1,721,113 research outputs found
Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening.
No full textFor a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load-step is formulated according to an implicit, backward-difference (stepwise-holonomic) scheme for time integration, with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonic convergence of an iterative predictor-corrector algorithm for the solution of the finite-step analysis problem. A version of this algorithm apt to both speed up and guarantee convergence is tested by an illustrative example
Energy properties of solutions to quasi-brittle fracture mechanics problems with piecewise linear cohesive crack models
No full textElastic-plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming
No full textFrames (and more general beam systems) subjected to monotonic loading are modelled by conventional finite elements with the traditional assumption of possible plastic deformations concentrated in pre-selected “critical sections”. The inelastic behaviour of these beam sections, i.e. the development of “plastic hinges”, is described by piece-wise-linear constitutive models allowing for hardening and/or softening, in terms of generalized stresses and conjugate kinematic variables.
The following topics are discussed: step-by-step analysis methods, both “exact” and stepwise holonomic; path bifurcations and overall stability; limit and deformation analyses combined, as an optimization problem under complementarity constraints apt to compute the safety factor (with respect to global or local failures); numerical tests of non-conventional algorithms by means of simple representative applications.
The objective of the paper is to provide a unified methodology and to propose novel procedures for inelastic analyses of frames up to failure, in the light of recent results in mathematical programming, particularly on complementarity theory
Static shakedown theorems in piecewise linearized poroplasticity
No full textA fully saturated two-phase solid or structure subjected to variable, in particular cyclic, external actions is described as a nonhardening poroelastoplastic material with piecewise linearized yield loci. With reference to a multifield finite element model, sufficient and
necessary conditions for shakedown are established by the static Melan's approach. Shakedown analysis by linear programming is briefly discussed
Dynamic shakedown analysis and bounds in non-associative poroplasticity with saturation hardening
No full textExtremum, convergence and stability properties of the finite-increment problem in elastic-plastic boundary element analysis.
No full textThe boundary element (BE) analysis is formulated by a symmetric (Galerkin weightedresidual, double-integration) approach, rather than by a traditional collocation or by a nonsymmetric-Galerkin approach. The internal variable associative elastoplastic material model is discretized in time by a stepwise-holonomic, backward-difference integration scheme: it is then enforced in a weighted-average sense over cells and reformulated in terms of cell generalized variables. In the above context the following results are established under suitable constitutive hypotheses; • (a) a minimum characterization of the solution to the discretized step-problem in finite increments; • (b) a convergence theorem concerning a conventional iterative algorithm for solving this problem; • (c) a proof of the stability of the marching solution method, in the sense of non-amplification of errors along a finite step sequence. An illustrative example corroborates the theoretical results
Dynamic shakedown and bounding theory for a class of nonlinear hardening discrete structural models
No full textShakedown analysis and bounding methods in elastic-plastic dynamics are dealt with here on the following basis: the model adopted for the constitutive (element) behavior is centered on a linear dependence of yield functions on (generalized) stresses and nonlinear dependence (hardening) of yield limits on sign-constraint internal variables which play here a central role in all developments; simple discrete structural models (basically trusses) are referred to; constrained optimization in finite dimensional spaces (nonlinear programming) is the mathematical
and computational context employed.
The contributions presented are as follows: a number of earlier results based on piecewiselinear plastic models are extended to nonlinear hardening; restrictions on the hardening rule are established for various conclusions to be valid; a systematic and unified theoretical framework is developed, so that shakedown theorems and various bounds are shown to be closely related.
The theoretical results expounded are illustrated by simple numerical examples
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