Experimentally Determined Stresses at Geometric Discontinuities Using Simple Stress Functions

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

doi:10.1061/(asce)em.1943-7889.0000916

Cited by 2 publications

(4 citation statements)

References 5 publications

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“…Unlike earlier approaches 7–9 based on a complicated stress function resulted from an extensive algebra to analytically impose the traction-free condition around the hole and explicitly include the effect of the applied load, excellent results are obtained here using CVM. The present hybrid-TSA approach based on CVM was compared with earlier approaches using the same number and source locations of the measured TSA input values (Figures 2 and 3).…”

Section: Discussionmentioning

confidence: 92%

“…37 The general solution contains numerous coefficients (theoretically infinite), called Airy coefficients, and which can be reduced by utilizing symmetry and/or satisfying the traction-free condition around the circular hole. Khaja and Rowlands 9 used the general solution of Airy stress function to solve for the hybrid stresses from the thermoelastic data. This approach is referred to herein as Simple Airy stress method .…”

Section: Relevant Equationsmentioning

confidence: 99%

“…The loaded plates in Figure 1(a) and (b) were previously stress-analyzed by hybridizing the thermal information with the Mitchell solution. 7–9 The Mitchell solution, which is the general solution of biharmonic equation in polar coordinates with assumption of periodic solution, consists of an infinite number of coefficients and its form depends on the geometry, loading, and boundary conditions, whether the component is boundedness at origin or infinity, and single-valued stresses and displacements. The coefficients can also be reduced by imposing the traction-free condition analytically along the boundary of the hole.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the previous approaches 7–9 where their analyses utilized complicated and restrictive stress functions because of the asymmetry about the x - or y -axes, the present analysis uses only one form of the stress function to solve both the central- and offset-loaded plates (Figure 1(a) and (b)). The advantageous of using this approach is considered to be more general and substantially involve simpler formulation than the previous approaches based on Mitchell solution.…”

Section: Introductionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 92%

Section: Relevant Equationsmentioning

confidence: 99%