supported boundaries is reduced to only 1% with infinite elements, even with a coarse mesh. Furthermore, this increased accuracy is achieved with lower computational costs.

KW - Boussinesq problem

KW - Far field domain

KW - Finite element method

KW - Infinite elements

KW - Unbounded problem

UR - http://www.scopus.com/inward/record.url?scp=84945127965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945127965&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)CP.1943-5487.0000391

DO - 10.1061/(ASCE)CP.1943-5487.0000391

M3 - Article

AN - SCOPUS:84945127965

VL - 29

JO - Journal of Computing in Civil Engineering

JF - Journal of Computing in Civil Engineering

SN - 0887-3801

IS - 6

M1 - 04014085

ER -