RI-IGABEM based on generalized-α method in 2D and 3D elastodynamic problems
The isogeometric analysis boundary element method (IGABEM) has a broad application prospect due to its exact geometric representation and good approximation properties. In this paper, a novel radial integration IGABEM (RI-IGABEM) based on the generalized-α method is proposed to solve 2D and 3D elast...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2021-09, Vol.383, p.113890, Article 113890 |
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| description | The isogeometric analysis boundary element method (IGABEM) has a broad application prospect due to its exact geometric representation and good approximation properties. In this paper, a novel radial integration IGABEM (RI-IGABEM) based on the generalized-α method is proposed to solve 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials. First of all, the elastostatics Kelvin fundamental solution is used as the fundamental solution of the problem. In order to preserve the advantage of IGABEM, i.e. only boundary is discretized, the radial integration method (RIM) is applied to transform the domain integral caused by the material heterogeneity and the inertia term into an equivalent boundary integral by means of applied points. In addition, using a simple transformation method, the rigid-body technique is applied to solve the strongly singular integrals, and the Telles scheme and the power series expansion method are used to solve the weakly singular integrals in RI-IGABEM respectively. Furthermore, the generalized-α method is adopted to solve the time domain problem, which can improve the stability of numerical results by effectively filtering out the false response of high frequency and minimizing the attenuation of low frequency response. A number of 2D and 3D examples, such as those with homogeneous materials, functionally gradient materials, and material defects and inclusions, are used to demonstrate the ability of the scheme to simulate the elastodynamic problems.
•A RI-IGABEM based on the generalized-α method is proposed for solving 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials.•The rigid-body technique is applied to solve the strongly singular integrals in RI-IGABEM through a simple transformation method.•The generalized-α method is applied in RI-IGABEM to solve the time domain problems.•Radial integration method is applied to transform the domain integrals into an equivalent boundary integrals. |
| doi_str_mv | 10.1016/j.cma.2021.113890 |
| format | Article |
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•A RI-IGABEM based on the generalized-α method is proposed for solving 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials.•The rigid-body technique is applied to solve the strongly singular integrals in RI-IGABEM through a simple transformation method.•The generalized-α method is applied in RI-IGABEM to solve the time domain problems.•Radial integration method is applied to transform the domain integrals into an equivalent boundary integrals.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2021.113890</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Attenuation ; Boundary element method ; Elastodynamic problems ; Elastodynamics ; Elastostatics ; Frequency response ; Functionally gradient materials ; Generalized-[formula omitted] method ; Heterogeneity ; Homogeneous and inhomogeneous materials ; Inclusions ; Integrals ; Isogeometric analysis boundary element method ; Mathematical analysis ; Power series ; Radial integration method ; Series expansion</subject><ispartof>Computer methods in applied mechanics and engineering, 2021-09, Vol.383, p.113890, Article 113890</ispartof><rights>2021 Elsevier B.V.</rights><rights>Copyright Elsevier BV Sep 1, 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-37a93b8d52533cd89b4a97a4692f05f3987848d00b4bc9c573cd6c7b963f792b3</citedby><cites>FETCH-LOGICAL-c325t-37a93b8d52533cd89b4a97a4692f05f3987848d00b4bc9c573cd6c7b963f792b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cma.2021.113890$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Xu, Chuang</creatorcontrib><creatorcontrib>Dai, Rui</creatorcontrib><creatorcontrib>Dong, Chunying</creatorcontrib><creatorcontrib>Yang, Huashi</creatorcontrib><title>RI-IGABEM based on generalized-α method in 2D and 3D elastodynamic problems</title><title>Computer methods in applied mechanics and engineering</title><description>The isogeometric analysis boundary element method (IGABEM) has a broad application prospect due to its exact geometric representation and good approximation properties. In this paper, a novel radial integration IGABEM (RI-IGABEM) based on the generalized-α method is proposed to solve 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials. First of all, the elastostatics Kelvin fundamental solution is used as the fundamental solution of the problem. In order to preserve the advantage of IGABEM, i.e. only boundary is discretized, the radial integration method (RIM) is applied to transform the domain integral caused by the material heterogeneity and the inertia term into an equivalent boundary integral by means of applied points. In addition, using a simple transformation method, the rigid-body technique is applied to solve the strongly singular integrals, and the Telles scheme and the power series expansion method are used to solve the weakly singular integrals in RI-IGABEM respectively. Furthermore, the generalized-α method is adopted to solve the time domain problem, which can improve the stability of numerical results by effectively filtering out the false response of high frequency and minimizing the attenuation of low frequency response. A number of 2D and 3D examples, such as those with homogeneous materials, functionally gradient materials, and material defects and inclusions, are used to demonstrate the ability of the scheme to simulate the elastodynamic problems.
