FINITE-ELEMENT ANALYSIS OF WAVE SCATTERING FROM SINGULARITIES

A combined analytic-finite element method is used for the efficient so lution of the Helmholtz equation in the presence of geometrical singul arities. In particular, time-harmonic waves in a membrane which contai ns one or more fixed-edge cracks (stringers) are investigated. The Dir ichlet-to-Neumann (DtN) map is used in the procedure, to enable the re placement of the original singular problem by an equivalent regular pr oblem, which is then solved by a finite element scheme. The method yie lds the solution in the entire membrane, as well as the dynamic ''stre ss intensity factor.'' Numerical results are presented for a circular membrane containing an edge stringer, two edge stringers and an intern al stringer. The first few critical wave numbers of the membrane are a lso found.