Sommario
Si studiano modelli discreti di telai elastoplastici. I legami tra momento flettente e rotazione plastica sono lineari a tratti. Si determina l'intera evoluzione delle deformazioni plastiche al crescere proporzionale e monotono dei carichi, formulando e risolvendo un “problema parametrico lineare di complementarietà”. La tecnica numerica alquanto efficiente adottata, è fornita da recenti risultati di R. W. Cottle. Il metodo è esteso a processi di caricamento “proporzionali a stadi”, tenendo conto, tra stadio e stadio, della irreversibilità della deformazione plastica.
Summary
Discrete models of elastoplastic beams and frames are considered. The plastic deformability laws (bending moments versus plastic rotations) are piecewise linearized. Plastic deformations are sought as they develop along a proportional loading process. The “historical” analysis in this sense, is shown to be ameneable to the solution of a “parametric linear complementarity problem”. Recent mathematical results on this problem, due to R. W. Cottle, are used to obtain numerical solutions. Extensions are pointed out to stepwise proportional loading paths, allowing for the irreversible nature of plastic deformations.
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Abbreviations
- λ :
-
vectors of plastic multipliers, auxiliary variables, positive constants
- gf :
-
vectors of plastic multipliers, auxiliary variables, positive constants
- κ :
-
vectors of plastic multipliers, auxiliary variables, positive constants
- H :
-
hardening coefficients
- α :
-
load factor
- Q :
-
generalized stresses (e.g. bending moments,M)
- p :
-
generalized plastic strains (e.g. relative rotationsϑ at critical sections)
- N :
-
block diagonal matrix
- Z :
-
matrix which transforms strains into corresponding stresses
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De Donato, O., Maier, G. Historical deformation analysis of elastoplastic structures as a parametric linear complementarity problem. Meccanica 11, 166–171 (1976). https://doi.org/10.1007/BF02133868
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DOI: https://doi.org/10.1007/BF02133868