Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Abstract

The vibration behaviour of ships is noticeably influenced by the surrounding water, which represents a fluid of high density. In this case, the feedback of the fluid pressure onto the structure cannot be neglected and a strong coupling scheme between the fluid domain and the structural domain is necessary. In this work, fast boundary element methods (BEMs) are used to model the semi-infinite fluid domain with the free water surface. Two approaches are compared: A symmetric mixed formulation is applied where a part of the water surface is discretized. The second approach is a formulation with a special half-space fundamental solution, which allows the exact representation of the Dirichlet boundary condition on the free water surface without its discretization. Furthermore, the influence of the compressibility of the water is investigated by comparing the solutions of the Helmholtz and the Laplace equation. The ship itself is modeled with the finite element method (FEM). A binary interface to the commercial finite element package ANSYS is used to import the mass matrix and the stiffness matrix. The coupled problems are formulated using Schur complements. To solve the resulting system of equations, a combination of a direct solver for the finite element matrix and a preconditioned GMRES for the overall Schur complement is chosen. The applicability of the approach is demonstrated using a realistic model problem.

Design sensitivity analysis of modal frequencies of elastic structures submerged in an infinite fluid domain

“…20,21 As a result the coupled finite element and boundary element (FE-BE) methods are usually preferred for the numerical simulation of fluid-structure interaction systems. 22,23 In spite of the advantages of solving the vibro-acoustic problems in unbounded fluid domain, the acoustic BEM makes the system of equations of the coupled FE-BE method have frequency-dependent coefficient matrices, which results in a typical nonlinear eigenvalue problem (NEP) in the modal analysis of submerged elastic structures. 24,25 Various methods have been presented to solve the NEPs (cf.…”

“…As is widely known, the BEM based on the Kirchhoff-Helmholtz integral equation suffers from the fictitious eigenfrequency problem for exterior wave propagation problems, 20,21 and the coupled FE-BE method inherits this problem. 22,23 In the response analysis, this problem is also referred to as the non-uniqueness difficulty as the numerical solutions are erroneous at the vicinities of fictitious eigenfrequencies. The Burton-Miller (BM) formulation 38 has been confirmed as an effective method to conquer this difficulty, and its real effect has been investigated in the previous work.…”

“…For the infinite fluid domain, the boundary element method (BEM) is more favorable since it can solve unbounded‐domain acoustic problems accurately and rigorously without any truncation or approximation of the problem domain 20,21 . As a result the coupled finite element and boundary element (FE‐BE) methods are usually preferred for the numerical simulation of fluid‐structure interaction systems 22,23 . In spite of the advantages of solving the vibro‐acoustic problems in unbounded fluid domain, the acoustic BEM makes the system of equations of the coupled FE‐BE method have frequency‐dependent coefficient matrices, which results in a typical nonlinear eigenvalue problem (NEP) in the modal analysis of submerged elastic structures 24,25 .…”

“…Furthermore, a small GEP is formulated to calculate the gradients of repeated eigenvalues. As is widely known, the BEM based on the Kirchhoff‐Helmholtz integral equation suffers from the fictitious eigenfrequency problem for exterior wave propagation problems, 20,21 and the coupled FE‐BE method inherits this problem 22,23 . In the response analysis, this problem is also referred to as the non‐uniqueness difficulty as the numerical solutions are erroneous at the vicinities of fictitious eigenfrequencies.…”

Solution of large scale elastic problems with the boundary element method

“…Representative works are those of Bapat and Liu (2010), Frangi and Bonnet (2010), Wang et al (2010), Wang and Yao (2011) and Yusa and Yoshimura (2013), while the application of FM/BEM to the solution of composite material problems is demonstrated in the works of Hu et al (2000), Kong et al (20002), Yao et al (2004), Liu et al (2005), Lei et al (2006) and Wang and Yao (2008). The FMM/BEM formulation alone or in combination with the Finite Element Method in the context of fluid structure interaction is demonstrated in the works of Gaul and Fischer (2017), Schneider (2008), Chen et al (2014), Wilkes and Duncan (2015).…”