Analysis of unloading waves from suddenly punched hole in an axially loaded elastic plate

Barclay, D. W.; Moodie, T. B.; Haddow, J. B.

doi:10.1016/0165-2125(81)90014-7

Cited by 11 publications

(6 citation statements)

References 5 publications

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“…Thus we are able to replace the intuitive feeling upon which scientists base their decision to use rational functions by a more deterministic approach. For example, we would be able to tell a priori that the Pade method used in [3] may be expected to be accurate.…”

Section: Introductionmentioning

confidence: 99%

Explicit Nearly Optimal Linear Rational Approximation with Preassigned Poles

Stenger¹

1986

Mathematics of Computation

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Section: Introductionmentioning

confidence: 99%

Explicit Nearly Optimal Linear Rational Approximation with Preassigned Poles

Stenger¹

1986

Mathematics of Computation

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“…The linear problem of wave propagation, due to the sudden punching of a circular hole in a thin isotropic classically elastic plate, subjected to an initial uniaxial tension field, has been considered by Haddow and Mioduchowski [1], and Barclay et al [2]. This problem involves three independent variables: a radial coordinate, an azimuthal coordinate and time.…”

Section: Introductionmentioning

confidence: 99%

Waves from a Suddenly Punched Hole in an Elastic Sheet Subjected to Finite Simple Tension

Jiang

Haddow

2003

Mathematics and Mechanics of Solids

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EVWUDFW We consider the plane stress unloading waves emanating from a suddenly punched circular hole in a thin elastic sheet, subjected to an initial finite deformation simple tension. The sheet is assumed to be hyperelastic, isotropic, incompressible and thin enough that the generalized plane stress approximation is valid. It is further assumed that the plugging of the hole is due to normal impact of a cylindrical projectile and that the impact velocity of the projectile is sufficiently high that the plugging can be assumed instantaneous. The governing equations of the problem are obtained in Lagrangian form with respect to a reference configuration that is the initial stretched configuration. A numerical scheme is proposed for the solution of the governing equations, and numerical results are obtained for the neo-Hookean strain energy function. However with some additional complication other isotropic strain energy functions can be considered.

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“…Thus we are able to replace the intuitive feeling upon which scientists base their decision to use rational functions by a more deterministic approach. For example, we would be able to tell a priori that the Padé method used in [3] may be expected to be accurate.…”

Section: <Cn^jjfrmentioning

confidence: 99%

Explicit, nearly optimal, linear rational approximation with preassigned poles

Stenger¹

1986

Math. Comp.

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Abstract. This paper gives explicit rational functions for interpolating and approximating functions on the intervals [-1,1], [0, oo], and [-oo, oo]. The rational functions are linear in the functions to be approximated, and they have preassigned poles. The error of approximation of these rationals is nearly as small as the error of best rational approximation with numerator and denominator polynomials of the same degrees. Regions of analyticity are described, which make it possible to tell a priori the accuracy which we can expect from this type of rational approximation.1. Introduction and Summary. In this paper we attempt to give a constructive, affirmative answer to each of the following questions.1. Given a function / and an interval /, is it possible to tell a priori whether or not one can accurately approximate / via a low-degree rational function?2. Can such a rational function be easily constructed explicitly, so that one encounters no poles on the interval of approximation?3. Can one use the Thiele algorithm to construct or evaluate this rational function? 4. Can one tell a priori when we can expect the Thiele algorithm, the e-algorithm, or the Padé method to produce an accurate low-degree rational approximation?5. Does the error of this rational function compare favorably with the error of the best possible rational approximation of the same degree?Although we cannot give an affirmative answer to the above questions in all cases, we shall describe classes of analytic functions which house nearly all of the cases encountered by the author in applications, and for which the answer to each of the above questions is "Yes".We shall develop a class of rational approximations for interpolation over [-1,1], [0, oo], and [-oo, oo]. These rational approximations share many of the features of SINC methods summarized in [23]. The interpolation points of these rationals are the same as the SINC interpolation points, and the classes of functions which low-degree rationals approximate accurately are the same as the classes which the SINC functions approximate accurately.Indeed, the error bounds for, e.g., approximation on [-1,1] of functions analytic on the unit disc are the same as the SINC bounds, i.e., rationals have the same optimality properties as SINC methods. In using rationals instead of SINC functions, we lose many of the simple relations that SINC functions satisfy, such as

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Analysis of unloading waves from suddenly punched hole in an axially loaded elastic plate

Cited by 11 publications

References 5 publications

Explicit Nearly Optimal Linear Rational Approximation with Preassigned Poles

Explicit Nearly Optimal Linear Rational Approximation with Preassigned Poles

Waves from a Suddenly Punched Hole in an Elastic Sheet Subjected to Finite Simple Tension

Explicit, nearly optimal, linear rational approximation with preassigned poles

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