Acoustic Fluid-structure Interaction Problems Research Articles

Parameter estimation in modelling frequency response of coupled systems using a stepwise approach

This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a major challenge in the field of parameter identification. We propose a stepwise approach consisting in subdividing the frequency spectrum such that the solution to a low-frequency subproblem serves as the starting point for the immediately higher frequency range. In the current work, two different inversion frameworks are used. The first approach is a gradient-based deterministic procedure that seeks the model parameters by minimising a cost function in the least squares sense and the second approach is a Bayesian inversion framework. The latter provides a potential way to assess the validity of the least squares estimate. In addition, it presents several advantages by providing invaluable information on the uncertainty and correlation between the estimated parameters. The methodology is illustrated on synthetic measurements with known design variables and controlled noise levels. The model problem is deliberately kept simple to allow for extensive numerical experiments to be conducted in order to investigate the nature of the local minima in full spectrum analyses and to assess the potential of the proposed method to overcome these. Numerical experiments suggest that the proposed methods may present an efficient approach to find material parameters and their uncertainty estimates with acceptable accuracy.

Verification and validation of dynamic response simulation codes for BWR fuel assemblies under seismic loading

The purpose of this study is to verify and validate two independently developed simulation codes for investigating dynamic response behaviors of fuel assemblies in a boiling water reactor (BWR) under seismic loading. The core of BWR consists of several hundreds of fuel assemblies. They are supported with both top guide and fuel support and are surrounded by coolant water. It is important to grasp their dynamic response behaviors under seismic loading for securing the structural integrity of the fuel assembly itself as well as for assessing control rod scrammability. For this evaluation of dynamic response behaviors, reliable simulation codes are required. In this study, we employ two different numerical simulation methods of acoustic fluid-structure interaction (AFSI) developed by the present authors independently. The one is a three-dimensional parallel finite element method for AFSI problems with solid elements based on a partitioned coupling approach, while the other is a finite element method of beam elements for fuel assemblies combining added mass matrix, which represents coupled inertia effects caused by coolant water. Both methods are implemented and applied to a problem of 368 fuel assemblies for verification and validation. The problem was set up based on the demonstration test performed by Nuclear Power Engineering Corporation in 1986. Both simulation results agreed well with each other, and the simulated results also agreed well with the experimental ones. In addition, we have discussed seismic response behaviors of fuel assemblies, which were not shown in the demonstration test. Finally, we conclude that the both developed simulation codes based on the proposed methods are powerful tools to grasp the behavior of huge number of fuel assemblies of BWR under seismic loading and to improve the seismic safety design of BWR core.

Isogeometric analysis for acoustic fluid-structure interaction problems

Modeling and analysis of the dynamic behavior of acoustic fluid-structure interaction problems are important in understanding engineering structural systems. Characterization of such coupled systems through analytical modeling is limited and often numerical modeling is sought-after. Recently, Isogeometric Analysis (IGA) has gained prominence in modeling and analyzing complex systems. In the present study, IGA with Non-Uniform Rational B-Splines (NURBS) is used to characterize the acoustic fluid-structure interaction problems and the performance is compared with the classical Finite Element solution. The gain in computational performance of IGA is demonstrated with case studies using a beam and a plate coupled to a cavity filled with an acoustic medium. To illustrate further, an application of acoustic fluid-structure problem using IGA, a car cavity in two dimension coupled to a beam is also demonstrated.

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

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.

Partitioned solution strategies for coupled BEM–FEM acoustic fluid–structure interaction problems

This paper investigates two FEM–BEM coupling formulations for acoustic fluid–structure interaction (FSI) problems, using the Finite Element Method (FEM) to model the structure and the Boundary Element Method (BEM) to represent a linear acoustic fluid. The coupling methods described interconnect fluid and structure using classical or localized Lagrange multipliers, allowing the connection of non-matching interfaces. First coupling technique is the well known mortar method, that uses classical multipliers and is compared with a new formulation of the method of localized Lagrange multipliers (LLM) for FSI applications with non-matching interfaces. The proposed non-overlapping domain decomposition technique uses a classical non-symmetrical acoustic BEM formulation for the fluid, although a symmetric Galerkin BEM formulation could be used as well. A comparison between the localized methodology and the mortar method in highly non conforming interface meshes is presented. Furthermore, the methodology proposes an iterative preconditioned and projected bi-conjugate gradient solver which presents very good scalability properties in the solution of this kind of problems.

