Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions
This Letter presents three-dimensional general solutions for static problems in thermo-elasticity of one-dimensional hexagonal quasi-crystals. Two displacement potentials are introduced to simplify the equilibrium equations in terms of displacement and temperature. Rigorous operator theory and gener...
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| Veröffentlicht in: | Physics letters. A 2012-05, Vol.376 (26-27), p.2004-2009 |
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| container_end_page | 2009 |
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| container_issue | 26-27 |
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| container_title | Physics letters. A |
| container_volume | 376 |
| creator | Li, X.Y. Li, P.D. |
| description | This Letter presents three-dimensional general solutions for static problems in thermo-elasticity of one-dimensional hexagonal quasi-crystals. Two displacement potentials are introduced to simplify the equilibrium equations in terms of displacement and temperature. Rigorous operator theory and generalized Almansiʼs theorem are applied to derive the general solutions in terms of five quasi-harmonic functions. To show the significance of the general solutions, a semi-infinite space and an infinite space, both of which are subjected to a heat source, are considered. In these two cases, closed form fundamental phonon–phason-elastic fields are expressed by elementary functions, which play an important role in numerical simulations.
► We present 3D static thermo-elastic general solutions for 1D hexagonal QCs. ► Thermo-phonon–phason field is expressed by five quasi-harmonic functions. ► Fundamental solutions for semi-infinite and infinite spaces are derived. |
| doi_str_mv | 10.1016/j.physleta.2012.04.049 |
| format | Article |
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► We present 3D static thermo-elastic general solutions for 1D hexagonal QCs. ► Thermo-phonon–phason field is expressed by five quasi-harmonic functions. ► Fundamental solutions for semi-infinite and infinite spaces are derived.</description><identifier>ISSN: 0375-9601</identifier><identifier>EISSN: 1873-2429</identifier><identifier>DOI: 10.1016/j.physleta.2012.04.049</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Computer simulation ; Displacement ; Exact solutions ; Fundamental solutions ; General solutions ; Heat sources ; Mathematical analysis ; Mathematical models ; One-dimensional hexagonal quasi-crystal ; Solid state physics ; Three dimensional ; Transverse isotropy</subject><ispartof>Physics letters. A, 2012-05, Vol.376 (26-27), p.2004-2009</ispartof><rights>2012 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c345t-19a1771943a37e7c851e957c37c2dd586838e90d73bf1dc35be0278a258277d73</citedby><cites>FETCH-LOGICAL-c345t-19a1771943a37e7c851e957c37c2dd586838e90d73bf1dc35be0278a258277d73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.physleta.2012.04.049$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>315,781,785,3551,27929,27930,46000</link.rule.ids></links><search><creatorcontrib>Li, X.Y.</creatorcontrib><creatorcontrib>Li, P.D.</creatorcontrib><title>Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions</title><title>Physics letters. A</title><description>This Letter presents three-dimensional general solutions for static problems in thermo-elasticity of one-dimensional hexagonal quasi-crystals. Two displacement potentials are introduced to simplify the equilibrium equations in terms of displacement and temperature. Rigorous operator theory and generalized Almansiʼs theorem are applied to derive the general solutions in terms of five quasi-harmonic functions. To show the significance of the general solutions, a semi-infinite space and an infinite space, both of which are subjected to a heat source, are considered. In these two cases, closed form fundamental phonon–phason-elastic fields are expressed by elementary functions, which play an important role in numerical simulations.
► We present 3D static thermo-elastic general solutions for 1D hexagonal QCs. ► Thermo-phonon–phason field is expressed by five quasi-harmonic functions. ► Fundamental solutions for semi-infinite and infinite spaces are derived.</description><subject>Computer simulation</subject><subject>Displacement</subject><subject>Exact solutions</subject><subject>Fundamental solutions</subject><subject>General solutions</subject><subject>Heat sources</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>One-dimensional hexagonal quasi-crystal</subject><subject>Solid state physics</subject><subject>Three dimensional</subject><subject>Transverse isotropy</subject><issn>0375-9601</issn><issn>1873-2429</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNqFkEtLAzEUhYMoWKt_QWbpZsY8ZiaTnVJ8geCmrkOa3OmkTCdtklH7702tgq6EC_fBdw7cg9AlwQXBpL5eFZtuF3qIqqCY0AKXqcQRmpCGs5yWVByjCWa8ykWNySk6C2GFcVJiMUHv884D5MauYQjWDarPYgd-7XLoVYhWZ0sYwKdzcP0YExEy12Zu-Kvp4EMtv6btqILNtd-FmDY1mKwdB6MSGn-bnKOTVvUBLr77FL3e381nj_nzy8PT7PY516ysYk6EIpwTUTLFOHDdVARExTXjmhpTNXXDGhDYcLZoidGsWgCmvFG0aijn6TxFVwffjXfbEUKUaxs09L0awI1BEswaWtZc4ITWB1R7F4KHVm68XSu_S5DcJy1X8idpuU9a4jKVSMKbgxDSI28WvAzawqDBWA86SuPsfxafDy6N0A</recordid><startdate>20120521</startdate><enddate>20120521</enddate><creator>Li, X.Y.</creator><creator>Li, P.D.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QQ</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>20120521</creationdate><title>Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions</title><author>Li, X.Y. ; Li, P.D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c345t-19a1771943a37e7c851e957c37c2dd586838e90d73bf1dc35be0278a258277d73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Computer simulation</topic><topic>Displacement</topic><topic>Exact solutions</topic><topic>Fundamental solutions</topic><topic>General solutions</topic><topic>Heat sources</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>One-dimensional hexagonal quasi-crystal</topic><topic>Solid state physics</topic><topic>Three dimensional</topic><topic>Transverse isotropy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, X.Y.</creatorcontrib><creatorcontrib>Li, P.D.</creatorcontrib><collection>CrossRef</collection><collection>Ceramic Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics letters. A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, X.Y.</au><au>Li, P.D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions</atitle><jtitle>Physics letters. A</jtitle><date>2012-05-21</date><risdate>2012</risdate><volume>376</volume><issue>26-27</issue><spage>2004</spage><epage>2009</epage><pages>2004-2009</pages><issn>0375-9601</issn><eissn>1873-2429</eissn><abstract>This Letter presents three-dimensional general solutions for static problems in thermo-elasticity of one-dimensional hexagonal quasi-crystals. Two displacement potentials are introduced to simplify the equilibrium equations in terms of displacement and temperature. Rigorous operator theory and generalized Almansiʼs theorem are applied to derive the general solutions in terms of five quasi-harmonic functions. To show the significance of the general solutions, a semi-infinite space and an infinite space, both of which are subjected to a heat source, are considered. In these two cases, closed form fundamental phonon–phason-elastic fields are expressed by elementary functions, which play an important role in numerical simulations.
► We present 3D static thermo-elastic general solutions for 1D hexagonal QCs. ► Thermo-phonon–phason field is expressed by five quasi-harmonic functions. ► Fundamental solutions for semi-infinite and infinite spaces are derived.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physleta.2012.04.049</doi><tpages>6</tpages></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Computer simulation Displacement Exact solutions Fundamental solutions General solutions Heat sources Mathematical analysis Mathematical models One-dimensional hexagonal quasi-crystal Solid state physics Three dimensional Transverse isotropy |
| title | Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions |
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