Structural‐acoustic coupling on non‐conforming meshes with quadratic shape functions

Abstract

SUMMARY Fully coupled finite element/boundary element models are a popular choice when modelling structures that are submerged in heavy fluids. To achieve coupling of subdomains with non‐conforming discretizations at their common interface, the coupling conditions are usually formulated in a weak sense. The coupling matrices are evaluated by integrating products of piecewise polynomials on independent meshes. The case of interfacing elements with linear shape functions on unrelated meshes has been well covered in the literature. This paper presents a solution to the problem of evaluating the coupling matrix for interfacing elements with quadratic shape functions on unrelated meshes. The isoparametric finite elements have eight nodes (Serendipity) and the discontinuous boundary elements have nine nodes (Lagrange). Results using linear and quadratic shape functions on conforming and non‐conforming meshes are compared for an example of a fluid‐loaded point‐excited sphere. It is shown that the coupling error decreases when quadratic shape functions are used. Copyright © 2012 John Wiley & Sons, Ltd.

An Adjoint Operator Approach for Sensitivity Analysis of Radiated Sound Power in Fully Coupled Structural-Acoustic Systems

“…The material data for structure and fluid and the geometrical data are listed in Table 1. These data are similar to those presented by Peters et al 18 On the exterior boundary of the spherical shell, the fluid-structure interaction needs to be considered because the light structure is immersed in heavy fluid, where the fluid is water. The interior of the shell is full of air, so the fluid-structure interaction is ignored.…”

“…New methods in elastoacoustics are frequently validated using submerged spheres. 17,18,34,36,41 This technique is continued in this section, where an elastic spherical shell with radius r is used as an example to test the proposed algorithm. The spherical shell is excited by a single concentrated force F at point A, see configuration in Fig.…”

Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

“…Excitation in the form of a concentrated force F applied at point A ( θ = 0) is considered, as shown in Figure . θ denotes the central angle between the calculated and excitation points, and the sound pressure p ( θ ) and displacement u ( θ ) at the surface of the sphere can be obtained in .…”

“…Excitation in the form of a concentrated force F applied at point A (Â D 0) is considered, as shown in Figure 3. Â denotes the central angle between the calculated and excitation points, and the sound pressure p.Â/ and displacement u.Â/ at the surface of the sphere can be obtained in [1,40]. Given the symmetry along the x axis, we can express the sound power on an arbitrary closed surface around the radiator as…”

2D Structural Acoustic Analysis Using the FEM/FMBEM with Different Coupled Element Types

“…However, few papers compared the performance of the different element types for coupled FEM/BEM. Peters et al (2012) used discontinuous linear boundary element with quadratic geometric interpolation coupled with eight-node isoparametric finite element to solve the 3D fluid structure interaction. Zhang, Zhang (2002) used discontinuous BEM coupled with FEM for elastostatics and fluid-structure interaction.…”