Use of the reciprocity theorem for axially symmetric transient problems

Kadioglu, N.; Ataoglu, S.

doi:10.1007/bf02637034

Cited by 2 publications

(5 citation statements)

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“…In general, this state can be used as the fundamental state in reciprocal theorem to compute the boundary and interior values of any problem defined in a cylindrical region, either. But for axially symmetric problems, another simpler fundamental state, which has been constructed by (Kadioglu and Ataoglu, 2005;2006), has been used to calculate the boundary values and this state was named as the first fundamental state in text. The construction of the second fundamental state can be seen to be a relatively easy problem in comparison with the first elastodynamic state but the expressions of the displacement and stress components of this state are very long, complicated and they are the functions of time t, the radial distance R from origin, and the polar angle θ while in the expressions of the first one has only R and t as independent variables.…”

Section: Discussionmentioning

confidence: 99%

“…In the first problem, it is accepted that this pressure is constant (Kadioglu and Ataoglu, 2005) while it varies with time in the second (Kadioglu and Ataoglu, 2006). The pressure is applied at t=0 in both problems.…”

Section: Sample Problemsmentioning

confidence: 99%

“…This case has been solved before by Kadioglu and Ataoglu (2005). But the results of it have been given in Table 1 since they will be used to calculate the inner values of displacement vector and stress tensor.…”

Section: Sample Problemsmentioning

confidence: 99%

“…Another elastodynamic state S R 1 [u R 1 , τ R 1 , f R 1 ] must be constructed for this purpose. If, in an infinite plane region, a body force, having the magnitude δ(t) acting at a specific point y, in the direction of Cartesian base vector, e k (k=1, 2) exists, the displacement vector u k due to this body force at an arbitrary point x and at the time t can be expressed as (Achenbach, 1973;2003;Kadioglu and Ataoglu, 2005):…”

Section: The Second Elastodynamic Statementioning

confidence: 99%

“…First stage is the determination of the unknown boundary values. For this purpose, the fundamental state given by Kadioglu and Ataoglu (2005) has been revised eliminating some zero terms. And, using this as the first elastodynamic state in reciprocity theorem, an integral equation has been obtained for a problem, representing a cylindrical cavity under a pressure which varies arbitrarily by time.…”

Section: Introductionmentioning

confidence: 99%

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Propagation of axial symmetric, transient waves from a cylindrical cavity

Kadioglu

Ataoglu

2010

KSCE J Civ Eng

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The aim is to determine the displacement and the stress fields for a cylindrical cavity under a transient pressure which is an arbitrary function of time. A fundamental solution, given by Kadioglu and Ataoglu, has been revised to be used in reciprocal theorem for the solutions of axially symmetric transient problems of elastodynamics. An integral equation, whose unknown is the radial displacement on the boundary, has been written, using this fundamental solution in reciprocal identity. The boundary values of two sample problems, have been determined by solving this integral equation. To calculate the propagation of the displacement field in the region for any axially symmetric problem, a second elastodynamic state has also been derived. This new elastodynamic state has been used in reciprocity theorem to compute the time-variations of the displacement and the stresses at any point in the region for both sample problems. Whole singularities arising in every stage of the formulation have been eliminated. The most interesting result of the presented solution is the representation of a propagating wave by two different two-dimensional integrals at any interior point. Each of these integrals is valid for a different time interval and these intervals are defined by the position of the mentioned interior point.

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Section: Discussionmentioning

confidence: 99%

Section: Sample Problemsmentioning

confidence: 99%

Section: Sample Problemsmentioning

confidence: 99%

Section: The Second Elastodynamic Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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