Coupled Analysis of Structural–Acoustic Problems Using the Cell-Based Smoothed Three-Node Mindlin Plate Element

Abstract

The cell-based smoothed finite element method (CS-FEM) using the original three-node Mindlin plate element (MIN3) has recently established competitive advantages for analysis of solid mechanics problems. The three-node configuration of the MIN3 is achieved from the initial, complete quadratic deflection via ‘continuous’ shear edge constraints. In this paper, the proposed CS-FEM-MIN3 is firstly combined with the face-based smoothed finite element method (FS-FEM) to extend the range of application to analyze acoustic fluid–structure interaction problems. As both the CS-FEM and FS-FEM are based on the linear equations, the coupled method is only effective for linear problems. The cell-based smoothed operations are implemented over the two-dimensional (2D) structure domain discretized by triangular elements, while the face-based operations are implemented over the three-dimensional (3D) fluid domain discretized by tetrahedral elements. The gradient smoothing technique can properly soften the stiffness which is overly stiff in the standard FEM model. As a result, the solution accuracy of the coupled system can be significantly improved. Several superior properties of the coupled CS-FEM-MIN3/FS-FEM model are illustrated through a number of numerical examples.