• Journal of the Korean Society for Precision Engineering
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• v.20 no.7
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• pp.208-216
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• 2003

In this paper, a two-dimensional electroelastic analysis is performed on a piezoelectric material with an open crack. The approach of Lekhnitskii's complex potential functions is used in the derivation and Bueckner's weight function theory is extended to piezoelectric materials. The stress intensity factors and the electric displacement intensity factor are calculated by the weight function theory.

• Journal of Ocean Engineering and Technology
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• v.24 no.3
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• pp.59-63
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• 2010

In this paper, an electroelastic analysis is performed on a piezoelectric material with an open crack in anti-plane deformation. Bueckner’s weight function theory is extended to piezoelectric materials in anti-plane deformation. The stress intensity factors and electric displacement intensity factor are calculated by the weight function theory.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.2
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• pp.149-156
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• 2012

In fracture mechanics, the weight function can be used for calculating stress intensity factors. In this paper, a two-dimensional electroelastic analysis is performed on a transversely isotropic piezoelectric material with an open crack. A plane strain formulation of the piezoelectric problem is solved within the Leknitskii formalism. Weight function theory is extended to piezoelectric materials. The stress intensity factors and electric displacement intensity factor are calculated by the weight function theory.

• Journal of Ocean Engineering and Technology
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• v.23 no.1
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• pp.146-151
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• 2009

In this paper, a weight function theory for the calculation of the mode III stress intensity factor in a rectilinear anisotropic body is formulated. This formulation employs Lekhnitskii's formalism for two dimensional anisotropic materials. To illustrate the method used for the weight function theory, we calculated the mode III stress intensity factor in a single edge-notched configuration.

• International Journal of Ocean System Engineering
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• v.3 no.3
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• pp.131-135
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• 2013

We construct the fundamental fields for 3-D arbitrarily shaped plane cracks in by differentiating with respect to a parameter of the crack. As an application of these fundamental fields, the total elastic energy release rate in combined mode cracking is computed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.2
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• pp.232-244
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• 1997

In this paper weight function theory is extended to the determination of the stress intensity factors for the mode I in elliptic crack. For the calculation of the fundamental fields Poisson's theorem and Ferrers's method were employed. Fundamental fields are constructed by single layer potentials with surface density of crack harmonic fundamental polynimials. Crack harmonic fundamental polynimials up to order four were given explicitly. As an example of the application of the weight function theory the stress intensity factors along crack tips in nearly penny-shaped elliptic crack are calculated.

• International Journal of Precision Engineering and Manufacturing
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• v.8 no.3
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• pp.60-63
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• 2007

Weight functions in fracture mechanics represent the stress intensity factors as weighted averages of the externally impressed boundary tractions and body forces. We extended the weight function theory for cracked linear elastic materials to calculate the notch stress intensity factor of a notched structure with anti-plane deformation. The well-known method of deriving weight functions by differentiation cannot be used for notched structures. By combining an appropriate singular field with a regular field, we derived weight functions for the notch stress intensity factor. Closed expressions of weight functions for notched cylindrical bodies are given as examples.

• East Asian mathematical journal
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• v.39 no.1
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• pp.29-36
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• 2023

In this paper, we consider φ-Laplacian nonlocal boundary value problems with singular weight function which may not be in L¹(0, 1). The existence and nonexistence of positive solutions to the given problem for parameter λ belonging to some open intervals are shown. Our approach is based on the fixed point index theory.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.491-497
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• 2015

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

• 연구논문집
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• s.28
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• pp.123-135
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• 1998

A shape function for element free Galerkin method is carved from Shepard interpolant of singular weight and consistency condition. Thus present shape function is an interpolation and has no singularities. The shape function is applied to cantilever bending problems and gives good results in comparison with beam theory. Finally it is shown that the coupling with finite element method is made easily without any additional treaties.