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On the homogenization of a laminate beam under transverse loading: extension of Pagano’s theory

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Abstract

Pagano’s flexural theory is extended in this work proposing two homogenization theories of flexure for laminated beams. The proposed homogenization approaches convert a given laminated beam configuration under transverse loading into a mechanically equivalent homogenized configuration resulting in a homogenized flexural rigidity or a flexural modulus. The theory thus developed converts a two-dimensional (2D) problem into an equivalent one-dimensional (1D) problem of transverse deflection of a macro-scale homogenized beam. The proposed homogenization approaches can be employed for a laminated beam with randomly oriented fiber directions having an asymmetric configuration, thereby eliminating the need to solve coupled partial differential equations by classical laminate theory. The proposed approaches thus extend the applicability of Pagano’s theory from being applied to \([0,\,90]\) laminates to a more general laminate. The applicability of the proposed homogenization approaches has also been discussed, and a comparison has been drawn with classical laminate theory. The proposed homogenization approaches are further successfully coupled with a progressive failure analysis framework based on anisotropic damage mechanics to demonstrate their applicability in meso-macro-coupling in laminated beam homogenization, which is highly appealing to the aeronautical field.

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Acknowledgements

The authors gratefully acknowledge the support of the Indian Academy of Sciences.

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Authors and Affiliations

  1. Structural Mechanics Group, Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India

    Harini Subramanian & Shantanu S. Mulay

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  1. Harini Subramanian
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  2. Shantanu S. Mulay
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Correspondence to Shantanu S. Mulay.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Subramanian, H., Mulay, S.S. On the homogenization of a laminate beam under transverse loading: extension of Pagano’s theory. Acta Mech 232, 153–176 (2021). https://doi.org/10.1007/s00707-020-02827-z

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  • DOI: https://doi.org/10.1007/s00707-020-02827-z

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