Dynamic Stress Concentration Factors in a Plane with Circular Hole Under the Action of Impact Nonaxisymmetric Loads

Onyshko, L. I.; Senyuk, M. M.; Onyshko, O. E.

doi:10.1007/s11003-015-9782-3

Cited by 2 publications

(5 citation statements)

References 2 publications

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“…The plots in Figs. 1, 2 are originally different from the results of calculations obtained for this case in [4], using the method of finite differences by the time coordinate. Therefore, the consid ered problem was also solved analytically.…”

Section: ( ) P P ∞ ∞mentioning

confidence: 68%

“…t That is the hoop stresses at the initial moment on the boundary are not zero as it is assumed in some publications [4,17].…”

Section: Formula Of Inversion Of Thementioning

confidence: 99%

“…The analytical solution of the problem is constructed in [1,4]. The transforms from the hoop stresses on the hole bound ary are determined by the formulas ( )…”

Section: ( ) P P ∞ ∞mentioning

confidence: 99%

“…Therefore, other methods for solving dynamic problems of the elasticity theory are widely used in the literature. In par ticular, in [3] and Article [4] in the equations, the time deriva tives are preliminarily replaced by finite differences with subse quent application to the obtained BIEM equations. Let us note that when using these methods, the solutions are found step by step over time, and therefore errors can accumulate.…”

Section: Introductionmentioning

confidence: 99%

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Determination of stress concentration near the holes under dynamic loadings

Maksymovych¹,

Solyar²,

Sudakov³

et al. 2021

Nauk. visn. nat. hirn. univ.

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Purpose. To develop an approach for determining the stress state of plate structural elements with holes under dynamic loads with controlled accuracy. Methodology. The study was carried out on the basis of the Laplace transform and the method of integral equations. Findings. An approach to determining the dynamic stresses at the holes in the plates is proposed, which includes: the Laplace transform in the time coordinate; a numerical method for determining transformants of displacements and stresses based on the method of integral equations; finding originals on the basis of Prudnikovs formula adapted to dynamic problems of elasticity theory. The problem of determining the Laplace images for displacements is reduced to solving singular integral equations. Integral equations were solved numerically based on the approaches developed in the boundary element method. To find displacements and stresses, the Laplace transform inversion formulas proposed by Prudnikov are adapted to dynamic problems. The study on dynamic stresses at holes of various shapes was carried out. Originality. A new approach to the regularization of the Prudnikov formula for inverting the Laplace transform as applied to dynamic problems of the theory of elasticity has been developed. For its implementation: convergence of Fourier series based on pre-set stresses at the initial time is improved; the remainder is taken into account in the conversion formula. Practical value. A method has been developed for calculating the stress concentration at holes of arbitrary shape in lamellar structural elements under dynamic loads. The proposed approach makes it possible to determine stresses with controlled accuracy. The studies performed at circular and polygonal holes with rounded tops can be used in strength calculations for dynamically loaded plates. The influence of Poissons ratio on the concentration of dynamic stresses is analyzed.

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Section: ( ) P P ∞ ∞mentioning

confidence: 68%

“…t That is the hoop stresses at the initial moment on the boundary are not zero as it is assumed in some publications [4,17].…”

Section: Formula Of Inversion Of Thementioning

confidence: 99%

“…The analytical solution of the problem is constructed in [1,4]. The transforms from the hoop stresses on the hole bound ary are determined by the formulas ( )…”

Section: ( ) P P ∞ ∞mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Determination of stress concentration near the holes under dynamic loadings

Maksymovych¹,

Solyar²,

Sudakov³

et al. 2021

Nauk. visn. nat. hirn. univ.

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show abstract

“…By using a modified finite-difference method with respect to time and the method of Fourier series with respect to the angular variable in the works of Onyshko et al (2015) it is got the time dependence of the dynamic stress concentration on the hole for plane dynamic problem of the theory of elasticity.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stress Concentration at the Boundary of an Incision at the Plate Under the Action of Weak Shock Waves

Mikulich

Shvabyuk

Sulym

2017

Acta Mechanica Et Automatica

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This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of weak shock waves. For solution of the problem it uses the integral and discrete Fourier transforms. Calculation of transformed dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the developed algorithm is based on the method of mechanical quadratures and collocation technique. For calculation of originals of the dynamic stresses it uses modified discrete Fourier transform. The algorithm is effective in the analysis of the dynamic stress state of defective plates.

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Dynamic Stress Concentration Factors in a Plane with Circular Hole Under the Action of Impact Nonaxisymmetric Loads

Cited by 2 publications

References 2 publications

Determination of stress concentration near the holes under dynamic loadings

Determination of stress concentration near the holes under dynamic loadings

Dynamic Stress Concentration at the Boundary of an Incision at the Plate Under the Action of Weak Shock Waves

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