Lumped mass finite element implementation of continuum theories with micro-inertia
SUMMARYContinuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro‐structured materials. Such terms, often called micro‐inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore...
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| Veröffentlicht in: | International journal for numerical methods in engineering 2013-11, Vol.96 (7), p.448-466 |
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| creator | Lombardo, Mariateresa Askes, Harm |
| description | SUMMARYContinuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro‐structured materials. Such terms, often called micro‐inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro‐inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro‐inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro‐inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm. Copyright © 2013 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nme.4570 |
| format | Article |
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Such terms, often called micro‐inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro‐inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro‐inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro‐inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm. 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J. Numer. Meth. Engng</addtitle><description>SUMMARYContinuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro‐structured materials. Such terms, often called micro‐inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro‐inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro‐inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro‐inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm. Copyright © 2013 John Wiley & Sons, Ltd.</description><subject>Algorithms</subject><subject>Continuums</subject><subject>critical time step</subject><subject>Exact sciences and technology</subject><subject>explicit dynamics</subject><subject>Finite element method</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Inertia</subject><subject>length scale</subject><subject>lumped mass</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>micro-inertia</subject><subject>Neumann expansion</subject><subject>Physics</subject><subject>Solid mechanics</subject><subject>Static elasticity (thermoelasticity...)</subject><subject>Structural and continuum mechanics</subject><subject>Time integration</subject><subject>Vectors (mathematics)</subject><issn>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp1kF1rFDEUhoMouLaCPyEggjfT5nOyuZTSL9hupVXsXchmTmjqJLMmGWr_vSm7VBC8OgfOw8N7XoQ-UHJECWHHKcKRkIq8QgtKtOoII-o1WrST7qRe0rfoXSkPhFAqCV-gm9UctzDgaEvBPqRQAcMIEVLFIW53m61hSnjy2E2phjTPEdd7mHKAgh9DvccxuDx1IUGuwR6iN96OBd7v5wH6fnb67eSiW12fX558WXWOa0E6SQAoGXpBecsJfkO9o8prx5Z8A0pIzwY3EM023PbabxiT1Do_eGoFWfacH6DPO-82T79mKNXEUByMo00wzcVQ0QspeqVpQz_-gz5Mc04tXaMEo7ynhP0VtmdKyeDNNodo85OhxDyXa1q55rnchn7aC21xdvTZJhfKC8-Ulkwx2bhuxz2GEZ7-6zPrq9O9d8-HUuH3C2_zT9MrrqT5sT43t1fk7uvdmpkL_gfilZcH</recordid><startdate>20131116</startdate><enddate>20131116</enddate><creator>Lombardo, Mariateresa</creator><creator>Askes, Harm</creator><general>Blackwell Publishing Ltd</general><general>Wiley</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>IQODW</scope><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>20131116</creationdate><title>Lumped mass finite element implementation of continuum theories with micro-inertia</title><author>Lombardo, Mariateresa ; Askes, Harm</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3940-50ee10d6413097efb1fc17f9c283be745f2dcd092b3a69fb2251acfdf1a408633</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Continuums</topic><topic>critical time step</topic><topic>Exact sciences and technology</topic><topic>explicit dynamics</topic><topic>Finite element method</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Inertia</topic><topic>length scale</topic><topic>lumped mass</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>micro-inertia</topic><topic>Neumann expansion</topic><topic>Physics</topic><topic>Solid mechanics</topic><topic>Static elasticity (thermoelasticity...)</topic><topic>Structural and continuum mechanics</topic><topic>Time integration</topic><topic>Vectors (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lombardo, Mariateresa</creatorcontrib><creatorcontrib>Askes, Harm</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><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>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lombardo, Mariateresa</au><au>Askes, Harm</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lumped mass finite element implementation of continuum theories with micro-inertia</atitle><jtitle>International journal for numerical methods in engineering</jtitle><addtitle>Int. J. Numer. Meth. Engng</addtitle><date>2013-11-16</date><risdate>2013</risdate><volume>96</volume><issue>7</issue><spage>448</spage><epage>466</epage><pages>448-466</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><coden>IJNMBH</coden><abstract>SUMMARYContinuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro‐structured materials. Such terms, often called micro‐inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro‐inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro‐inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro‐inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm. Copyright © 2013 John Wiley & Sons, Ltd.</abstract><cop>Chichester</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/nme.4570</doi><tpages>19</tpages></addata></record> |
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| subjects | Algorithms Continuums critical time step Exact sciences and technology explicit dynamics Finite element method Fundamental areas of phenomenology (including applications) Inertia length scale lumped mass Mathematical analysis Mathematical models micro-inertia Neumann expansion Physics Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Time integration Vectors (mathematics) |
| title | Lumped mass finite element implementation of continuum theories with micro-inertia |
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