Derivation of New Time Domain Boundary Integral Equations of Elastodynamics

摘要

Traditional time domain boundary integral equations of elastodynamics is based on the time-dependent fundamental solution of elastodynamics, and using the reciprocal theorem in dynamics. The time-dependent fundamental solution is the response of infinite elastic space subjected by a concentrate inpulsive force at point P and instant τ. The response includes not only pressure wave and shear wave, but also Laplace wave, which has a speed between P and S waves. In this paper new time domain boundary integral equations are derived directly from the initial boundary value problem of elastodynamics partial differential equations, and using weighted residual integral equations and integral identities. Acoording to the integral equations derived, the spherical convergent P and S waves are apllied as the kernel functions respectively in the time domain integral equations. In this way, the new system of time domain integral equations derived is much simpler than traditional one, and their physical meaning is quite clear. For the new time domain boundary integral equations of elastodynamics, the corresponding time domain boundary element method developed for traditional TDBIE can be applied, and the efficiency could be enhanced significantly. Furthermore, some boundary type meshless methods can also be developed based on the presented new boundary integral equation.