Study On New Algorithms For2D Structure-Sound Interaction Problems Based On Meshless Methods

The work of this thesis was supported by National Natural Science Foundation ofChina “Computation and analysis of structure-sound coupled problems in the mediumfrequency range for thin wall structures”(No.10872075). This thesis presents some newalgorithms based on meshless methods, such as element-free Galerkin (EFG) method,meshless weighted least-square (MWLS) method, meshless Galerkin least-square (MGLS)method, coupled partition of unity method and improved meshless weighted least-square(IMWLS) method, to formulate a general way of solving the density of the uncoupledsound field and structure-sound interaction problems.This paper proposes the formulation of the meshless weighted least-squares methodfor the Helmholtz equation based on the moving least-squares (MLS) approximation. Thevariational formulation is constructed based on the least-squares discretization. MWLSmethod combines the advantages of the Galerkin method and the collocation method andovercomes the disadvantage of the computational burden of the Galerkin method and theinstability of the collocation method. The computational parameters of MWLS are chosenbased on a thorough numerical study of one-dimensional analyses. With severaltwo-dimensional examples, we prove that the MWLS method is more efficient than EFGmethod， and can offer an accurate and simulation of high wave number of acousticalwaves.To avoid solving the ill-conditioned system of algebraic equations in the conventionalmoving least-square (MLS) method, we develop the improved moving least-square (IMLS)approximation to construct the shape functions of EFG method and MWLS method, whichare called improved element-free Galerkin (IEFG) method and improved meshlessweighted least squares (IMWLS) method, respectively. A detailed dispersion analysis forthe MWLS and IMWLS methods, including the impacts of different meshless parameterson the dispersion error for both methods, is made in solving wave propagation problems. The MGLS method, which is not sensitive to boundary conditions as the least-squaremethod, is introduced to solve the interior sound field and analyze the dispersion error.Finally, a general formulation of the coupled PUM-IMWLS method for solvingstructure-sound interaction problems is proposed and applied to several two-dimensionalstructure-sound interaction examples.