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Influence of Shear Correction Factors on Eigenfrequencies of Layered Plates

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Advances in Mechanics of Materials and Structural Analysis

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 80))

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Abstract

In this paper layered composite plates subjected to static loading are considered. The theory is based on a multi-field functional, where the associated Euler–Lagrange equations include besides the global plate equations formulated in stress resultants, the local in-plane equilibrium in terms of stresses and a constraint which enforces the correct shape of warping through the thickness. Within representative volume elements out of plane warping displacements are interpolated with layerwise cubic functions in thickness direction and constant shape throughout the reference surface. Elimination of warping and Lagrange parameters by static condensation leads to a material matrix for the stress resultants and to shear correction factors for layered plates. For linear elasticity and constant thickness the computation can be done once in advance. The condensed material matrix is used in displacement based elements along with the enhanced strain method or in mixed hybrid elements with standard nodal degrees of freedom.

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Authors and Affiliations

  1. Fachgebiet Festkörpermechanik, Technische Universität Darmstadt, Franziska-Braun-Str. 7, 64287, Darmstadt, Germany

    Friedrich Gruttmann

  2. Institut für Baustatik, Karlsruher Institut für Technologie, Kaiserstr. 12, 76131, Karlsruhe, Germany

    Werner Wagner

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  1. Friedrich Gruttmann
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  2. Werner Wagner
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Correspondence to Friedrich Gruttmann .

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Editors and Affiliations

  1. Institute of Mechanics Faculty of Mechanical Engineering, Otto-von-Guericke-University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Fakultät 5, Abt. 1, Hochschule Bremen, Bremen, Bremen, Germany

    Frank Jablonski

  3. Institut für Mechanik, Technische Universität Berlin, Berlin, Germany

    Wolfgang H. Müller

  4. Institute of Mechanics, Faculty of Mechanical Engineering, Otto-von-Guericke-University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Konstantin Naumenko

  5. Institute for Lightweight Construction and Design (KLuB), Technische Universität Darmstadt, Darmstadt, Germany

    Patrick Schneider

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Gruttmann, F., Wagner, W. (2018). Influence of Shear Correction Factors on Eigenfrequencies of Layered Plates. In: Altenbach, H., Jablonski, F., Müller, W., Naumenko, K., Schneider, P. (eds) Advances in Mechanics of Materials and Structural Analysis. Advanced Structured Materials, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-70563-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-70563-7_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70562-0

  • Online ISBN: 978-3-319-70563-7

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