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Energy release rate for constrained and unconstrained modes in a delaminated beam-plate subjected to compressive load

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Abstract

This paper presents elastic buckling and post-buckling analysis of an axially loaded isotropic beam-plate with an across-the-width delamination located at a given depth, subjected to in-plane compression. A simple analytical model for determining the global buckling load of the plate with delamination and the mode shape is developed, for various delamination depths and lengths. The influence of applied load on the displacement for a given crack length and depth is studied in the post-buckling state where the nonlinear large rotations are included. It is observed that the global buckling load for local delamination buckling increases with the increase in delamination depth from the upper surface, for a given delamination length, and the buckling load decreases if delamination length increases for a given delamination depth. In the post-buckling analysis, the displacement increases as the applied load increases. Strain energy release rate is calculated in the post-buckling state for both unconstrained and constrained local buckling modes.

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Abbreviations

\({{\varvec{a}}}\) :

Spanwise location of crack

\({{\varvec{b}}}\) :

Crack length

:

Depth from the upper surface

:

Depth from the lower surface

:

Depth of beam

\({{\varvec{l}}}\) :

Length of beam

b :

\({{\varvec{b}}} /{{\varvec{l}}}\)(non-dimensional)

a :

\({{\varvec{a}}} /{{\varvec{l}}}\)(non-dimensional)

\({\hbox {d}_{2}}\) :

(non-dimensional)

\({\hbox {d}_{3}}\) :

(non-dimensional)

\({P}_{i}\) :

Applied compressive load in ith region

\({D}_{i}\) :

Flexural rigidity of ith region

\({w}_{i}\) :

Transverse deflection of ith beam

\({A}_{\mathrm{ci}}\) :

Area of cross section of ith region

G:

Energy release rate

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Authors and Affiliations

  1. Structural Technologies Division, CSIR-National Aerospace Laboratories, Bangalore, India

    Lalitha Chattopadhyay

  2. Birla Institute of Technology and Science, Pilani, Hyderabad, India

    Pushkar Kumar Jain

Authors
  1. Lalitha Chattopadhyay
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  2. Pushkar Kumar Jain
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Correspondence to Lalitha Chattopadhyay.

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Chattopadhyay, L., Jain, P.K. Energy release rate for constrained and unconstrained modes in a delaminated beam-plate subjected to compressive load. Arch Appl Mech 86, 907–919 (2016). https://doi.org/10.1007/s00419-015-1069-5

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  • DOI: https://doi.org/10.1007/s00419-015-1069-5

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