Elastodynamic Boundary Research Articles

Transient elastodynamic boundary element analysis based on time-stepping scheme. Study on one-dimensional problems.

A boundary element technique based on the time-stepping formulae is proposed for the transient elastodynamic problems. The acceleration term of the basic differential equation of elastodynamics is approximated by finite difference on time, Newmark's single-step formula and Wilson's formula. This approximation enables boundary element formulation by using the same fundamental solution as that of the steady-state elastodynamic equation. The present paper deals only with the one-dimensional problem under an impact force to confirm the effectiveness of the method. The numerical examples reveal that the Wilson θ method is the most suitable scheme among the three to incorporate with the Boundary Element Method, and that the proposed method is promising for two- or three-dimensional problems and other complicated coupled problems.

Influence of the reflected rayleigh wave on a propagating edge crack

In experimental studies of rapid crack propagation in solids, specimens in the two dimensional single edge notch configuration are commonly used. If the motion of the crack tip differs significantly from steady motion, then Rayleigh surface waves are generated at the crack tip, and these waves propagate along the crack faces in the direction of crack growth. These surface waves can overtake the propagating crack tip. Several investigators have recently observed that the available data suggest that these reflected surface waves play a role in the crack arrest process [1,2]. The purpose here is to give a preliminary report on the evidence available in the theory of elastic crack propagation which supports this suggestion on the influence of surface waves. The elastodynamic boundary value problem which would serve as a model of this process is extremely difficult to solve, and it is unlikely that a solution in which the surface waves effects are separated from other effects will be available in the near future.

Earthquake strong motion simulated by stress drop models

Shallow strike slip earthquakes on vertical faults are modelled as two-dimensional antiplane strain ruptures in a uniformly prestressed homogeneous halfspace. Behind the rupture front, which is specified, the stress drops to a lower value. The elastodynamic boundary value problem is solved with a finite difference method. Several cases are studied, which include symmetric and one-directional rupture propagation, surface faulting, multiple events, variable rupture velocity, sticking and rebreaking of the fault plane. The time function of displacement, velocity and acceleration are interpreted as signals generated by events in the focus, namely starting, stopping and breaking through the surface of the rupture. The model explains peak velocity and peak acceleration in the near field of M≈5.5–6 earthquakes; which are typically about 0.2 m/s and 5 m/s2 at 10 km epicentral distance, if the rupture velocity is close to the shear wave velocity. Sticking of the fault does not alter the accelerograms significantly, but it increases the seismic moment in simple events and decreases it in multiple events.