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Shear correction factors for layered plates and shells

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Abstract

In this paper layered composite shells 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 shell 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 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 and shells. For linear elasticity 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 the usual 5 or 6 nodal degrees of freedom. This allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems. The interlaminar shear stresses are evaluated via the constitutive law by back substitution of the eliminated parameters. The computed transverse shear stresses are automatically continuous at the layer boundaries and zero at the outer surfaces. Furthermore, the integrals of the shear stresses coincide exactly with the shear forces without introduction of further constraints.

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Authors and Affiliations

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

    F. Gruttmann

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

    W. Wagner

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  1. F. Gruttmann
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  2. W. Wagner
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Correspondence to W. Wagner.

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Dedicated to Prof. em. Dr.-Ing. habil. Dr.-Ing. E.h. Dr. h.c. mult. Erwin Stein on the occasion of his 85th birthday.

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Gruttmann, F., Wagner, W. Shear correction factors for layered plates and shells. Comput Mech 59, 129–146 (2017). https://doi.org/10.1007/s00466-016-1339-2

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  • DOI: https://doi.org/10.1007/s00466-016-1339-2

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