•A RI-IGABEM based on the generalized-α method is proposed for solving 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials.•The rigid-body technique is applied to solve the strongly singular integrals in RI-IGABEM through a simple transformation method.•The generalized-α method is applied in RI-IGABEM to solve the time domain problems.•Radial integration method is applied to transform the domain integrals into an equivalent boundary integrals.</description><subject>Attenuation</subject><subject>Boundary element method</subject><subject>Elastodynamic problems</subject><subject>Elastodynamics</subject><subject>Elastostatics</subject><subject>Frequency response</subject><subject>Functionally gradient materials</subject><subject>Generalized-[formula omitted] method</subject><subject>Heterogeneity</subject><subject>Homogeneous and inhomogeneous materials</subject><subject>Inclusions</subject><subject>Integrals</subject><subject>Isogeometric analysis boundary element method</subject><subject>Mathematical analysis</subject><subject>Power series</subject><subject>Radial integration method</subject><subject>Series expansion</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEUhYMoWKsP4C7gesb8TCYJrmqttVARRNchk2Q0Q2emJlOhvpUv4jOZMq69m8uFc-45fABcYpRjhMvrJjetzgkiOMeYComOwAQLLjOSrmMwQahgGReEnYKzGBuURmAyAevnVbZazm4Xj7DS0VnYd_DNdS7ojf9yNvv5hq0b3nsLfQfJHdSdhfQOuo2OQ2_3nW69gdvQVxvXxnNwUutNdBd_ewpe7xcv84ds_bRczWfrzFDChoxyLWklLCOMUmOFrAotuS5KSWrEaioFF4WwCFVFZaRhPIlKwytZ0ppLUtEpuBr_puCPnYuDavpd6FKkIoyhUhRY0qTCo8qEPsbgarUNvtVhrzBSB2iqUQmaOkBTI7TkuRk9LtX_9C6oaLzrjLM-ODMo2_t_3L--WHII</recordid><startdate>20210901</startdate><enddate>20210901</enddate><creator>Xu, Chuang</creator><creator>Dai, Rui</creator><creator>Dong, Chunying</creator><creator>Yang, Huashi</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20210901</creationdate><title>RI-IGABEM based on generalized-α method in 2D and 3D elastodynamic problems</title><author>Xu, Chuang ; Dai, Rui ; Dong, Chunying ; Yang, Huashi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-37a93b8d52533cd89b4a97a4692f05f3987848d00b4bc9c573cd6c7b963f792b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Attenuation</topic><topic>Boundary element method</topic><topic>Elastodynamic problems</topic><topic>Elastodynamics</topic><topic>Elastostatics</topic><topic>Frequency response</topic><topic>Functionally gradient materials</topic><topic>Generalized-[formula omitted] method</topic><topic>Heterogeneity</topic><topic>Homogeneous and inhomogeneous materials</topic><topic>Inclusions</topic><topic>Integrals</topic><topic>Isogeometric analysis boundary element method</topic><topic>Mathematical analysis</topic><topic>Power series</topic><topic>Radial integration method</topic><topic>Series expansion</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xu, Chuang</creatorcontrib><creatorcontrib>Dai, Rui</creatorcontrib><creatorcontrib>Dong, Chunying</creatorcontrib><creatorcontrib>Yang, Huashi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xu, Chuang</au><au>Dai, Rui</au><au>Dong, Chunying</au><au>Yang, Huashi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>RI-IGABEM based on generalized-α method in 2D and 3D elastodynamic problems</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2021-09-01</date><risdate>2021</risdate><volume>383</volume><spage>113890</spage><pages>113890-</pages><artnum>113890</artnum><issn>0045-7825</issn><eissn>1879-2138</eissn><abstract>The isogeometric analysis boundary element method (IGABEM) has a broad application prospect due to its exact geometric representation and good approximation properties. In this paper, a novel radial integration IGABEM (RI-IGABEM) based on the generalized-α method is proposed to solve 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials. First of all, the elastostatics Kelvin fundamental solution is used as the fundamental solution of the problem. In order to preserve the advantage of IGABEM, i.e. only boundary is discretized, the radial integration method (RIM) is applied to transform the domain integral caused by the material heterogeneity and the inertia term into an equivalent boundary integral by means of applied points. In addition, using a simple transformation method, the rigid-body technique is applied to solve the strongly singular integrals, and the Telles scheme and the power series expansion method are used to solve the weakly singular integrals in RI-IGABEM respectively. Furthermore, the generalized-α method is adopted to solve the time domain problem, which can improve the stability of numerical results by effectively filtering out the false response of high frequency and minimizing the attenuation of low frequency response. A number of 2D and 3D examples, such as those with homogeneous materials, functionally gradient materials, and material defects and inclusions, are used to demonstrate the ability of the scheme to simulate the elastodynamic problems.
•A RI-IGABEM based on the generalized-α method is proposed for solving 2D and 3D elastodynamic problems of homogeneous and inhomogeneous materials.•The rigid-body technique is applied to solve the strongly singular integrals in RI-IGABEM through a simple transformation method.•The generalized-α method is applied in RI-IGABEM to solve the time domain problems.•Radial integration method is applied to transform the domain integrals into an equivalent boundary integrals.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cma.2021.113890</doi></addata></record> |
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| subjects | Attenuation Boundary element method Elastodynamic problems Elastodynamics Elastostatics Frequency response Functionally gradient materials Generalized-[formula omitted] method Heterogeneity Homogeneous and inhomogeneous materials Inclusions Integrals Isogeometric analysis boundary element method Mathematical analysis Power series Radial integration method Series expansion |
| title | RI-IGABEM based on generalized-α method in 2D and 3D elastodynamic problems |
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