SOLVING THE PROBLEM OF ELECTRO-MAGNETO-ELASTIC BENDING OF A MULTIPLY CONNECTED PLATE
The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electro-magneto-elastic plates. Moreover, with the help of conformal mappings, expansion of holomorphic functions into the Laurent series or Faber polynomia...
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| Veröffentlicht in: | Journal of applied mechanics and technical physics 2022-08, Vol.63 (4), p.676-687 |
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| container_title | Journal of applied mechanics and technical physics |
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| creator | Kaloerov, S. A. Seroshtanov, A. V. |
| description | The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electro-magneto-elastic plates. Moreover, with the help of conformal mappings, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the generalized least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular value decomposition. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electro-magneto-elastic state is studied. |
| doi_str_mv | 10.1134/S0021894422040150 |
| format | Article |
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A. ; Seroshtanov, A. V.</creator><creatorcontrib>Kaloerov, S. A. ; Seroshtanov, A. V.</creatorcontrib><description>The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electro-magneto-elastic plates. Moreover, with the help of conformal mappings, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the generalized least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular value decomposition. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electro-magneto-elastic state is studied.</description><identifier>ISSN: 0021-8944</identifier><identifier>EISSN: 1573-8620</identifier><identifier>DOI: 10.1134/S0021894422040150</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Analytic functions ; Applications of Mathematics ; Boundary conditions ; Classical and Continuum Physics ; Classical Mechanics ; Conformal mapping ; Edge cracks ; Elastic bending ; Elastic plates ; Fluid- and Aerodynamics ; Least squares method ; Linear algebra ; Mathematical analysis ; Mathematical Modeling and Industrial Mathematics ; Mechanical Engineering ; Mechanical properties ; Physical properties ; Physics ; Physics and Astronomy ; Plate material ; Polynomials ; Singular value decomposition</subject><ispartof>Journal of applied mechanics and technical physics, 2022-08, Vol.63 (4), p.676-687</ispartof><rights>Pleiades Publishing, Ltd. 2022</rights><rights>Pleiades Publishing, Ltd. 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-6025b8c02ee5a8cad895ac5aa25bf1d0a146611c714fa481993190454a0b3a6f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0021894422040150$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0021894422040150$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Kaloerov, S. A.</creatorcontrib><creatorcontrib>Seroshtanov, A. V.</creatorcontrib><title>SOLVING THE PROBLEM OF ELECTRO-MAGNETO-ELASTIC BENDING OF A MULTIPLY CONNECTED PLATE</title><title>Journal of applied mechanics and technical physics</title><addtitle>J Appl Mech Tech Phy</addtitle><description>The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electro-magneto-elastic plates. Moreover, with the help of conformal mappings, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the generalized least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular value decomposition. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electro-magneto-elastic state is studied.</description><subject>Analytic functions</subject><subject>Applications of Mathematics</subject><subject>Boundary conditions</subject><subject>Classical and Continuum Physics</subject><subject>Classical Mechanics</subject><subject>Conformal mapping</subject><subject>Edge cracks</subject><subject>Elastic bending</subject><subject>Elastic plates</subject><subject>Fluid- and Aerodynamics</subject><subject>Least squares method</subject><subject>Linear algebra</subject><subject>Mathematical analysis</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mechanical Engineering</subject><subject>Mechanical properties</subject><subject>Physical properties</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Plate material</subject><subject>Polynomials</subject><subject>Singular value decomposition</subject><issn>0021-8944</issn><issn>1573-8620</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLw0AQhRdRsFZ_gLcFz6szm02yOabptg1sk9JuBU9hmyZi0bYm7cF_74YIHkTmMDDve2_gEXKP8IjoiacVAEcZCcE5CEAfLsgA_dBjMuBwSQadzDr9mty07Q4AIonhgJhVrp_TbErNTNHFMh9pNaf5hCqtErPM2TyeZsrkTOl4ZdKEjlQ27nCHxHS-1iZd6Bea5FnmeDWmCx0bdUuuavveVnc_e0jWE2WSGdP5NE1izUqM5IkFwP2NLIFXlW9labcy8m3pW-vONW7BoggCxDJEUVshMYo8jED4wsLGs0HtDclDn3tsDp_nqj0Vu8O52buXBQ_doAQvdBT2VNkc2rap6uLYvH3Y5qtAKLryij_lOQ_vPa1j969V85v8v-kbqqRnVw</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Kaloerov, S. 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Moreover, with the help of conformal mappings, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the generalized least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular value decomposition. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electro-magneto-elastic state is studied.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0021894422040150</doi><tpages>12</tpages></addata></record> |
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| subjects | Analytic functions Applications of Mathematics Boundary conditions Classical and Continuum Physics Classical Mechanics Conformal mapping Edge cracks Elastic bending Elastic plates Fluid- and Aerodynamics Least squares method Linear algebra Mathematical analysis Mathematical Modeling and Industrial Mathematics Mechanical Engineering Mechanical properties Physical properties Physics Physics and Astronomy Plate material Polynomials Singular value decomposition |
| title | SOLVING THE PROBLEM OF ELECTRO-MAGNETO-ELASTIC BENDING OF A MULTIPLY CONNECTED PLATE |
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