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SUMMARYAn iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid-solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non-linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non-linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain.

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

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International audienceThe present paper describes a procedure that improves efficiency, stability and reduces artificial energy dissipation of the standard time-domain direct boundary element method (BEM) for acoustics and el-astodynamics. Basically, the developed procedure modifies the boundary element convolution-related vector, being very easy to implement into existing codes. A stabilization parameter is introduced into the recent-in-time convolution operations and the operations related to the distant-in-time convolution contributions are approximated by matrix interpolations. As it is shown in the numerical examples presented at the end of the text, the proposed formulation substantially reduces the BEM computational cost, as well as its numerical insta-bilities

SUMMARYThe present paper describes an unconditionally stable algorithm to integrate the equations of motion in time. The standard FEM displacement model is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green's function of the mechanical system in nodal co-ordinates. In the present 'implicit Green's function approach' (ImGA), mechanical system Green's functions are not explicitly computed; rather they are implicitly considered through an iterative pseudo-forces process. Under certain simplifying hypothesis, iterations are not necessary and the ImGA becomes cheaper than standard Newmark/Newton-Raphson algorithm. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach.