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A Procedure for Multiple Damage Identification in Elastic Beams
No full textThis paper concerns with the identification of multiple cracks in a beam by measurements of the damage-induced variations in the
static deflection of the beam under a prescribed load condition. Each crack is simulated by an equivalent linear elastic rotational
spring connecting the two adjacent segments of the beam. Sufficient conditions on the static measurements which allow for the
unique identification of the damage are presented and discussed for beams under various sets of boundary conditions. The analysis is
based on an explicit expression of the crack-induced variation in the static deflection of the beam. The present results are obtained by
non trivial extension of recent results given by the authors regarding the identification of a single crack in a beam by static tests
The Hu-Washizu variational principle for the identification of imperfections in beams
No full textThis paper presents a procedure for the identification of imperfections of structural parameters based on displacement measurements by static tests. The proposed procedure is based on the well-known Hu-Washizu variational principle, suitably modified to account for the response measurements, which is able to provide closed-form solutions to some inverse problems for the identification of structural parameter imperfections in beams
Crack detection in elastic beams by static measurements
No full textThis paper deals with the
identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the
beam. The crack is simulated by an equivalent linear spring
connecting the two adjacent segments of the beam. Sufficient conditions on static measurements which allow for the unique
identification of the crack are presented and discussed. The inverse analysis provides exact closed-form expressions of position and severity of the crack as functions of deflection measurements for different boundary conditions. The theoretical results are confirmed by a comparison with static measurements on
steel beams with a crack. Extension of the presented analysis to multiple cracks is briefly discussed
Multi-cracked Euler-Bernoulli beams: Mathematical modeling and exact solutions
No full textLocalized flexibility models of cracks enable one for simple and effective representation of the behavior of damaged beams and frames. Important applications, such as the determination of closed-form solutions
and the development of diagnostic methods of analysis have attracted the interest of many researchers in
recent years. Nevertheless, certain fundamental questions have not been completely clarified yet. One of
these issues concerns with the mechanical justification of the macroscopic model of rotational elastic
spring commonly used to describe the presence of an open crack in a beam under bending deformation.
Two main analytical formulations have been recently proposed to take into account the singularity generated by the crack. The crack is represented by suitable Dirac’s delta functions either in the beam’s flexural rigidity or in the beam’s flexural flexibility. Both approaches require some caution due to
mathematical subtleties of the analysis. Motivated by these considerations, in this paper we propose a
justification of the rotational elastic spring model of an open crack in a beam in bending deformation.
We show that this localized flexibility model of a crack is the variational limit of a family of one-dimensional
beams when the flexural stiffness of these beams tends to zero in an interval centered at the
cracked cross-section and, simultaneously, the length of the interval vanishes in a suitable way. We also
show that the static and dynamic problem for the flexibility model of cracked beam can be formulated
within the classical context of the theory of distributions, avoiding the hindrances encountered in previous
approaches to the problem. In addition, the proposed treatment leads to a simple and efficient determination
of exact closed form solutions of both static and dynamic problems for beams with multiple
cracks
Detecting Multiple Open Cracks in Elastic Beams by Static Tests
No full textThis paper concerns with the
identification of multiple open cracks in a beam by measurements
of the damage-induced variations in the static deflection of the
beam under a prescribed load condition. Each crack is simulated by
an equivalent linear spring connecting the two adjacent segments
of beam. Sufficient conditions on the static measurements which
allow for the unique identification of the damage are presented
and discussed for nonuniform beams under some ideal boundary
conditions. The inverse analysis is based on an explicit
expression of the crack-induced variation in the deflection of the
beam under a given load distribution and it provides exact
closed-form expressions of position and severity of the cracks in
terms of the measured data. The theoretical results are confirmed
by a comparison with static tests carried out on a steel beam with
localized damages
Theorems of restricted dynamic shakedown
No full textDynamic shakedown for a rate-independent material with internal variables is addressed in the hypothesis that the load values are restricted to those of a specified load history of finite or even infinite duration, thus ruling out the possibility-typical of classical shakedown theory-of indefinite load repetitions. Instead of the usual approach to dynamic shakedown, based on the bounded plastic work criterion, another approach is adopted here, based on the adaptation time criterion. Static, kinematic and mixed-form theorems are presented, which characterize the minimum adaptation time (MAT), a feature of the structure-load system, but which are also able to assess whether plastic work is finite or not in the case of infinite duration load histories, where they then prove to be equivalent to known shakedown theorem
Shakedown problems for material models with internal variables
No full textThe classical shakedown theory is reconsidered with the objective of extending it to a quite general constitutive law for rate-insensitive elastic-plastic material models endowed with dual internal variables and thermodynamic potential. The statical and kinematical shakedown theorems, the corresponding approaches to the shakedown load multiplier problem and a deformation bounding theorem are presented and discussed with a view of further developments
Gaussian and non-Gaussian stochastic sensitivity analysis of discrete structural system
No full textThe derivatives of the response of a structural system with respect to the system parameters are termed sensitivities. They play an important role in assessing the effect of uncertainties in the mathematical model of the system and in predicting changes of the response due to changes of the design parameters. In this paper, a time domain approach for evaluating the sensitivity of discrete structural systems to deterministic, as well as to Gaussian or non-Gaussian stochastic input is presented. In particular, in the latter case, the stochastic input has been assumed to be a delta-correlated process and, by using Kronecker algebra extensively, cumulant sensitivities of order higher than two have been obtained by solving sets of algebraic or differential equations for stationary and non-stationary input, respectively. The theoretical background is developed for the general case of multi-degrees-of-freedom (MDOF) primary system with an attached secondary single-degree-of-freedom (SDOF) structure. However, numerical examples for the simple case of an SDOF primary-secondary structure, in order to explore how variations of the system parameters influence the system, are presented. Finally, it should be noted that a study of the optimal placement of the secondary system within the primary one should be conducted on an MDOF structure
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