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  <front xmlns:xlink="http://www.w3.org/1999/xlink">
    <journal-meta>
      <journal-id journal-id-type="elibrary">75504</journal-id>
      <journal-title-group>
        <journal-title>Magazine of Civil Engineering</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Magazine of Civil Engineering</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2712-8172</issn>
    </journal-meta>
    <article-meta xmlns:xlink="http://www.w3.org/1999/xlink">
      <article-id pub-id-type="publisher-id">7</article-id>
      <article-id pub-id-type="doi">10.18720/MCE.89.7</article-id>
      <title-group>
        <article-title>Mixed finite-element method in V.I. Slivker’s semi-shear thin-walled bar theory</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Смешанный метод конечных элементов  в полусдвиговой теории тонкостенных стержней В.И. Сливкера</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0000-0003-3850-424X</contrib-id>
          <contrib-id contrib-id-type="scopus">56091980300</contrib-id>
          <name>
            <surname>Lalin</surname>
            <given-names>Vladimir</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>vllalin@yandex.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0000-0002-2299-3096</contrib-id>
          <contrib-id contrib-id-type="scopus">56296687300</contrib-id>
          <name>
            <surname>Rybakov</surname>
            <given-names>Vladimir</given-names>
          </name>
          <xref ref-type="aff" rid="aff2"/>
          <email>fishermanoff@mail.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Ivanov</surname>
            <given-names>Sergey</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>serzikserzik@gmail.com</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Azarov</surname>
            <given-names>Artur</given-names>
          </name>
          <xref ref-type="aff" rid="aff1"/>
          <email>alexio009@mail.ru</email>
        </contrib>
      </contrib-group>
      <aff id="aff1">Peter the Great St. Petersburg Polytechnic University</aff>
      <aff id="aff2">Peter the Great Saint Petersburg Polytechnic University</aff>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2019-09-19">
        <day>19</day>
        <month>09</month>
        <year>2019</year>
      </pub-date>
      <issue>5</issue>
      <issue-id pub-id-type="publisher-id">89</issue-id>
      <fpage>79</fpage>
      <lpage>93</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://engstroy.spbstu.ru/userfiles/files/2019/5(89)/07.pdf"/>
      <abstract xml:lang="en">
        <p>Mixed variational formulation of static and dynamic problems for thin-walled beams is presented. Stiffness and mass matrixes are derived from the Reissner-like functional. Shear deformation is taken into account by using Slivker’s semi-shear theory of thin-walled bars. Corresponding Euler equations are derived from the proposed mixed functional. Linear Hermite polynomials were considered as approximation for all the internal forces and displacements functions. The exact analytical solutions to some particular eigenfrequency and static problems for thin-walled beam are obtained from mixed formulation. The effect of “spurious” frequencies in thin-walled beam spectrum is discussed. Comparison of the numerical results from the mixed and classical finite element methods is presented.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>mixed finite element method</kwd>
        <kwd>thin-walled beam</kwd>
        <kwd>Slivker’s semi-shear theory</kwd>
        <kwd>Reissner’s functional</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
