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A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes

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Sommario

Si formulano, con notazione matriciale, generali leggi costitutive linearizzate a tratti e dotate di normalità, e se ne discutono alcune proprietà e la specializzazione ad usuali tipi di incrudimento (in particolare cinematico ed isotropo). Riferendosi a modelli strutturali per elementi finiti, si ottengono i risultati seguenti:a) la soluzione olonoma per dati carichi e distorsioni viene caratterizzata da sei proprietà estremali di natura “quadraticolineare”, due di validità generale, quattro di validità condizionata;b) corrispondenti teoremi in ambito differenziale vengono proposti per analogia; si danno degli enunciati di confronto tra soluzioni olonome ed anolonome;c) si fornisce un teorema sull'assestamento in campo elastico sotto azioni esterne variabili in presenza di forze d'inerzia e resistenze viscose, generalizzando alle structure incrudenti un teorema di Ceradini, e per specializzazione ai casi quasi-statici quello di Melan;d) si propone un metodo per valutare in assenza di scarichi locali, o delimitare superiormente il coefficiente di sicurezza nei confronti di rotture locali dovute a limitata deformabilità plastica.

Summary

General piecewise linear constitutive laws with associated flow rules are formulated in matrix notation; some properties and specializations (in particular to kinematic and isotropic hardening) are discussed.

With reference to finite element models of structures and, hence, in matrix-vector description, the following results are achieved:

a) the holonomic solutions to the analysis problem for given loads and dislocations are shown to be characterized by means of six “quadratic-linear” minimum principles, two of general, four of conditioned validity;b) the incremental counterparts of the above theorems are indicated by analogy; some comparison properties concerning holonomic and nonholonomic solutions, are pointed out;c) a shakedown theorem is established for variable repeated loads and dislocations, with allowance for inertia forces and viscous damping, i. e. a generalization to workhardening structures of Ceradini's and (in quasi-static situations) Melan's theorems;d) a method is proposed for evaluating under holonomy hypothesis, or bounding from above, the safety factor with respect to local failure due to limited plastic strain capacity.

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Authors and Affiliations

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

    Giulio Maier

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  1. Giulio Maier
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The study presented here forms part of a research program supported by the C.N.R. (Gruppo Plasticità).

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Maier, G. A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica 5, 54–66 (1970). https://doi.org/10.1007/BF02133524

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