Acoustic Finite Element Methods for Unbounded Domains

摘要

Theories of infinite elements to model problems with open boundaries in the finite element (FE) method are discussed. To model the unbounded domain of static problems, two different principles are described: exponential decay function infinite elements and mapped infinite elements. Infinite elements for dynamic problems were developed from both these theories by including a periodic factor in the shape functions of the elements. A term is also included in the shape functions of the dynamic infinite element based on mapping theory, in order to model the correct decay of the solution in the far field of acoustic problems. A harmonic analysis was performed in order to compare results from FE-models comprising the dynamic infinite elements with results from FE-models comprising a Sommerfeldt radiation condition. An FE-solution of a cylindrical source in a unbounded medium was compared with the analytical solution given by the Hankel function. The dynamic mapped infinite elements give a very good agreement with the analytical solution.