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A nonlinear composite shell element with continuous interlaminar shear stresses

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Abstract

A numerical model for layered composite structures based on a geometrical nonlinear shell theory is presented. The kinematic is based on a multi-director theory, thus the in-plane displacements of each layer are described by independent director vectors. Using the isoparametric apporach a finite element formulation for quadrilaterals is developed. Continuity of the interlaminar shear stresses is obtained within the nonlinear solution process. Several examples are presented to illustrate the performance of the developed numerical model.

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Abbreviations

Ω:

reference surface

ξα :

convected coordinates of the shell middle surface

iζ:

coordinate in thickness direction

i h :

thickness of layer i

Xo :

position vector of the reference surface

iXo :

position vector of midsurface of layer i

t k :

orthonormal basis system in the reference configuration

ia k :

orthonormal basis system of layer i

δiW:

axial vector

Ro :

orthonormal tensor in the reference configuration

iR:

orthonormal tensor of layer i

iσ:

Cauchy stress tensor

iP:

First Piola-Kirchhoff stress tensor

iq:

vector of interlaminar stresses

inα,imα :

vector of stress resultants and stress couple resultants

v x :

components of the normal vector of boundary Ωα

iNαβ, iQα, iMαβ :

stress resultants and stress couple resultants of First Piola-Kirchhoff tensor

\({}^i\tilde N^{\alpha \beta } ,{}^i\tilde Q^\alpha ,{}^i\tilde M^{\alpha \beta } \) :

stress resultants and stress couple resultants of Second Piola-Kirchhoff tensor

iεαβ, iκαβ, iγαβ :

strains of layer i

ΛK :

transformation matrix

uo :

displacement vector of layer 1

iβα :

local rotational degrees of freedom of layer i

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Authors and Affiliations

  1. Institut für Baumechanik und Numerische Mechanik, Universität Hannover, Appelstr. 9A, D-30167, Hannover, Germany

    F. Gruttmann, W. Wagner & L. Meyer

  2. Institut für Mechanik, Technische Hochschule Darmstadt, Hochschulstr. 1, D-64289, Darmstadt, Germany

    P. Wriggers

Authors
  1. F. Gruttmann
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  2. W. Wagner
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  3. L. Meyer
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  4. P. Wriggers
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Communicated by S. N. Atluri, May 19, 1993

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Gruttmann, F., Wagner, W., Meyer, L. et al. A nonlinear composite shell element with continuous interlaminar shear stresses. Computational Mechanics 13, 175–188 (1993). https://doi.org/10.1007/BF00370134

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