Alternative solution methods for crack problems in plane anisotropic elasticity, with examples

Azhdari, Abbas; Obata, Makoto; Nemat‐Nasser, Sia

doi:10.1016/s0020-7683(99)00137-7

Cited by 31 publications

(6 citation statements)

References 31 publications

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“…In this case, the Airy stress function can be expressed in terms of two arbitrary analytical functions F 1 (z 1 ) and F 2 (z 2 ) as = 2ℜ [F 1 (z 1 ) + F 2 (z 2 )] , ( = 1, 2), (9) in which ℜ determines the real parts of complex numbers. In this case, the Airy stress function can be expressed in terms of two arbitrary analytical functions F 1 (z 1 ) and F 2 (z 2 ) as = 2ℜ [F 1 (z 1 ) + F 2 (z 2 )] , ( = 1, 2), (9) in which ℜ determines the real parts of complex numbers.…”

Section: Figurementioning

confidence: 99%

“…The characteristic equation normally has distinct complex roots ( 1 ≠ 2 ) in anisotropic problems. In this case, the Airy stress function can be expressed in terms of two arbitrary analytical functions F 1 (z 1 ) and F 2 (z 2 ) as = 2ℜ [F 1 (z 1 ) + F 2 (z 2 )] , ( = 1, 2), (9) in which ℜ determines the real parts of complex numbers. To further simplify the formulations, two new complex potentials Φ 1 (z 1 ) = dF 1 ∕dz 1 and Φ 2 (z 2 ) = dF 2 ∕dz 2 may be used along with Equations (9) and (3) to determine the in-plane stress field as in (10).…”

Section: Figurementioning

confidence: 99%

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On higher order parameters in cracked composite plates under far‐field pure shear

Ghouli

Ayatollahi

Nejati

2019

Fatigue Fract Eng Mat Struct

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This paper presents the analytical solution of the crack tip fields as well as the crack parameters in an infinitely large composite plate with a central crack subjected to pure shear loading. To this end, the complex variable method is employed to formulate an asymptotic solution for the crack tip fields in an anisotropic plane. Using a stress-based definition of the crack tip modes of loading, only the mode II crack parameters are found to be non-zero under pure shear load. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non-singular term, ie, the T-stress. Unlike the isotropic materials, in which the T-stress is zero under pure shear, it is found that the T-stress is non-zero for the case of anisotropic materials, being the only material-dependent crack tip stress parameter. The veracity of our exact crack tip fields is assessed and verified through a comparison made with respect to the finite element (FE) solution. Finally, we demonstrate the significance of the T-stress on stresses near the crack tip in composite plates under pure shear loads.

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Section: Figurementioning

confidence: 99%

Section: Figurementioning

confidence: 99%

On higher order parameters in cracked composite plates under far‐field pure shear

Ghouli

Ayatollahi

Nejati

2019

Fatigue Fract Eng Mat Struct

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“…Since Fisher-Crisps [21] has shown that the elastic modulus of functionally graded material derived from current conventional methods has a discrepancy with the actual value, using such a functionally graded elastic modulus will most certainly extend the computational time but will not necessarily improve accuracy. Although anisotropy introduces additional material properties that render the basic field equation better structured, more accurate and easier to solve, as suggested by Azhdari et al [22], many simplified FE models assume isotropic conditions. A good example is a recent study by Dong and Darvell [12], who represented a ceramic-cement substrate under indentation by an FE model with isotropy and obtained reasonable agreement in calculated and observed values of the contact radius.…”

Section: Materials Propertiesmentioning

confidence: 99%

Finite element analysis of stress distribution and the effects of geometry in a laser-generated single-stage ceramic tile grout seal using ANSYS

Lim

Lawrence

et al. 2004

Proceedings of the Institution of Mechanical Engineers, Part B:

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Optimization of the geometry (curvature of the vitrified enamel layer) of a laser-generated single-stage ceramic tile grout seal has been carried out using a finite element (FE) model. The overall load-bearing capacities and load-displacement plots of three selected geometries were determined experimentally by the indentation technique. Simultaneously, an FE model was developed utilizing the commercial ANSYS package to simulate the indentation. Although the loaddisplacement plots generated by the FE model consistently displayed stiffer identities than the experimentally obtained results, there was reasonably close agreement between the two sets of results. Stress distribution profiles of the three FE models at failure loads were analysed and correlated so as to draw an implication on the prediction of a catastrophic failure through an analysis of FE-generated stress distribution profiles. It was observed that although increased curvatures of the vitrified enamel layer do enhance the overall load-bearing capacity of the singlestage ceramic tile grout seal and bring about a lower nominal stress, there is a higher build-up in stress concentration at the apex that would inevitably reduce the load-bearing capacity of the enamel glaze. Consequently, the optimum geometry of the vitrified enamel layer was determined to be flat.

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“…In this case the equilibrium states of the material can be represented by two complex potentials defined in two complex planes [1][2][3][4][5][6][7][8][9][10]. We shall use Guz's representation of the elastic state [1], without initial deformation, in a weakly modified form due to Soos [10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of three equal collinear cracks in an orthotropic solid

et al. 2015

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We consider a homogeneous elastic, orthotropic solid containing three equal collinear cracks, loaded in tension by symmetrically distributed normal stresses. Following Guz's representation theorem and solving Riemann-Hilbert problems we determine the expressions of the complex potentials. Using the asymptotic analysis, we obtain the asymptotic values of the incremental stress and displacement fields. We determine the tangential stresses near the crack tips. Using the maximum tangential stress criterion and numerical computations we study the interaction problem for a Graphite-epoxy fiber reinforced composite material.

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Alternative solution methods for crack problems in plane anisotropic elasticity, with examples

Cited by 31 publications

References 31 publications

On higher order parameters in cracked composite plates under far‐field pure shear

On higher order parameters in cracked composite plates under far‐field pure shear

Finite element analysis of stress distribution and the effects of geometry in a laser-generated single-stage ceramic tile grout seal using ANSYS

Mathematical modeling of three equal collinear cracks in an orthotropic solid

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