Dynamic and static analysis of cracks using the hypersingular formulation of the Boundary Element Method

Abstract

A new methodology for computing dynamic stress intensity factors in the frequency domain based on the mixed boundary element method, a combination of the equations corresponding to the integral representations of displacements and tractions, is proposed and analysed. The expressions of hypersingular fundamental solution are presented and their singular parts extracted. Also, a discontinuous Singular-Quarter-Point element is constructed. Finally, various parametric computations and applications are described in order to illustrate the simplicity and accuracy of the proposed method as applied to both static and dynamic problems. ? 1998 John Wiley & Sons, Ltd.

Two-dimensional numerical approach for the vibration isolation analysis of thin walled wave barriers in poroelastic soils

“…When x i ∈ Γ, both the SBIE and the HBIE contain singular integrals, being at most weakly singular those associated with U * , at most strongly singular (Cauchy Principal Value integrals) those associated with T * and D * , and at most hypersingular (Hadamard Finite Part integrals) those associated with S * . The treatment of those integrals for this problem is analogous to that of acoustics [11] and elastodynamics [33,15] problems. The treatment of the HBIE is based on a regularization process that requires the integrands (excluding the term r −2 ) belong to the Hölder function space C 1,α [30].…”

“…After some algebraic manipulations using the relationships between wavenumbers given by Eqs. (12), (15), (19) and (22) …”

On modelling SH‐waves in a class of inhomogeneous anisotropic media via the Boundary Element Method

“…1 redefined as x 2 = x 1 , x 3 = x 2 , and x 1 = x 3 . Following [19] the displacements and the tractions are written as u 3…”

“…We cite e.g. the works of Chirino and Abascal [3] (dual BEM), Fidelinski et al [11] (mixed BIEM) and non-hypersingular traction BIE derivations by Zhang and Gross [27], Zhang and Achenbach [25]. An interesting study on the accuracy and stability of hyper-singular traction BIEs can be found in Rangelov et al [18].…”

Dynamic interaction of multiple shear bands

“…For the numerical solution, each shear band has been subdivided into a number Q of elements. In order to describe the square-root singularity 25 , two different kinds of shape function have been adopted: quadratic function for the elements interior to the shear band and square-root function (the so called ‘quarter-point element’s’ 26 , 27 ) at the shear band tips.…”