• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.123-137
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• 2011

We review a series of crack problems arising in the general deformations of a linearly elastic solid (Mode-I, Mode-II and Mode-III crack) and, perhaps more significantly, when the contribution of surface effects are taken into account. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. We show that the deformations of an elastic solid containing a single crack can be decoupled into in-plane (Mode-I and Mode-II crack) and anti-plane (Mode-III crack) parts, even when the surface mechanics is introduced. In particular, it is shown that, in contrast to classical fracture mechanics (where surface effects are neglected), the incorporation of surface elasticity leads to the more accurate description of a finite stress at the crack tip. In addition, the corresponding stress fields exhibit strong dependency on the size of crack.

• 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.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.225-239
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• 2005

Applications of the Trefftz boundary element method (BEM) to anti-plane electroelastic problems are presented in this paper. Both direct and indirect methods with domain decomposition are discussed in details. Each crack is treated as semi-infinite thin slit defined in a subregion, for which a particular solution of the anti-plane problem, satisfying exactly the crack-face condition, is derived. The stress intensity factors defined at each crack tip can be directly computed from the coefficients of the particular solution. The performance of the proposed formulation is assessed by two examples and comparison is made with results obtained by other approaches. The Trefftz boundary element approach is demonstrated to be suitable for the analysis of the anti-plane problem of piezoelectric materials.

• Journal of Mechanical Science and Technology
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• v.14 no.9
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• pp.920-927
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• 2000

A multi-layered orthotropic material with a center crack is subjected to an anti-plane shear loading. The problem is formulated as a mixed boundary value problem by using the Fourier integral transform method. This gives a Fredholm integral equation of the second kind. The integral equation is solved numerically and anti-plane shear stress intensity factors are analyzed in terms of the material orthotropy for each layer, number of layers, crack length to layer thickness and the order of the loading polynomial. Also, the case of monolithic and hybrid composites are investigated in terms of the local fiber volume fraction and the global fiber volume fraction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2172-2179
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• 2002

In this paper, we examine the dynamic electromechanical behavior of an edge crack in a piezoelectric ceramic layer bonded between two elastic layers under the combined anti-plane mechanical shear and in-plane electric transient loadings. We adopted both the permeable and impermeable crack boundary conditions. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic energy release rate are presented to show the dependences upon the geometry, material combination, electromechanical coupling coefficient and electric field.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.975-992
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• 2017

In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$, $m{\geq}3$, admitting commuting ${\ast}$-Ricci and pseudo anti-commuting ${\ast}$-Ricci tensor, respectively. As the applications, we prove that there do not exist ${\ast}$-Einstein metrics on Hopf hypersurfaces as well as ${\ast}$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.

• Journal of Power Electronics
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• v.11 no.1
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• pp.45-50
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• 2011

This paper proposes a method for comparing and evaluating anti-windup proportional-integral (PI) control strategies. The so-called PI plane is used and its coordinate is composed of the error and the integral state. In addition, an anti-windup PI controller with integral state prediction is proposed. The anti-windup scheme can be easily analyzed and evaluated on the PI plane in detail. Representative anti-windup methods are experimentally applied to the speed control of a vector-controlled induction motor driven by a pulse width modulated (PWM) voltage-source inverter (VSI). The experimental results compare the anti-windup PI controllers. It is empathized that the initial value of the integral state at the beginning of the linear range dominates the control performance in terms of overshoot and settling time.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1500-1511
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• 2004

In this paper, the anti-plane transient response of a central crack normal to the interface between a piezoelectric ceramics and two same elastic materials is considered. The assumed crack surfaces are permeable. By virtue of integral transform methods, the electro elastic mixed boundary problems are formulated as two set of dual integral equations, which, in turn, are reduced to a Fredholm integral equation of the second kind in the Laplace transform domain. Time domain solutions are obtained by inverting Laplace domain solutions using a numerical scheme. Numerical values on the quasi-static stress intensity factor and the dynamic energy release rate are presented to show the dependences upon the geometry, material combination, electromechanical coupling coefficient and electric field.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.496-505
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• 2000

A semi-infinite parallel crack propagated with constant velocity in two bonded anisotropic strip under anti-plane clamped displacement is analyzed. Using Fourier integral transform a Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are determined, where the results give the more general expression applicable to the extent of the anisotropic material having one plane of elastic symmetry for the parallel crack. The dynamic stress intensity factor and energy release rate are also obtained as a closed form, which are the results applicable to the problem both of dynamic and static crack under the same geometry as this study. The stress intensity factor approaches zero at the critical crack velocity which is less than the shear wave velocity, but in typical case of isotropic or orthotropic material agrees with the velocity of shear wave. Also a circular shear stress around crack tip is considered, from which the stress is shown to be approximately symmetric about the horizontal axis. Referring to the maximum stress criteria, it could be shown that a brenched crack is formed by crack growth as crack velocity increases.