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A refined theory for laminated beams: Part I—A new high order approach

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Abstract

This paper presents a new displacement-based one-dimensional model for the analysis of multilayered composite beams. The kinematic restriction of cross sections rigid in their own planes is introduced. The axial displacements over the cross sections are represented in terms of explicitly defined piecewise polynomial warping functions with discontinuous derivatives at the interlaminae, whereas the amplitude of the displacements along the beam axis is established by means of a variational formulation. It is proved that the proposed representation of the axial displacements yields the exact solution of the ‘interior domain problem’ for a beam subjected to a transverse load varying according to a polynomial law. It is shown that two or three coordinate functions are sufficient to yield continuous distributions of equilibrated stresses except for small neighborhoods of the constrained cross sections, where a higher number of warping functions could be used in order to obtain a better accuracy. The numerical results show excellent agreement with plane stress finite element and plane strain exact solutions.

Sommario

In questo lavoro viene presentato un nuovo modello monodimensionale per l'analisi di travi composite multistrato. Viene introdotta l'ipotesi di indeformabilita delle sezioni nel proprio piano mentre gli spostamenti assiali nella sezione sono rappresentati facendo uso di funzioni ‘ingobbamento’ definite sull'intera altezza e con derivata discontinua all'in erlamina. Infine, l'ampiezza degli spostamenti lungo l'asse della trave è determinata facendo uso di una formulazione variazionale. Si mostra come la rappresentazione degli spostamenti assiali proposta sia in grado di fornire la soluzione esatta, ‘all'interno del dominio’, per una trave soggetta ad un carico trasversale variabile con legge nolinomiale. Due o tre funzioni coordinate sono sufficienti a fornire distribuzioni di sforzi che verificano l'equilibrio anche all'interlamina, a meno di zone rislrette in vicinanza di sezioni vincolate. I risultati numerici mostrano un eccellente accordo con soluzioni agli elementi finiti in stato piano di tensione e con soluzioni esatte in stato piano di deformazione.

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Authors and Affiliations

  1. Istituto li Tecnica delle Costruzioni, Università di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Marco Savoia

  2. Dipartimento di Costruzioni, Università di Firenze, Plazza Brunelleschi 6, 50121, Firenze, Italy

    Ferdinando Laudiero & Antonio Tralli

Authors
  1. Marco Savoia
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  2. Ferdinando Laudiero
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  3. Antonio Tralli
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Savoia, M., Laudiero, F. & Tralli, A. A refined theory for laminated beams: Part I—A new high order approach. Meccanica 28, 39–51 (1993). https://doi.org/10.1007/BF00990288

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