Analysis Of The Acoustics And The Functionally Graded Coatings By Boundary Element Method

The application range of boundary element methods is confined in engineering by the difficulty of evaluation of the nearly singular integrals for a long time. In this, thesis is introduced a regularization algorithm to tackle the problems of the nearly singular integrals. In the algorithm, the singular factor is removed from the kernel functions of boundary integral equation so that singular integrals are successfully calculated. The regularization formulation is obtained in order to apply the regularization algorithm to acoustics boundary element methods. The accuracy of the calculation of the nearly singular integrals in acoustics BEMS has been greatly improved.The fundamental solution of the helmholtz integral equation in a three-dimensional free space is given. Some typical examples illustrate that the proposed algorithm can effectively evaluate the physical parameters at inner points very close to the boundary.Moreover, the analytic formulations of the nearly singular integrals are introduced into the boundary element method (BEM) of the coating structures. The strength of the coating structures under Hertzian type pressure is modeled by BEM. The isotropic and functionally graded coatings are considered, respectively. The Tresca stress contours in the coating structures are portrayed. The numerical results show that there are stress discontinuities at the coating-substrate interface when the isotropic coating is used. The discontinuity could be attenuated when the isotropic coating is replaced by the functionally coating. In addition, the maximum value of Tresca stress in the coating could be reduced.The physical parameters of the near-boundary-point in acoustics BEM is evaluated successfully by utilizing the regularization algorithm. Thereafter, it makes that the application of boundary element methods in engineering is widened.