Generalized solutions of beams with jump discontinuities on elastic foundations

Yavari, Arash; Sarkani, Shahram; Reddy, J. N.

doi:10.1007/s004190100169

Cited by 39 publications

(12 citation statements)

References 10 publications

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“…when the R discontinuities due to internal springs and along-axis supports occur at distinct locations with respect to the S flexural-stiffness steps). Note that applications of the method by Yavari et al [4] have been also proposed by Yavari et al [5] for equilibrium stability problems and beams on elastic foundations [6].…”

Section: Introductionmentioning

confidence: 95%

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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Section: Introductionmentioning

confidence: 95%

Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

Failla

2010

Arch Appl Mech

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“…of the original beam, and (r + 2s) additional conditions. Extensions of the method to equilibrium stability problems and beams on elastic foundations have been also presented (Yavari and Sarkani, 2001a;Yavari et al, 2001b).…”

Section: Introductionmentioning

confidence: 98%

On Euler–Bernoulli discontinuous beam solutions via uniform-beam Green’s functions

Failla

Santini

2007

International Journal of Solids and Structures

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The bending problem of Euler-Bernoulli discontinuous beams is dealt with. The purpose is to show that uniform-beam Green's functions can be used to build efficient solutions for beams with internal discontinuities due to along-axis constraints and flexural-stiffness jumps. Specifically, upon deriving the equilibrium equation in the space of generalized functions, first it is seen that the original bending problem may be recast as linear superposition of a principal and an auxiliary bending problem, both involving a uniform reference beam and homogeneous boundary conditions. Then, based on the Green's functions of the reference beam, closed-form solutions are developed for the principal beam response, while the auxiliary beam response is obtained by solving, in general, (r + 2s) algebraic equations written at the discontinuity locations, being r the number of discontinuities due to along-axis constraints, and s the number of flexural-stiffness jumps. In this manner, an appreciable reduction of computational effort is achieved as compared to alternative analytical solutions in the literature.

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“…Yavari et al (2000) used the auxiliary beam method to solve the governing equations for uniform Euler-Bernoulli and Timoshenko beams with various jump discontinuities; Yavari et al (2001b) derived the differential equations in terms of single displacement and rotation functions for non-uniform beams with transverse and rotation jumps. This approach has been also applied to beams with elastic foundation (Yavari et al (2001a)) and slender beam-columns (Yavari and Sarkani (2001)). These procedures, however, do require the enforcements of continuity conditions at each jump, and hence additional integration constants are needed.…”

Section: Introductionmentioning

confidence: 98%

Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams

Palmeri

Cicirello

2011

International Journal of Solids and Structures

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a b s t r a c tDirac's delta functions enable simple and effective representations of point loads and singularities in a variety of structural problems, leading very often to elegant and otherwise unworkable closed-form solutions. This is the case of cracked beams under static loads, whose theoretical and practical significance has attracted in recent years the interest of many researchers. Nevertheless, analytical formulations currently available for this problem are not completely satisfactory, either in terms of computational efficiency, when the continuity conditions must be enforced with auxiliary equations, or in terms of physical consistency, when the singularities in the beam's flexural rigidity are represented with Dirac's delta functions having a questionable negative sign. These considerations motivate the present study, which offers a novel and physically-based modelling of slender Euler-Bernoulli beams and short Timoshenko beams with any number and severity of cracks, conducing in both cases to exact closed-form solutions. For validation purposes, a standard finite element code is used, along with two nascent deltas (uniform and Gaussian density functions) to describe a smeared increase in the bending flexibility around the abscissa of the crack.

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Generalized solutions of beams with jump discontinuities on elastic foundations

Cited by 39 publications

References 10 publications

Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

On Euler–Bernoulli discontinuous beam solutions via uniform-beam Green’s functions

Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams

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