Experimentally Determined Stresses Associated with Elliptical Holes Using Polar Coordinates

Khaja, A. A.; Rowlands, R. E.

doi:10.1111/str.12018

Cited by 12 publications

(3 citation statements)

References 31 publications

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“…The thermal signals in conjunction with the Mitchell solution were hybridized to determine the full-field stress for different geometrical discontinuities and loading conditions. 11–14 The individual stresses in a tensile loaded plate containing a single-sided deep U-notch were experimentally determined from recorded load-induced and the full form of the Mitchell solution. 15 Recently, a finite, complicated-shaped plate containing an asymmetrical, irregularly shaped hole was thermally stress-analyzed while imposing the traction-free conditions on the internal and external boundaries.…”

Section: Introductionmentioning

confidence: 99%

Hybrid stress analysis of a near-surface circular hole in finite structures

Alshaya

Lin

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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The ability to stress-analyze complicated structures from recorded load-induced temperatures is demonstrated. The considered structures have a near-surface hole and subjected to a concentrated load. The complexity of the structure is simplified by conformal mapping, the traction-free condition on the boundary of the hole is analytically satisfied by analytic continuation, and the equilibrium and compatibility conditions are satisfied by means of Airy stress function in complex-variable formulation. For isotropic member that is cyclically loaded within its elastic range, the produced in-phase temperature variations are linearly proportional to the local changes in the normal stresses. Even though no recorded thermal data were used at or near to the edges, the present hybrid method simultaneously separates the load-induced temperatures into the individual stress components, determines reliably the boundary stress and hence the stress concentration, and smooths the measured input data. Unlike prior capabilities of using geometrical symmetry to simply the stress function representation, the present analysis retains all the terms in the stress functions. Therefore, the considered hybrid stress analysis approach of such complex structures extends significantly the applicability of thermoelastic stress analysis compared to prior capabilities and is considered to be the most complicated formulation of the hybrid complex-variable method to date. To support the reliability of the present hybrid method, the results were compared with finite element predictions and previous results based on Mitchell solution.

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Section: Introductionmentioning

confidence: 99%

Hybrid stress analysis of a near-surface circular hole in finite structures

Alshaya

Lin

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…As the bases of numerical and experiments methods [1][2][3], analytical and semi-analytical methods are of great interest for determining scattering problems around an elliptical cavity. An exact expression was derived by Unger [4] for a path-independent integral surrounding an elliptical hole in an infinite plate under the Tresca yield condition.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of elastic waves by an arbitrary cavity in an inhomogeneous medium with density variation

Hei

Yang

Wang

et al. 2016

Mathematics and Mechanics of Solids

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Based on complex function theory, an analytical solution for the dynamic stress concentration due to an arbitrary cylindrical cavity in an infinite inhomogeneous medium is investigated. Two different conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. By assuming that the medium density continuously varies in the horizontal direction with an exponential law and the elastic modulus is constant, the complex-value displacements and stresses of the inhomogeneous medium are explicitly obtained. The distribution of the dynamic stress for the case of an elliptical cavity are obtained and discussed in detail via a numerical example. The results show that the wavenumber, inhomogeneous parameters, and different values of aspect ratio have a significant influence on the dynamic stress concentration factors around the elliptical cavity.

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“…2. The magnitude of angle was determined by passing a MATLAB subroutine incrementally cos ψ sin ψ 2 cosψ sinψ sin ψ cos ψ 2 sinψ cosψ sinψ cosψ sinψ cosψ cos ψ sin ψ σ σ θθ σ θ (6) through sets of three neighboring points on the edge of the hole. A second-order polynomial was fitted to these coordinates whose derivative provided the tangential, -and normal -directions at the mid-location of these three points [7].…”

Section: Imposing Traction-free Boundary Conditions On Edge Of Holementioning

confidence: 99%

Thermoelastic Stress Analysis of a Finite Structure Containing an Asymmetrical-Oriented, Arbitrarily-Shaped Hole

Philip¹,

Rowlands²

2017

JMEA

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Stresses, particularly those at geometric discontinuities, influence the structural integrity of engineering components. Motivated by the prevalence of complicated-shaped perforated components, the objective of this paper is to demonstrate the ability to stress analyze loaded finite members containing asymmetrical, irregularly-shaped cutouts. Recognizing the difficulties in obtaining purely theoretical or numerical solutions for these situations, the paper presents an expeditious means of experimentally stress analyzing such structures. Processing the load-induced temperature information with a series representation of a stress function provides the independent stress components reliably full-field, including on the edge of a hole. The stresses satisfy equilibrium and strains satisfy compatibility. In addition to being able to stress analyze complicated shapes using real, rather than complex variables, the technique is significant in which it smooths the recorded thermal information, is widely applicable, and requires neither differentiating the measured data nor knowing the elastic properties or external boundary conditions. The latter is extremely important since the external loading is often unknown in practice. That the approach provides the independent stresses is also significant since fatigue analyses and strength criteria typically necessitate knowing the individual components of stress. Present results are supported by those from a finite element analysis, strain gage measurements and load equilibrium.

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Experimentally Determined Stresses Associated with Elliptical Holes Using Polar Coordinates

Cited by 12 publications

References 31 publications

Hybrid stress analysis of a near-surface circular hole in finite structures

Hybrid stress analysis of a near-surface circular hole in finite structures

Dynamic analysis of elastic waves by an arbitrary cavity in an inhomogeneous medium with density variation

Thermoelastic Stress Analysis of a Finite Structure Containing an Asymmetrical-Oriented, Arbitrarily-Shaped Hole

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