No Cover Image

Journal article 286 views 149 downloads

Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics

Chennakesava Kadapa Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 117, Issue: 5, Pages: 543 - 573

Swansea University Author: Chennakesava Kadapa Orcid Logo

Check full text

DOI (Published version): 10.1002/nme.5967

Abstract

In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes...

Full description

Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa44783
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2018-10-06T13:19:59Z
last_indexed 2019-06-05T10:55:51Z
id cronfa44783
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2019-05-29T15:21:29.6966145</datestamp><bib-version>v2</bib-version><id>44783</id><entry>2018-10-06</entry><title>Novel quadratic B&#xE9;zier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics</title><swanseaauthors><author><sid>de01927f8c2c4ad9dcc034c327ac8de1</sid><ORCID>0000-0001-6092-9047</ORCID><firstname>Chennakesava</firstname><surname>Kadapa</surname><name>Chennakesava Kadapa</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2018-10-06</date><deptcode>SCS</deptcode><abstract>In this paper, we present novel techniques of using quadratic B&#xE9;zier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes with quadratic B&#xE9;zier triangular/tetrahedral elements from the corresponding quadratic Lagrange elements that can be easily generated using the existing mesh generators. Numerical issues arising in the case of nearly incompressible materials are addressed using the consistent B&#x2010;bar formulation, thus reducing the finite element formulation to the one consisting only of displacements. The higher&#x2010;order spatial discretisation and the non&#x2010;negative nature of Bernstein polynomials are shown to yield significant computational benefits. The optimal spatial convergence of the B&#x2010;bar formulation for the quadratic triangular and tetrahedral elements is demonstrated by computing error norms in displacement and stresses. The applicability and computational efficiency of the proposed elements for elastodynamic simulations are demonstrated by studying several numerical examples involving real&#x2010;world geometries with complex features. Numerical results obtained with the standard linear triangular and tetrahedral elements are also presented for comparison.</abstract><type>Journal Article</type><journal>International Journal for Numerical Methods in Engineering</journal><volume>117</volume><journalNumber>5</journalNumber><paginationStart>543</paginationStart><paginationEnd>573</paginationEnd><publisher/><issnPrint>00295981</issnPrint><keywords>B&#xE9;zier elements; Bernstein polynomials; Explicit elastodynamics; B-bar formulation; Connecting rod</keywords><publishedDay>3</publishedDay><publishedMonth>2</publishedMonth><publishedYear>2019</publishedYear><publishedDate>2019-02-03</publishedDate><doi>10.1002/nme.5967</doi><url>https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5967</url><notes/><college>COLLEGE NANME</college><department>Computer Science</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SCS</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2019-05-29T15:21:29.6966145</lastEdited><Created>2018-10-06T10:56:09.5808667</Created><path><level id="1">College of Science</level><level id="2">Computer Science</level></path><authors><author><firstname>Chennakesava</firstname><surname>Kadapa</surname><orcid>0000-0001-6092-9047</orcid><order>1</order></author></authors><documents><document><filename>0044783-01112018091745.pdf</filename><originalFilename>44783.pdf</originalFilename><uploaded>2018-11-01T09:17:45.2070000</uploaded><type>Output</type><contentLength>3636872</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2019-10-04T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2019-05-29T15:21:29.6966145 v2 44783 2018-10-06 Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics de01927f8c2c4ad9dcc034c327ac8de1 0000-0001-6092-9047 Chennakesava Kadapa Chennakesava Kadapa true false 2018-10-06 SCS In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes with quadratic Bézier triangular/tetrahedral elements from the corresponding quadratic Lagrange elements that can be easily generated using the existing mesh generators. Numerical issues arising in the case of nearly incompressible materials are addressed using the consistent B‐bar formulation, thus reducing the finite element formulation to the one consisting only of displacements. The higher‐order spatial discretisation and the non‐negative nature of Bernstein polynomials are shown to yield significant computational benefits. The optimal spatial convergence of the B‐bar formulation for the quadratic triangular and tetrahedral elements is demonstrated by computing error norms in displacement and stresses. The applicability and computational efficiency of the proposed elements for elastodynamic simulations are demonstrated by studying several numerical examples involving real‐world geometries with complex features. Numerical results obtained with the standard linear triangular and tetrahedral elements are also presented for comparison. Journal Article International Journal for Numerical Methods in Engineering 117 5 543 573 00295981 Bézier elements; Bernstein polynomials; Explicit elastodynamics; B-bar formulation; Connecting rod 3 2 2019 2019-02-03 10.1002/nme.5967 https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5967 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2019-05-29T15:21:29.6966145 2018-10-06T10:56:09.5808667 College of Science Computer Science Chennakesava Kadapa 0000-0001-6092-9047 1 0044783-01112018091745.pdf 44783.pdf 2018-11-01T09:17:45.2070000 Output 3636872 application/pdf Accepted Manuscript true 2019-10-04T00:00:00.0000000 true eng
title Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
spellingShingle Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
Chennakesava Kadapa
title_short Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
title_full Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
title_fullStr Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
title_full_unstemmed Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
title_sort Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
author_id_str_mv de01927f8c2c4ad9dcc034c327ac8de1
author_id_fullname_str_mv de01927f8c2c4ad9dcc034c327ac8de1_***_Chennakesava Kadapa
author Chennakesava Kadapa
author2 Chennakesava Kadapa
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 117
container_issue 5
container_start_page 543
publishDate 2019
institution Swansea University
issn 00295981
doi_str_mv 10.1002/nme.5967
college_str College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Computer Science{{{_:::_}}}College of Science{{{_:::_}}}Computer Science
url https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5967
document_store_str 1
active_str 0
description In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes with quadratic Bézier triangular/tetrahedral elements from the corresponding quadratic Lagrange elements that can be easily generated using the existing mesh generators. Numerical issues arising in the case of nearly incompressible materials are addressed using the consistent B‐bar formulation, thus reducing the finite element formulation to the one consisting only of displacements. The higher‐order spatial discretisation and the non‐negative nature of Bernstein polynomials are shown to yield significant computational benefits. The optimal spatial convergence of the B‐bar formulation for the quadratic triangular and tetrahedral elements is demonstrated by computing error norms in displacement and stresses. The applicability and computational efficiency of the proposed elements for elastodynamic simulations are demonstrated by studying several numerical examples involving real‐world geometries with complex features. Numerical results obtained with the standard linear triangular and tetrahedral elements are also presented for comparison.
published_date 2019-02-03T03:58:51Z
_version_ 1737026889505046528
score 10.8781185