Search

This paper provides a modified complex potential for the fundamental solution, which is composed of a principal part and a complementary part. The suggested complex potential satisfies the traction free condition along the boundary of half-plane in advance. After using the Somigliana identity or the Betti's reciprocal theorem between the physical field and the field of the fundamental solution, a complex variable boundary integral equation (BIE) for the notch problem in elastic half-plane is obtained. A compact derivation for the BIE is presented. By using the BIE, multiple notch problems of elastic half-plane can be solved numerically. In the method, there is no limitation for the configuration of notches. Many problems with the elliptic notch or the square notch are solved successfully. For the periodic notch problem, the remainder estimation technique is suggested. This technique provides an effective way for the solution of periodic notch problem. [ABSTRACT FROM AUTHOR]

This paper investigates the degenerate scale problem for plane elasticity in a multiply connected region with an outer elliptic boundary. Inside the elliptic boundary, there are many voids with arbitrary configurations. The problem is studied on the relevant homogenous boundary integral equation. The suggested solution is derived from a solution of a relevant problem. It is found that the degenerate scale and the non-trivial solution along the elliptic boundary in the problem are same as in the case of a single elliptic contour without voids. The present study mainly depends on integrations of several integrals, which can be integrated in a closed form. [ABSTRACT FROM AUTHOR]

This paper investigates the Zener–Stroh crack with curved configuration in plane elasticity. A singular integral equation is suggested to solve the problem. Formulae for evaluating the SIFs and T-stress at the crack tip are suggested. If the curve configuration is a product of a small parameter and a quadratic function, a perturbation method based on the singular integral equation is suggested. In the method, the singular integral equation can be expanded into a series with respect to the small parameter. Therefore, many singular integral equations can be separated from the same power order for the small parameter. These singular integral equations can be solved successively. The solution of the successive singular integral equations will provide results for stress intensity factors and T-stress at the crack tip. It is found that the behaviors for the solution of SIFs and T-stress in the Zener–Stroh crack and the Griffith crack are quite different. This can be seen from the presented comparison results. [ABSTRACT FROM AUTHOR]

This paper proposes a Trefftz method for evaluating the T-stress for cracks emanating from a hole in a rectangular plate. In this method, the displacement and the stress field are an elasticity solution, which is derived from complex potentials. The complex potentials are assumed in a series form with undetermined coefficients. After using the minimum potential energy principle, an algebraic equation for the undetermined coefficients can be formulated. The coefficients can be obtained from the equation, and the whole stress field is determined. Stress intensity factor and T-stress can be evaluated immediately from the known solution. Merit of the suggested method is addressed. For three particular cases, R=0, R/w=0.25 and R/w=0.5, the computed results are tabulated. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Using complex variable function, an elementary solution of a single-edge crack problem for half-plane is proposed. The elementary solution is obtained by distributing the dislocation density along the prospective place of crack, and it is composed of the principal part and the complementary part. Based on the elementary solution and the principle of superposition, a system of Cauchy singular integral equations for periodic group edge crack problems of half-plane in antiplane elasticity can be formulated. In the solution of the singular integral equation, the influences of many neighbouring groups on the central group are evaluated exactly. In addition, the influences on the central group by the many remote groups are considered approximately. By using a semi-open quadrature rule, the singular integral equations are solved and the stress intensity factors at the crack tips are evaluated. Several numerical examples are given. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a hypersingular integral equation for the antiplane elasticity curved crack problems of circular regions is suggested. The original complex potential is formulated on a distribution of the density function along a curve, where the density function is the COD (crack opening displacement). The modified complex potential can also be established, provided the circular boundary is traction free or fixed. Using the proposed modified complex potential and the boundary condition, the hypersingular integral equation is obtained. The curve length method is suggested to solve the integral equation numerically. By using this method, the usual integration rule on the real axis can be used to the curved crack problems. In order to prove that the suggested method can be used to solve more complicated cases of the curved cracks, several numerical examples are given. [ABSTRACT FROM AUTHOR]