“…In addition to the present use of real, rather than complex, variables being mathematically convenient for such problems, the current approach avoids the need for mapping and extends capability. For example, based on Reference [30], it would be more difficult to experimentally stress analyse the arbitrarily shaped hole or the loaded hole in an orthotropic material or to carry out the superposition described in References [40–42] using complex rather than real variables.…”
Section: Summary Discussion and Conclusionmentioning
This paper determines the individual components of stress experimentally in a finite tensile plate containing an elliptical hole using a series representation of an Airy stress function in terms of polar coordinates. The Airy coefficients are evaluated from measured temperature information. As well as satisfying force equilibrium, the thermoelastic results are substantiated independently using strain gages and finite element analysis. Employing real, rather than the commonly used complex, variables can be easier for such problems, avoids inconveniences associated with conformal mapping and the concept is applicable to experimental analysis of arbitrarily shaped and/or loaded cut-outs.
“…In addition to the present use of real, rather than complex, variables being mathematically convenient for such problems, the current approach avoids the need for mapping and extends capability. For example, based on Reference [30], it would be more difficult to experimentally stress analyse the arbitrarily shaped hole or the loaded hole in an orthotropic material or to carry out the superposition described in References [40–42] using complex rather than real variables.…”
Section: Summary Discussion and Conclusionmentioning
This paper determines the individual components of stress experimentally in a finite tensile plate containing an elliptical hole using a series representation of an Airy stress function in terms of polar coordinates. The Airy coefficients are evaluated from measured temperature information. As well as satisfying force equilibrium, the thermoelastic results are substantiated independently using strain gages and finite element analysis. Employing real, rather than the commonly used complex, variables can be easier for such problems, avoids inconveniences associated with conformal mapping and the concept is applicable to experimental analysis of arbitrarily shaped and/or loaded cut-outs.
“…, 7 with kind permission from Springer Science and Business Media).Figure 3.Thermoelastic data source locations ( m = 849 data points) for the plate in Figure 1(b) (reprinted from Lin et al . , 8 with kind permission from Elsevier).…”
Section: Methodsmentioning
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%
“…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. Although the effect of the external applied load is implicitly included in the measured data, previous approaches 7,8 explicitly accounted for the effect of the load and consequently formulated a complicated stress function. In contrast with the prior applications of the CVM while utilizing geometrical and loading symmetry to retain only the odd and real coefficients of the stress function, the present method considers asymmetrical cases, which necessitate retaining all the terms in the stress function.…”
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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