A time-dependent discontinuous Galerkin finite element approach in two-dimensional elastodynamic problems based on spherical Hankel element framework
In this paper, a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions is suggested for solving two-dimensional elastodynamic problems. The main idea is to use spherical Hankel shape functions derived from corresponding radial basis functions instead of classical...
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| Veröffentlicht in: | Acta mechanica 2018-12, Vol.229 (12), p.4977-4994 |
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| creator | Izadpanah, E. Shojaee, S. Hamzehei-Javaran, S. |
| description | In this paper, a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions is suggested for solving two-dimensional elastodynamic problems. The main idea is to use spherical Hankel shape functions derived from corresponding radial basis functions instead of classical Lagrange shape functions. Among the advantages of the proposed interpolation, containing the first and second kind of Bessel functions in complex space as well as the polynomial ones can be pointed out, while the classic Lagrange interpolation is only able to contain polynomial functions. The validity and accuracy of the present method are fully demonstrated using several numerical examples. For this purpose, five numerical examples are considered, and the results obtained from the proposed method (Hankel-based TD-FEM) and the Lagrange-based TD-FEM are compared with the exact analytical solutions. The results show that the use of Hankel functions in TD-FEM leads to more accurate and stable solutions rather than those obtained from the classic TD-FEM. |
| doi_str_mv | 10.1007/s00707-018-2287-z |
| format | Article |
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The main idea is to use spherical Hankel shape functions derived from corresponding radial basis functions instead of classical Lagrange shape functions. Among the advantages of the proposed interpolation, containing the first and second kind of Bessel functions in complex space as well as the polynomial ones can be pointed out, while the classic Lagrange interpolation is only able to contain polynomial functions. The validity and accuracy of the present method are fully demonstrated using several numerical examples. For this purpose, five numerical examples are considered, and the results obtained from the proposed method (Hankel-based TD-FEM) and the Lagrange-based TD-FEM are compared with the exact analytical solutions. The results show that the use of Hankel functions in TD-FEM leads to more accurate and stable solutions rather than those obtained from the classic TD-FEM.</description><identifier>ISSN: 0001-5970</identifier><identifier>EISSN: 1619-6937</identifier><identifier>DOI: 10.1007/s00707-018-2287-z</identifier><language>eng</language><publisher>Vienna: Springer Vienna</publisher><subject>Basis functions ; Bessel functions ; Classical and Continuum Physics ; Control ; Dynamical Systems ; Elastodynamics ; Engineering ; Engineering Thermodynamics ; Finite element method ; Galerkin method ; Hankel functions ; Heat and Mass Transfer ; Interpolation ; Original Paper ; Polynomials ; Radial basis function ; Shape functions ; Solid Mechanics ; Theoretical and Applied Mechanics ; Time dependence ; Vibration</subject><ispartof>Acta mechanica, 2018-12, Vol.229 (12), p.4977-4994</ispartof><rights>Springer-Verlag GmbH Austria, part of Springer Nature 2018</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Acta Mechanica is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-336fdd1a2829125a2f2e11470b66c173504e6fdb1b27b2401dbf24e65e0294343</citedby><cites>FETCH-LOGICAL-c355t-336fdd1a2829125a2f2e11470b66c173504e6fdb1b27b2401dbf24e65e0294343</cites><orcidid>0000-0003-0952-9085</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00707-018-2287-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00707-018-2287-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Izadpanah, E.</creatorcontrib><creatorcontrib>Shojaee, S.</creatorcontrib><creatorcontrib>Hamzehei-Javaran, S.