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Geometrical non-linear analysis of structures by finite elements

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Sommario

Nella nota si presenta una analisi generale di problemi geometricamente non lineari. Lo studio è effettuato ricorrendo al metodo degli elementi finiti e basandosi su una formulazione teorica che esprime l'equilibrio incrementale per mezzo della stazionarietà dell'energia potenziale totale incrementale.

Lo studio si articola nell'alternanza di due fasi distinte: dapprima si prevede la configurazione della struttura in seguito ad un certo incremento di carico esterno successivamente si corregge, mediante un procedimento iterativo, tale valutazione approssimata in modo da giungere ad una situazione equilibrata tra forze esterne e forze interne. Il metodo usato in questa fase è quello ben noto di Newton Raphson.

Diviene così possibile determinare la curva carichi-spostamenti anche in momenti successivi al buckling e si può determinare inoltre il carico critico tenendo conto della deformata precedente l'instabilità.

Summary

The paper shows a comprehensive analysis of geometrically non linear structural problems by the finite element method.

The theoretical approach is based on a variational principle stating the incremental equilibrium through the stationarity of a functional that could be defined as the incremental total potential energy. The analysis is carried out in two distinct phases: first a prediction of the behaviour of the structure subjected to an increment of load then a correction by means of Newton Raphson method of the results obtained in the previous incremental step.

The approach makes it possible to determine the complete load deflection curve either in the prebuckling region or in the postbuckling one and to find out the critical load taking into account the deflection prior to buckling (non linearized buckling analysis).

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Authors and Affiliations

  1. Istituto di Scienza e Tecnica delle Costruzioni, Politecnico di Milano, Italy

    Duilio Benedetti & Luigi Cedolin

  2. Civil Engineering Department, University of Southampton, UK

    Carlos Brebbia

Authors
  1. Duilio Benedetti
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  2. Carlos Brebbia
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  3. Luigi Cedolin
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This work has been sponsored by C.N.R. (the Italian Council of Research).

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Benedetti, D., Brebbia, C. & Cedolin, L. Geometrical non-linear analysis of structures by finite elements. Meccanica 7 (Suppl 1), 35–44 (1972). https://doi.org/10.1007/BF02133603

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