Recent Developments in Finite Element Methods for Structural

The study of structural acoustics involves modeling acoustic radiation and scattering, primarily in exterior regions, coupled with elastic and structural wave propagation. This paper reviews recent progress in nite element analysis that renders computation a practical tool for solving problems of structural acoustics. The cost-eeectiveness of nite element methods is composed of several ingredients. Boundary-value problems in unbounded domains are inappropriate for direct discretization. Employing DtN methodology yields an equivalent problem that is suitable for nite element analysis by posing impedance relations at an artiicial exterior boundary. Well-posedness of the resulting continuous formulations is discussed, leading to simple guidelines for practical implementation and verifying that DtN boundary conditions provide a suitable basis for computation. Approximation by Galerkin nite element methods results in spurious dispersion, degrading with reduced wave resolution. Accuracy is improved by Galerkin/least-squares and related technologies on the basis of detailed examinations of discrete errors in simpliied settings, relaxing wave-resolution requirements. This methodology is applied to time-harmonic problems of acoustics and coupled problems of structural acoustics. Space-time nite element methods based on time-discontinuous Galerkin/least-squares are derived for transient problems of structural acoustics. Numerical results validate the superior performance of Galerkin/least-squares nite elements for problems of structural acoustics. A comparative study of the cost of computation demonstrates that Galerkin/least-squares nite element methods are economically competitive with boundary element methods, the prevailing numerical approach to exterior problems of acoustics. EEcient iterative methods are derived for solving the large-scale matrix problems that arise in structural acoustics computation of realistic conngurations at high wavenumbers. An a posteriori error estimator and adaptive strategy are developed for time-harmonic acoustic problems and the role of adaptivity in reducing the cost of computation is addressed. 1 INTRODUCCION The study of structural acoustics and uid-structure interaction involves the solution of problems of acoustic radiation and scattering, elastic and structural wave propagation, and their interaction. Only relatively few, simple cases can be solved analytically and when the wavelength is of the same order as characteristic length scales asymptotic methods usually cannot be employed. Thus, most conngurations of practical interest must be solved by standard computational tools such as boundary element, nite diierence and nite element methods. Exterior problems of wave propagation pose a unique challenge to computation since the unbounded region is inappropriate for direct implementation of computational techniques. The derivation of mathematically sound continuous formulations that provide c 1996 by CIMNE, Barcelona (Spain).