</creatorcontrib><title>A time-dependent discontinuous Galerkin finite element approach in two-dimensional elastodynamic problems based on spherical Hankel element framework</title><title>Acta mechanica</title><addtitle>Acta Mech</addtitle><description>In this paper, a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions is suggested for solving two-dimensional elastodynamic problems. The main idea is to use spherical Hankel shape functions derived from corresponding radial basis functions instead of classical Lagrange shape functions. Among the advantages of the proposed interpolation, containing the first and second kind of Bessel functions in complex space as well as the polynomial ones can be pointed out, while the classic Lagrange interpolation is only able to contain polynomial functions. The validity and accuracy of the present method are fully demonstrated using several numerical examples. For this purpose, five numerical examples are considered, and the results obtained from the proposed method (Hankel-based TD-FEM) and the Lagrange-based TD-FEM are compared with the exact analytical solutions. The results show that the use of Hankel functions in TD-FEM leads to more accurate and stable solutions rather than those obtained from the classic TD-FEM.</description><subject>Basis functions</subject><subject>Bessel functions</subject><subject>Classical and Continuum Physics</subject><subject>Control</subject><subject>Dynamical Systems</subject><subject>Elastodynamics</subject><subject>Engineering</subject><subject>Engineering Thermodynamics</subject><subject>Finite element method</subject><subject>Galerkin method</subject><subject>Hankel functions</subject><subject>Heat and Mass Transfer</subject><subject>Interpolation</subject><subject>Original Paper</subject><subject>Polynomials</subject><subject>Radial basis function</subject><subject>Shape functions</subject><subject>Solid Mechanics</subject><subject>Theoretical and Applied Mechanics</subject><subject>Time dependence</subject><subject>Vibration</subject><issn>0001-5970</issn><issn>1619-6937</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kcFqHSEUhqW00Ns0D5Cd0LWpOjrOLC-hTQqBbtq1OOMxMXdGpzqXkLxH3zfnMiVZFUHx-P0_5_gTciH4peDcfK24ccO46JiUnWHP78hOtKJnbd-Y92THORdM94Z_JJ9qfcCbNErsyN89XeMMzMMCyUNaqY91zGmN6ZiPlV67CcohJhpiiitQmGA-UW5ZSnbjPcWn9TEzjyapxpzchIyra_ZPyc1xpMgNKKp0cBU8zYnW5R5KHJG8cekA06tpKG6Gx1wOn8mH4KYK5__OM_L7-7dfVzfs9uf1j6v9LRsbrVfWNG3wXjjZyV5I7WSQIIQyfGjbUZhGcwVIDGKQZpCKCz8EiSUNXPaqUc0Z-bL5YpN_jlBX-5CPBWeoVgqpWqX7niN1uVF3-Bk2ppDX4kZcHnDAnCBErO91q6ToOqlRIDbBWHKtBYJdSpxdebKC21NcdovLYlz2FJd9Ro3cNBXZdAflrZX_i14AxNCbGA</recordid><startdate>20181201</startdate><enddate>20181201</enddate><creator>Izadpanah, E.</creator><creator>Shojaee, S.</creator><creator>Hamzehei-Javaran, S.</creator><general>Springer Vienna</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L6V</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope><orcidid>https://orcid.org/0000-0003-0952-9085</orcidid></search><sort><creationdate>20181201</creationdate><title>A time-dependent discontinuous Galerkin finite element approach in two-dimensional elastodynamic problems based on spherical Hankel element framework</title><author>Izadpanah, E. ; 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The main idea is to use spherical Hankel shape functions derived from corresponding radial basis functions instead of classical Lagrange shape functions. Among the advantages of the proposed interpolation, containing the first and second kind of Bessel functions in complex space as well as the polynomial ones can be pointed out, while the classic Lagrange interpolation is only able to contain polynomial functions. The validity and accuracy of the present method are fully demonstrated using several numerical examples. For this purpose, five numerical examples are considered, and the results obtained from the proposed method (Hankel-based TD-FEM) and the Lagrange-based TD-FEM are compared with the exact analytical solutions. The results show that the use of Hankel functions in TD-FEM leads to more accurate and stable solutions rather than those obtained from the classic TD-FEM.</abstract><cop>Vienna</cop><pub>Springer Vienna</pub><doi>10.1007/s00707-018-2287-z</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0003-0952-9085</orcidid></addata></record> |
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| subjects | Basis functions Bessel functions Classical and Continuum Physics Control Dynamical Systems Elastodynamics Engineering Engineering Thermodynamics Finite element method Galerkin method Hankel functions Heat and Mass Transfer Interpolation Original Paper Polynomials Radial basis function Shape functions Solid Mechanics Theoretical and Applied Mechanics Time dependence Vibration |
| title | A time-dependent discontinuous Galerkin finite element approach in two-dimensional elastodynamic problems based on spherical Hankel element framework |
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