Interface Jacobian‐based Co‐Simulation

Co‐simulation is a prominent method to solve multi‐physics problems. Multi‐physics simulations using a co‐simulation approach have an intrinsic advantage. They allow well‐established and specialized simulation tools for different fields and signals to be combined and reused with minor adaptations in contrast to the monolithic approach. However, the partitioned treatment of the coupled system poses the drawback of stability and accuracy challenges. If several different subsystems are used to form the co‐simulation scenario, these issues are especially important. In this work, we propose a new co‐simulation algorithm based on interface Jacobians. It allows for the stable and accurate solution of complex co‐simulation scenarios involving several different subsystems. Furthermore, the Interface Jacobian‐based Co‐Simulation Algorithm is formulated such that it enables parallel execution of the participating subsystems. This results in a high‐efficient procedure. Furthermore, the Interface Jacobian‐based Co‐Simulation Algorithm handles algebraic loops as the co‐simulation scenario is defined in residual form. Copyright © 2014 John Wiley & Sons, Ltd.     

Coupled adjoint‐based sensitivities in large‐displacement fluid‐structure interaction using algorithmic differentiation

A methodology for the calculation of gradients with respect to design parameters in general fluid‐structure interaction problems is presented. It is based on fixed‐point iterations on the adjoint variables of the coupled system using algorithmic differentiation. This removes the need for the construction of the analytic Jacobian for the coupled physical problem, which is the usual limitation for the computation of adjoints in most realistic applications. The formulation is shown to be amenable to partitioned solution methods for the adjoint equations. It also poses no restrictions to the nonlinear physics in either the fluid or structural field, other than the existence of a converged solution to the primal problem from which to compute the adjoints. We demonstrate the applicability of this procedure and the accuracy of the computed gradients on coupled problems involving viscous flows with geometrical and material nonlinearities in the structural domain.     

Generalized Robin–Neumann explicit coupling schemes for incompressible fluid‐structure interaction: Stability analysis and numerics

We introduce a new class of explicit coupling schemes for the numerical solution of fluid‐structure interaction problems involving a viscous incompressible fluid and an elastic structure. These methods generalize the arguments reported in [Comput. Methods Appl. Mech. Engrg., 267:566–593, 2013, Numer. Math., 123(1):21–65, 2013] to the case of the coupling with thick‐walled structures. The basic idea lies in the derivation of an intrinsic interface Robin consistency at the space semi‐discrete level, using a lumped‐mass approximation in the structure. The fluid–solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface. Based on these methods, a new, parameter‐free, Robin–Neumann iterative procedure is also proposed for the partitioned solution of implicit coupling. A priori energy estimates, guaranteeing the stability of the schemes and the convergence of the iterative procedure, are established within a representative linear setting. The accuracy and performance of the methods are illustrated in several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

Partitioned procedures are appealing for solving complex fluid‐structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added‐mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin‐Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection‐based incompressible CFD and finite element–based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid‐structure interfaces embedded in structured non–body‐conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex‐dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, α_f, on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler‐Bernoulli beam interacting with a two‐dimensional incompressible inviscid flow. Both studies reveal a trade‐off between stability and accuracy: smaller values of α_f tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of α_f that optimizes this trade‐off is derived and discussed.     

A flow‐aligning algorithm for convection‐dominated problems

This paper proposes and studies an algorithm for aligning a triangulation with a given convection field. Approximate solutions of convection‐dominated problems on flow‐aligned meshes typically have sharper internal layers, less over and undershooting and higher accuracy. The algorithm we present can be imported easily into any 2D finite element solver, does not change the number of meshpoints, and can improve solution quality quite dramatically. This improvement in solution quality on the flow‐aligned triangulation is illustrated for both the usual Galerkin method and the streamline‐diffusion method. Copyright © 1999 John Wiley & Sons, Ltd.     

