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Meccanica

, Volume 28, Issue 3, pp 217–225 | Cite as

A refined theory for laminated beams: Part II—An iterative variational approach

  • Marco Savoia
  • Antonio Tralli
  • Ferdinando Laudiero
Article

Abstract

This paper presents a displacement-based one-dimensional model for the analysis of laminated composite beams, based on the assumption of cross sections rigid in their own planes. The proposed model is mainly focused on the boundary layer analysis. The representation of the axial displacements is given as products between line functions and warping modes of the cross section. Both the sets of unknown functions are determined by means of a variational formulation in order to obtain the ‘best choice’ for the thickness coordinate functions. The minimization of the total potential energy functional is reduced to a sequence of linear problems by means of a gradient technique. Various examples referring to simply supported and cantilever beams, subjected to distributed or concentrated loads, are solved. The results for stress distributions are found to be in excellent agreement with exact plane strain and finite element plane stress solutions even at very low distances from the end sections.

Key words

Composite structures Laminated beams Boundary layer analysis 

Sommario

In questo lavoro viene presentato un modello monodimens onale agli spostamenti per l'analisi di travi in laminato multistrato fondato sull'ipotesi di sezioni indeformabili nel proprio piano. Il modello è finalizzato principalmente allo studio degli effetti di bordo. Gli spostamenti assiali vengono espressi attraverso prodotti fra funzioni di linea e modi di ingobbamento della sezione. Entrambi gli insiemi di funzioni incognite sono determinati attraverso una formulazione variazionale allo scopo di ottimizzare le forme di ingobbamento della sezione. La minimizzazione del funzionale dell'energia potenziale totale viene ridotta ad una sequenza di problemi lineari mediante una tecnica tipo gradiente operando alternativamente le varizioni rispetto ai due insiemi di funzioni incognite. Negli esempi risolti, gli stati tensionali ottenuti risultano in eccellente accordo con soluzioni esatte (in stato piano di deformazione) e con soluzioni agli elementi finiti (in stato piano di tensione) anche in prossimità delle sezioni estreme libere o vincolate.

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Marco Savoia
    • 1
  • Antonio Tralli
    • 2
  • Ferdinando Laudiero
    • 2
  1. 1.1 stituto di Tecnica delle CostruzioniUniversità di BolognaBolognaItaly
  2. 2.Di partimento di CostruzioniUniversità di FirenzeFirenzeItaly

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