SUMMARYA linear y method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson y method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and¯ux (for scalar waves) is assumed in the time interval yDt. A comparison between numerical results obtained from the standard formulation and from the linear y method studied here shows the latter to be more stable than the former. The eect of varying y for dierent values of time steps is also studied in this paper. #

In the present paper the traditional BEM formulation for time-domain scalar wave propagation analysis is extended to a new class of problems. A procedure to consider linear time interpolation for boundary tractions is worked out. Time discontinuities are included by adding to the standard BEM equation the integral equation for velocities. Numerical examples are presented in order to assess the accuracy of the proposed formulation.1998 John Wiley & Sons, Ltd.

The present paper is concerned with the development of a scheme based on iterative coupling of two boundary element formulations to obtain time-domain numerical solution of dynamic non-linear problems. The domain is divided into two sub-domains: the sub-domain that presents non-linear behaviour is modelled by the D-BEM formulation (D: domain) whereas the sub-domain that behaves elastically is modelled by the TD-BEM formulation (TD, time-domain). The solution of the problem is obtained independently in each sub-domain and the variables at common interfaces are computed iteratively. Two examples are presented, in order to verify the potentialities of the proposed methodology. q

This work presents a boundary element method formulation for the analysis of scalar wave propagation problems. The formulation presented here employs the so-called operational quadrature method, by means of which the convolution integral, presented in time-domain BEM formulations, is substituted by a quadrature formula, whose weights are computed by using the Laplace transform of the fundamental solution and a linear multistep method. Two examples are presented at the end of the article with the aim of validating the formulation.

This work presents alternative time-marching schemes for performing elastodynamic analysis by the Boundary Element Method. The use of the static fundamental solution and the maintenance of the domain integral associated to the accelerations characterize the formulation employed in this work. It is called D-BEM, D meaning domain. Time response is obtained by employing step-by-step time-marching procedures similar to those adopted in the Finite Element Method. Among all integration procedures, Houbolt scheme became the most popular used to march in time with D-BEM formulation, in spite of the presence of a high numerical damping. In order to improve the integration, this work presents alternative schemes that can be used to perform elastodynamic analysis by the BEM with a better damping control. In order to verify the accuracy of the proposed scheme, three examples are presented and discussed at the end of this work.

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