We answer a question from A. V. Abanin and P. T. Tien about so-called almost subadditive weight functions in the sense of Braun-Meise-Taylor. Using recent knowledge of a growth index for functions, crucially appearing...
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We answer a question from A. V. Abanin and P. T. Tien about so-called almost subadditive weight functions in the sense of Braun-Meise-Taylor. Using recent knowledge of a growth index for functions, crucially appearing in the ultraholomorphic setting, we are able to show the existence of weights such that there does not exist an equivalent almost subadditive function and hence almost subadditive weights are a proper subclass. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
This paper presents a weight function technique for calculating the stress intensity factors for composite repairs to cracks emanating from an internal notch, corrosion blend out, or a free edge under arbitrary loadin...
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This paper presents a weight function technique for calculating the stress intensity factors for composite repairs to cracks emanating from an internal notch, corrosion blend out, or a free edge under arbitrary loading in rib stiffened panels. The predictions are compared with both finite element and experimental values. This methodology represents a significant extension to existing assessment and design formulae that are currently limited to the case of uniform loading and flat unstiffened panels. (C) 2003 Published by Elsevier Ltd.
作者：
Jones, RPeng, DPitt, SWallbrink, CMonash Univ
DSTO Ctr Struct Mech Dept Engn Mech Clayton Vic 3800 Australia Monash Univ
Dept Engn Mech Clayton Vic 3800 Australia DSTO
Air Vehicles Div Platform Sci Lab Melbourne Vic 3001 Australia Monash Univ
Monash BHP Maintenance Technol Inst Dept Mech Engn Clayton Vic 3800 Australia
This paper presents simple approximate formulae for calculating the weight functions associated with cracks emanating from a notch under arbitrary loading. These weight functions are exact both for short cracks and fo...
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This paper presents simple approximate formulae for calculating the weight functions associated with cracks emanating from a notch under arbitrary loading. These weight functions are exact both for short cracks and for long cracks. A range of examples are presented to demonstrate the accuracy of the present method. (C) 2003 Published by Elsevier Ltd.
A variational principle introduced by Sham to determine elastic fields with unbounded strain energy in finite homogeneous bodies is extended to piecewise homogeneous bodies. It is shown that the modification involves ...
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A variational principle introduced by Sham to determine elastic fields with unbounded strain energy in finite homogeneous bodies is extended to piecewise homogeneous bodies. It is shown that the modification involves only an additional known body force like term in the functional. The resulting displacement-based finite element method determines the weight functions for all three fracture modes and for both traction and displacement boundaries in a unified manner. Numerical examples for two-dimensional cracks in layered isotropic bodies are presented.
The properties of orthogonal collocation on finite elements with respect to the choice of orthogonal polynomials are studied. A simplified algorithm for the calculation of the collocation points, weight functions and ...
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The properties of orthogonal collocation on finite elements with respect to the choice of orthogonal polynomials are studied. A simplified algorithm for the calculation of the collocation points, weight functions and discretization matrices for first and second order derivatives is presented in terms of the Lagrangian interpolation polynomial. The effect of Legendre and Chebyshev polynomials on the average value of the dependent variable is checked. It is found that the Legendre polynomial gives the better results at the centre and on the average as compare to the Chebyshev polynomial. (c) 2006 Elsevier Inc. All rights reserved.
weight functions with a parameter are introduced into an iteration process to increase the order of the convergence and enhance the behavior of the iteration process. The parameter can be chosen to restrict extraneous...
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weight functions with a parameter are introduced into an iteration process to increase the order of the convergence and enhance the behavior of the iteration process. The parameter can be chosen to restrict extraneous fixed points to the imaginary axis and provide the best basin of attraction. The process is demonstrated on several examples. Published by Elsevier Inc.
The focus of the paper is on the analysis of skew-symmetric weight functions for interfacial cracks in two-dimensional anisotropic solids. It is shown that the Stroh formalism proves to be an efficient tool for this c...
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The focus of the paper is on the analysis of skew-symmetric weight functions for interfacial cracks in two-dimensional anisotropic solids. It is shown that the Stroh formalism proves to be an efficient tool for this challenging task. Conventionally, the weight functions, both symmetric and skew-symmetric, can be identified as non-trivial singular solutions of a homogeneous boundary-value problem for a solid with a crack. For a semi-infinite crack, the problem can be reduced to solving a matrix Wiener-Hopf functional equation. Instead, the Stroh matrix representation of displacements and tractions, combined with a Riemann-Hilbert formulation, is used to obtain an algebraic eigenvalue problem, which is solved in a closed form. The proposed general method is applied to the case of a quasi-static semi-infinite crack propagating between two dissimilar orthotropic media: explicit expressions for the weight functions are evaluated and then used in the computation of the complex stress intensity factor corresponding to a general distribution of forces acting on the crack faces.
The recently developed complex Taylor series expansion method for computing weight functions (WCTSE) of arbitrary 2D crack geometry is further studied. Improvements on several aspects are made to raise solution accura...
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The recently developed complex Taylor series expansion method for computing weight functions (WCTSE) of arbitrary 2D crack geometry is further studied. Improvements on several aspects are made to raise solution accuracy. Wide-range weight functions are determined for four different crack geometries. Methods for accuracy assessment using the Green's function or severe load conditions are proposed. The WCTSE numerical weight function and the conventional analytical weight function approaches are shown to be complementary. It is envisaged that combination of the two approaches will lead to more widespread applications of the weight function methods for fracture and crack growth analyses. (C) 2015 Elsevier Ltd. All rights reserved.
Stress intensity factors from finite element analysis, are presented for internal circumferential cracks in cylindrical components subjected to a range of through wall stress distributions. Cylinders with ratios of in...
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Stress intensity factors from finite element analysis, are presented for internal circumferential cracks in cylindrical components subjected to a range of through wall stress distributions. Cylinders with ratios of internal to external radii in the range 0.1 to 0.9 have been considered for a full range of dimensionless crack depths from 0.02 to 0.95. A set of weight functions for each of the cylindrical geometries has been developed and the accuracy of these has been examined using the finite element results. General conclusions have been drawn concerning the merits of the various types of weight function. (C) 2001 Elsevier Science Ltd. All rights reserved.
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