An accurate and efficient scheme for acoustic-structure interaction problems based on unstructured mesh

Abstract

This paper focuses on the accurate and efficient numerical implementation of acoustic-structure coupling formulations using the edge-based smoothed finite element method for the flexible shell and the gradient-weighted finite element method for the acoustic fluid field, namely, the ES/GW-FEM. The shell is discretized using the simplest linear triangular elements and the edge-based smoothing domain is then constructed. By introducing an edge local coordinate system, the edge-based smoothing operation is performed on the smoothing domain. As for the acoustic fluid domain, the tetrahedron elements are adopted. A compacted support domain is then constructed and the gradient weighted operation is performed on the support domain. To model the exterior acoustic domain, an artificial boundary is introduced and the Dirichlet-to-Neumann (DtN) boundary condition is imposed. Based on the appropriate compatibility and equilibrium conditions on the interface boundaries, the coupled ES/GW-FEM formulation is finally obtained. Both the interior acoustic-structure coupled problems and exterior acoustic-structure coupled problems are available as the DtN boundary is considered. Numerical examples demonstrate that the coupled ES/GW-FEM achieves much higher accuracy and works more reliable compared with the coupled FEM/FEM in solving practical engineering problems.

Dispersion Error Analysis of Stable Node-Based Finite Element Method for the Helmholtz Equation

“…The problem has analytical eigenvalues corresponding to the wave number k = nπ, n ∈ N, for which the global error tends to infinity. The global error indicator in terms of velocity is defined with the form of [29][30][31]…”

“…The dispersion error increases conspicuously with the increasing wave number due to the overly-stiff property of the FEM model [29][30][31][32][33]. In order to eliminate the dispersion error effectively, a discretized model with proper stiffness is needed [29][30][31][32].…”

“…The dispersion error increases conspicuously with the increasing wave number due to the overly-stiff property of the FEM model [29][30][31][32][33]. In order to eliminate the dispersion error effectively, a discretized model with proper stiffness is needed [29][30][31][32]. For this purpose, a strain smoothing method was proposed by Chen [34,35], and a generalized gradient smoothing (GGS) technique [36][37][38] has been further formulated by Liu.…”

“…The prominent inherent properties of the NS-FEM make it much attractive. However, the NS-FEM model exhibits "overly-soft" when it comes to time-dependent problems [29][30][31][32] such as dynamic problems and acoustic problems. As the "overly-soft" property can lead to temporal instability [37,38], the NS-FEM cannot be used for acoustic problems directly.…”

“…One is processed based on the squared-residual stabilization technique proposed by Beissel and Belytschko [43], and has been further developed by other researchers [44][45][46][47][48][49]. Another is processed by combining the "overly-stiff" FEM with the "overly-soft" NS-FEM, such as the alpha finite element method (α-FEM) [29] and the hybrid smoothed finite element method (H-SFEM) [31,50,51]. All these methods make the NS-FEM temporal stability and provide very accurate results; however, no matter which methodology is employed, there is always a parameter which has great influence on the calculation results.…”