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《Earthquake Engineering and Engineering Vibration》 1982-04
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A FINITE MODEL FOR PROBLEMS OF TRANSIENT SCALAR WAVES IN AN INFINITE ELASTIC MEDIUM

Liao Zhenpeng (Institute of Engineering Mechanics, Academia Sinica)  
A method of artificial boundary to transmit completely the incident scalar waves in a finite computational grid is first discussed and then the transmitting formulas in compact form is expressed in terms of node displacements. The analytical results and actual numerical tests indicate that this method enjoys a distinct advantage in cancelling waves reflected from the boundary for waves of any incident angle. The error analysis has revealed an obvious superiority of this method over the current viscous approaches and Paraxial Approximation. In the worst case-incident angleapproaching 90? the amplitudes of reflection waves from the boundary forincident wave of unity amplitude are by the Nth order approximation of this method, but are equal to 1 by the latter two methods. The of this method is always less than 1 when andwill be much smaller when N increases. This method is easily implemented by either finite element or finite difference method and suitable for nonlinear analysis. Further generalization of the method to frequency domain and to elastic vector wave propagation cases is pointed out as well.
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