A numerical procedure for regularized integral equations for elastostatic problems of flat cracks in opening mode

Abstract

Abdract-The regularid integral equations for flat cracks in opening mode are solved numerically by means of a simple procedure using new interpolation functions. The convergence and the accmncy of the method are tested on problems of circular and elliptical cracks embedded in the infinite medium, which admit analytical solutions. Computational results ensure the validity of this new approach. then they are compared with those already obtained without reguk&ation by the authors.

A non‐hypersingular time‐domain BIEM for 3‐D transient elastodynamic crack analysis

“…Applying equation (15) to a crack as depicted in Figure 1, substituting the resulting equation into Hooke's law (2), taking the limit process x + A', and invoking the rraction-free boundary condition ( (16) can also be obtained by using the conventional derivation in conjunction with a regulari~ation technique as presented by Sladek and Sladekl8. I 9 in Laplace-transformed domain, the novel derivation based on the two-state conservation integral (14) is rather simple and straightforward.…”

“…I 9 in Laplace-transformed domain, the novel derivation based on the two-state conservation integral (14) is rather simple and straightforward. The unknown quantities of the non-hypersingular traction BIEs (16) are the crack opening displacements and their derivatives, where the latter have the physical meaning of dislocation densities. Once the crack opening displacements have been calculated by solving the non-hypersingular traction BIEs (1 6), all other field quantities at an arbitrary internal point of the solid, such as the displacements, the strains and the stresses can be immediately computed by making use of the corresponding representation formulas for these quantities.…”

“…In this section, a numerical solution procedure is presented for solving the non-hypersingular traction BIEs (16). A collocation method in conjunction with a time-stepping scheme is applied.…”

“…. , N ) , the non-hypersingular traction BIEs (16) are converted into a system of linear algebraic equations:…”

A Singular Integral Equation Solution for the Linear Elastic Crack Opening Displacement of an Arbitrarily Shaped Plane Crack: Part I Finite‐part Integral Solutions

“…The regularized integral equations for non-planar tridimensional cracks in elastostatics can be found in [ 11. However, because of the lengthy expression of the kernel and its complexity, effective numerical investigations can be achieved only in the case of planar cracks [ 2 ] . For such a geometry the singular integral equation (SIE) approach has been developed and applied by several authors [3,4].…”