Non-hypersingular Boundary Integral Equation Research Articles

Dynamic stress concentration for multiple multilayered inclusions embedded in an elastic half-space subjected to SH-waves

The dynamic stress concentration factor (DSCF) is evaluated along the interfaces of multiple multilayered inclusions embedded in a half-space when subjected to a plane harmonic SH-wave. A weak form of Helmholtz equation is utilized to derive a non-hypersingular boundary integral equations to compute the stresses. Eliminating the need to rely on hypersingular integrals, greatly simplifies the procedure. The numerical results obtained by the proposed method, are validated against analytical solutions.Various contributing factors that can influence the DSCF are investigated, including multiple scattering, layering, stiffness of the adjacent inclusions, and impedance contrast of the layers. The DSCF is found to be highly prone to these changes, particularly with the soft materials. Therefore, accurate analysis of stresses requires models that consider multiple scattering and layering. The presented result could be used for predicting the seismic failure of pipes and underground tunnels and for estimating the stress failure in strong ground motion seismology due to subsurface irregularities.

3-D Transient Dynamic Crack Analysis by a Novel Time-Domain BEM

A novel non-hypersingular time-domain traction BEM is presented for three-dimensional (3D) transient elastodynamic crack analysis. The initialboundary value problem is formulated as a set of nonhypersingular time-domain traction boundary integral equations (BIEs). To solve the time-domain traction BIEs, a time-stepping scheme based on the convolution quadrature formula of Lubich (1988a,b; 1994) for temporal discretization and a collocation method for spatial discretization is adopted. Numerical examples are given for an unbounded solid with a penny-shaped crack under a tensile and shear impact loading. A comparison of the present time-domain BEM with the conventional one shows that the novel time-domain method is much more stable and less sensitive to the choice of the used timesteps. keyword: 3-D Time-domain boundary element method, Non-hypersingular boundary integral equations, Transient elastodynamic crack analysis, Elastodynamic stress intensity factors.

Non-hypersingular boundary integral equations for 3-D non-planar crack dynamics

We derive a non-hypersingular boundary integral equation, in a fully explicit form, for the time-domain analysis of the dynamics of a 3-D non-planar crack, located in an infinite homogeneous isotropic medium. The hypersingularities, existent in the more straightforward expression, are removed by way of a technique of regularization based on integration by parts. The variables are denoted in terms of a local Cartesian coordinate system, one of the axes of which is always held locally perpendicular to the potentially curved surface of the crack. Also given, in a fully explicit form, are the expressions for the off-fault stress and displacement field, as well as the special form of the equations for the case in which the fault is planar.

Non-hypersingular boundary integral equations for two-dimensional non-planar crack analysis

SUMMARY We derive a set of non-hypersingular boundary integral equations, both elastodynamic and elastostatic, for the analysis of arbitrarily shaped 2-D anti-plane and in-plane cracks located in an infinite homogeneous isotropic medium, rendered in a unified nomenclature for all cases. The hypersingularities that appear in the usual formulations for the dynamic cases, existent both at the source point and at the wavefront, are removed by way of a regularization technique based on integration by parts. The equations for the in-plane cases are presented in terms of a local Cartesian coordinate system, one of the axes of which is always held locally tangential to the crack trace. The expressions for the elastic field at any point on the model plane are also given. Our formulations are shown to yield accurate numerical results, as long as appropriate stabilization measures are taken in the numerical scheme. The numerical applicability of our method to non-planar crack problems is illustrated by simulations of dynamic growth of a hackly crack which has small off-plane side-branches. The results imply that the branching of a crack brings about a significant decrease in the crack-tip stress concentration level and consequently may play an essential role in the arrest of earthquake rupturing.