BEAM RESPONSE DERIVED FROM A 3-D HYBRID BOUNDARY INTEGRAL METHOD IN ELASTODYNAMICS

The aim of the present paper is to associate a new symmetric boundary integral method to well-known symmetric domain methods with the purpos e of improving solutions. Multifield problems arise from acoustic and hydroacoustic radiation of mechanical systems with vibrating surfaces. Instead of discretising the mechanical system with finite elements, t he proposed boundary integral method is effective because the boundary data are of primary interest. Thus, the problem dimension is reduced by one and symmetry is preserved. As the method is based on test funct ions, which analytically fulfil the homogeneous field equations, high accuracy is gained. From a single-field variational principle for a 3- D linear, elastodynamic state, a three-field hybrid principle is devel oped by Hamilton's principle and by decoupling displacements in the do main from those on the boundary. Compatibility is enforced in a weak s ense. For investigating steady-state vibrations, the functional is tra nsformed in the frequency domain. Superimposed singular fundamental so lutions of the Lame-Navier held equations generated by Dirac functions and weighted by generalised loads are used as test functions in the d omain. In the absence of body forces, they cancel the remaining domain integral in the hybrid principle and lead to a boundary integral form ulation. The boundary variables are discretised by boundary elements. A symmetric dynamic stiffness matrix equation is gained which relates nodal displacements and tractions on the boundary. An application of t he hybrid boundary integral method is derived. Because acoustic and hy droacoustic radiation in 2-D is predominantly generated by bending wav es, the 3-D hybrid method is adopted for 1-D beams. As the boundary of a finite beam degenerates to two nodes, no shape functions are needed . This is why the theory is shown to give analytical results of dynami cal beam analysis. (C) 1997 Academic Press Limited.