A parallel iterative partitioned coupling analysis system for large-scale acoustic fluid–structure interactions

In many engineering fields, dynamic response in fluid---structure interaction (FSI) is important, and some of the FSI phenomena are treated as acoustic FSI (AFSI) problems. Dynamic interactions between fluids and structures may change dynamic characteristics of the structure and its response to external excitation parameters such as seismic loading. This paper describes a parallel coupling analysis system for large-scale AFSI problems using iterative partitioned coupling techniques. We employ an open source parallel finite element analysis system called ADVENTURE, which adopts an efficient preconditioned iterative linear algebraic solver. In addition, we have recently developed a parallel coupling tool called ADVENTURE_Coupler to efficiently handle interface variables in various parallel computing environments. We also employ the Broyden method for updating interface variables to attain robust and fast convergence of fixed-point iterations. This paper describes key features of the coupling analysis system developed, and we perform tests to validate its performance for several AFSI problems. The system runs efficiently in a parallel environment, and it is capable of analyzing three-dimensional-complex-shaped structures with more than 20 million degrees-of-freedom (DOFs). Its numerical results also show good agreement with experimental results.

Parallel BDD-based monolithic approach for acoustic fluid-structure interaction

Parallel BDD-based monolithic algorithms for acoustic fluid-structure interaction problems are developed. In a previous study, two schemes, NN-I + CGC-FULL and NN-I + CGC-DIAG, have been proven to be efficient among several BDD-type schemes for one processor. Thus, the parallelization of these schemes is discussed in the present study. These BDD-type schemes consist of the operations of the Schur complement matrix-vector (Sv) product, Neumann-Neumann (NN) preconditioning, and the coarse problem. In the present study, the Sv product and NN preconditioning are parallelized for both schemes, and the parallel implementation of the solid and fluid parts of the coarse problem is considered for NN-I + CGC-DIAG. The results of numerical experiments indicate that both schemes exhibit performances that are almost as good as those of single solid and fluid analyses in the Sv product and NN preconditioning. Moreover, NN-I + CGC-DIAG appears to become more efficient as the problem size becomes large due to the parallel calculation of the coarse problem.

A Monolithic Approach Based on the Balancing Domain Decomposition Method for Acoustic Fluid-Structure Interaction

A scalable and efficient monolithic approach based on the Balancing Domain Decomposition (BDD) method for acoustic fluid-structure interaction problems is developed. The BDD method is a well-known domain decomposition method for non-overlapping sub-domains, which consists of Neumann-Neumann (NN) preconditioning and coarse grid correction. In this study, we derive four types of BDD method, considering two options for NN preconditioning (NN-I and NN-C) and two options for coarse grid correction (CGC-FULL and CGC-DIAG). From the results of numerical experiments, the combination of NN-I and CGC-FULL turns out to be the most efficient scheme, showing fast convergence property irrespective of the number of sub-domains, DOFs of fluid and solid domains, and the added-mass effect of fluid. The combination of NN-I and CGC-DIAG is also expected to be an efficient scheme in some situations in a parallel environment.

A coupled ES-FEM/BEM method for fluid–structure interaction problems

The edge-based smoothed finite element method (ES-FEM) developed recently shows some excellent features in solving solid mechanics problems using triangular mesh. In this paper, a coupled ES-FEM/BEM method is proposed to analyze acoustic fluid–structure interaction problems, where the ES-FEM is used to model the structure, while the acoustic fluid is represented by boundary element method (BEM). Three-node triangular elements are used to discretize the structural and acoustic fluid domains for the important adaptability to complicated geometries. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and the gradient smoothing operation is applied over the edge-based smoothing domains. The global equations of acoustic fluid–structure interaction problems are then established by coupling the ES-FEM for the structure and the BEM for the fluid. The gradient smoothing technique applied in the structural domain can provide the important and right amount of softening effects to the “overly-stiff” FEM model and thus improve the accuracy of the solutions of coupled system. Numerical examples of acoustic fluid–structure interaction problems have been used to assess the present formulation, and the results show that the accuracy of present method is very good and even higher than those obtained using the coupled FEM/BEM with quadrilateral mesh.

DISPLACEMENT/PRESSURE BASED MIXED FINITE ELEMENT FORMULATIONS FOR ACOUSTIC FLUID-STRUCTURE INTERACTION PROBLEMS

SUMMARY We present reliable finite element discretizations based on displacement/pressure interpolations for the analysis of acoustic fluid—structure interaction problems. The finite element interpolations are selected using the inf-sup condition, and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation. We show that with our analysis procedure no spurious non-zero frequencies are encountered, as heretofore calculated with other displacement-based discretizations. ( 1997 by John Wiley & Sons, Ltd.