An Integral Equation for Damage Identification of Euler-Bernoulli Beams under Static Loads

Paola, Mario Di; Bilello, C.

doi:10.1061/(asce)0733-9399(2004)130:2(225)

Cited by 40 publications

(22 citation statements)

References 29 publications

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“…Numerical integration would be necessary, instead, if the existing methods in the literature were resorted to. It is also worth remarking that the proposed formulation appears particularly suitable for those applications, such as damage sensitivity, damage identification, or optimization, where a large number of solutions shall be built for different sets of discontinuity parameters [8,23,24]. In fact, even if the primitives μ [k] (y) and β [k] (y) are not available for the beam profile, the response variables here derived, Eq.…”

Section: Discussionmentioning

confidence: 99%

General finite element description for non-uniform and discontinuous beam elements

Failla

Impollonia

2011

Arch Appl Mech

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The theory of generalized functions is used to address the static equilibrium problem of Euler-Bernoulli non-uniform and discontinuous 2-D beams. It is shown that if simple integration rules are applied, the full set of response variables due to end nodal displacements and to in-span loads can be derived, in a closed form, for most common beam profiles and arbitrary discontinuity parameters. On this basis, for finite element analysis purposes, a non-uniform and discontinuous beam element is implemented, for which the exact stiffness matrix and the fixed-end load vector are derived. Upon computing the nodal response, no numerical integration is required to build the response variables along the beam element.

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Section: Discussionmentioning

confidence: 99%

General finite element description for non-uniform and discontinuous beam elements

Failla

Impollonia

2011

Arch Appl Mech

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“…Further, recognize that setting ψ − 0 = ψ + 0 = 0 in Eqs. (16) leads to the MGFs of the beam shown in Fig. 6, where w 0 = 1 is applied where no rotation discontinuity occurs.…”

Section: Moment Green's Functionsmentioning

confidence: 99%

“…(16) the B.C. are set, which lead to a matrix equation A (w) c (w) = v (w) formally identical to Eq.…”

Section: Moment Green's Functionsmentioning

confidence: 99%

“…Among the analytical methods to solve discontinuous beams, noteworthy are also the virtual distortion method pursued by Di Paola and Bilello [16], who have built a bending-moment integral solution for stepped beams with internal rotational springs; or the solution method by Stankovic and Atanackovic [17], who have built weak solutions for a stepped beam on an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

“…(8) for a point force occurring at a deflection discontinuity) and the pertinent MGFs (either Eq (17). or Eqs (16). for a point moment occurring at a rotation discontinuity) and then included in Eq.…”

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Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

Failla

2010

Arch Appl Mech

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Euler-Bernoulli arbitrary discontinuous beams acted upon by static loads are addressed. Based on appropriate Green's functions here derived in a closed form, the response variables are obtained: (a) for stepped beams with internal springs, as closed-form functions of the beam discontinuity parameters, without enforcing neither internal nor boundary conditions; (b) for stepped beams with internal springs and along-axis supports, as closed-form functions of the unknown reactions of the along-axis supports only, to be computed by enforcing pertinent conditions. A remarkable reduction in computational effort is achieved, in this manner, compared to competing methods in the literature.

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The Hu–Washizu variational principle for the identification of imperfections in beams

Caddemi

Paola

2008

Numerical Meth Engineering

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This 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

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An Integral Equation for Damage Identification of Euler-Bernoulli Beams under Static Loads

Cited by 40 publications

References 29 publications

General finite element description for non-uniform and discontinuous beam elements

General finite element description for non-uniform and discontinuous beam elements

Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

The Hu–Washizu variational principle for the identification of imperfections in beams

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