An Optimized Generalized Integration Rules for Error Reduction of Acoustic Finite Element Model

Abstract

In the finite element method (FEM), the accuracy in acoustic problems will deteriorate with the increasing frequency due to the “dispersion effect”. In order to minimize discretization error, a novel optimized generalized integration rules (OGIR) is introduced into FEM for the reduction of discretization error. In the present work, the adaptive genetic algorithm (AGA) is implemented to sight the optimized location of integration points. Firstly, the generalized integration rules (GIR) is used to parameterize the Gauss point location, then the relationship between the location parameterize of the integration points and discretization error is derived in detail, and the optimized location of the integration points is found through the optimization procedure, and then the OGIR–FEM is finally proposed to solve the acoustic problem. It also can be directly used to solve the optional acoustic problem, including the damped problems. Numerical example involving distorted meshes indicates that present OGIR–FEM has a superior error reducing performance in comparison with the other error reducing finite elements. These researches indicate that the proposed method can be more widely applied to solving practical acoustic problems with more accurate solutions.