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Structural-acoustic coupling on non-conforming meshes with quadratic shape functions. (English) Zbl 1246.74063

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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S15 Boundary element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
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