On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature1

Helsing, Johan; Jönsson, Anders

doi:10.1115/1.1427691

Cited by 27 publications

(12 citation statements)

References 3 publications

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“…3) of three wedges containing a thin wedge with the angle H 0 , which is taken 5°, 1°and 0.1°. With the purpose to provide benchmarks (Helsing and Jonsson, 2002) for comparison with data, which may be obtained by other methods, we present numerical results in table with eight correct significant digits. To make the comprehension of the data easier, they are also presented diagrammatically in Figs.…”

Section: Numerical Resultsmentioning

confidence: 99%

Plane elasticity problem for a multi-wedge system with a thin wedge

Linkov

Rybarska-Rusinek

2010

International Journal of Solids and Structures

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a b s t r a c tThe paper presents a method for studying a system of elastic wedges containing a thin wedge with the angle H 0 , which may be arbitrary small. An analysis shows that the considered problem, involving 2-D vectors of tractions and displacements, cannot be solved by straight-forward extension of the method previously worked out by the authors for analogous scalar problems. The difficulty arises because of the disclosed feature of the dependences between the Mellin transformed displacements and tractions at the boundaries of a thin wedge: they are linearly dependent when their Taylor's expansions in H 0 are represented by the first terms only. The difficulty is removed by using the consequences of the linear dependence and by an appropriate re-arrangement of variables. Then simple physical models, simulating the influence of a thin wedge on a multi-wedge system, become available. The models cover the cases of a very rigid and very compliant thin wedge and also intermediate cases. The ranges of the models applicability are studied analytically and illustrated by numerical results.

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Section: Numerical Resultsmentioning

confidence: 99%

Plane elasticity problem for a multi-wedge system with a thin wedge

Linkov

Rybarska-Rusinek

2010

International Journal of Solids and Structures

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“…It is known that numerical codes should be verified before their use in applications [34][35][36]. The present solution is useful for this purpose since ordinary differential equations can be solved numerically with a very high accuracy with no difficulty.…”

Section: Discussionmentioning

confidence: 97%

Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

2018

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Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications.

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“…With purpose to provide benchmarks [9] for comparison with data, which may be obtained by other methods, below we present results with eight significant digits. (The actual accuracy of calculations was ten digits what is confirmed by (i) starting Muller's iterations from various initial points and (ii) comparing with results, obtained by alternative methods, for the particular cases of two similar wedges comprising a system with the contact being the axis of symmetry.…”

Section: (S /2) = P T (S) In Particular the Boundary Values Of Thementioning

confidence: 99%

Interface conditions simulating influence of a thin elastic wedge with smooth contacts

Linkov

Rybarska-Rusinek

2010

Arch Appl Mech

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The paper presents a method for deriving interface conditions simulating the influence of a thin wedge in a multi-wedge system with smooth contacts. It consists in successive (i) employing the Mellin's transform, (ii) separation of the symmetric and anti-symmetric parts of a solution, (iii) distinguishing terms tending to infinity, when the wedge angle tends to zero, (iv) appropriate re-arrangement of the terms to avoid degeneration, (v) using truncated power series in equations for the thin wedge and (vi) inspection of the characteristic determinant and finding models simulating the influence of the thin wedge for various combinations of parameters. The paper extends and improves the results previously obtained by the authors for a harmonic problem. The analysis leads to three physical models of contact interaction, which cover all the ratios of shear modules of a thin wedge and neighbour wedges. Numerical examples illustrate the accuracy provided by the method employed and the models derived.

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On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature1

Abstract: Converged normalized stress intensity factors for a matrix crack interacting with an elastic cylinder are presented. The new results differ from previously published results in several examples. The need for better error analysis in computational fracture mechanics is emphasized.

Cited by 27 publications

References 3 publications

Plane elasticity problem for a multi-wedge system with a thin wedge

Plane elasticity problem for a multi-wedge system with a thin wedge

Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

Interface conditions simulating influence of a thin elastic wedge with smooth contacts

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