A hybrid variational‐collocation immersed method for fluid‐structure interaction using unstructured T‐splines

We present a hybrid variational‐collocation, immersed, and fully‐implicit formulation for fluid‐structure interaction (FSI) using unstructured T‐splines. In our immersed methodology, we define an Eulerian mesh on the whole computational domain and a Lagrangian mesh on the solid domain, which moves arbitrarily on top of the Eulerian mesh. Mathematically, the problem reduces to solving three equations, namely, the linear momentum balance, mass conservation, and a condition of kinematic compatibility between the Lagrangian displacement and the Eulerian velocity. We use a weighted residual approach for the linear momentum and mass conservation equations, but we discretize directly the strong form of the kinematic relation, deriving a hybrid variational‐collocation method. We use T‐splines for both the spatial discretization and the information transfer between the Eulerian mesh and the Lagrangian mesh. T‐splines offer us two main advantages against non‐uniform rational B‐splines: they can be locally refined and they are unstructured. The generalized‐α method is used for the time discretization. We validate our formulation with a common FSI benchmark problem achieving excellent agreement with the theoretical solution. An example involving a partially immersed solid is also solved. The numerical examples show how the use of T‐junctions and extraordinary nodes results in an accurate, efficient, and flexible method. Copyright © 2015 John Wiley & Sons, Ltd.     

水下目标吸声材料和结构的研究

全面了解和掌握水下吸声材料及结构在应用频率范围内其不同温度、压力等环境下的声学性能,对于水下目标结构的声隐身设计具有重要意义.结合近年来水下目标吸声材料和结构的应用及研究,从材料声学设计的角度,讨论了水下吸声材料的声学特性和研究进展.还对水下吸声结构的形式、吸声机理和应用情况进行了归纳和评述.最后预测了水下目标吸声材料和结构的发展趋势.     

T‐stress evaluations for nonhomogeneous materials using an interaction integral method

A new equivalent domain integral of the interaction integral is derived for the computation of the T‐stress in nonhomogeneous materials with continuous or discontinuous properties. It can be found that the derived expression does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the integral domain contains material interfaces. Therefore, the present method can be used to extract the T‐stress of nonhomogeneous materials with complex interfaces effectively. The interaction integral method in conjunction with the extended FEM is used to solve several representative examples to show its validity. Finally, using this method, the influences of material properties on the T‐stress are investigated. Numerical results show that the mechanical properties and their first‐order derivatives affect the T‐stress greatly, while the higher‐order derivatives affect the T‐stress slightly. Copyright © 2012 John Wiley & Sons, Ltd.     

Charge‐induced clustering in multifield particulate flows

The present work extends recent results in Zohdi (Int. J. Solids Struct., in press; Proc. Roy. Soc., in press) to develop models and robust solution strategies for the direct simulation of the dynamical flow of charged particles undergoing simultaneous contact, surface reactions and heat transfer. Emphasis is placed on the possibility of particle clustering which can lead to the formation of cluster‐structures within the particulate flow. A recursive ‘staggering’ solution scheme is developed, whereby the time‐steps are adaptively adjusted to control the rates of convergence within each time‐step, and hence, the error associated with the incomplete resolution of the coupled interaction between the various fields and associated constraints. Representative numerical simulations are provided in order to illustrate the character of the model and the solution strategy. Copyright © 2004 John Wiley & Sons, Ltd.     

FeCrAl纤维多孔材料梯度结构吸声性能的研究

根据前期对单层FeCrAl纤维多孔材料吸声性能的系统研究,对纤维多孔结构进行了优化设计,梯度结构是以孔隙度递减的方式排列而成.分别对单层和梯度结构的吸声性能进行了测试,结果表明,在常温常声压条件下,3层梯度结构低频吸声性能较单层材料有明显提高,而且能够在一个较宽频率范围内的稳态吸声系数平稳延伸,最大值为1;在常温高声强140dB条件下,该结构仍保持较好的稳态吸声性能,在1600～6400Hz宽频范围内的吸声系数均达到0.9以上;在高温常声压条件下,梯度结构的吸声性能受到温度影响有所下降,且吸声系数不随频率的升高而增加,从而在测试频率范围内出现第一峰值频率.虽然梯度结构的高温吸声性能变差,但是较单层材料的吸声性能要好得多.因此,FeCrAl纤维多孔材料梯度结构是一种适用于多种特殊环境的吸声体.     

Explicit strategies for incompressible fluid‐structure interaction problems: Nitsche type mortaring versus Robin–Robin coupling

We discuss explicit coupling schemes for fluid‐structure interaction problems where the added mass effect is important. In this paper, we show the close relation between coupling schemes by using Nitsche's method and a Robin–Robin type coupling. In the latter case, the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators. Recalling the explicit method proposed in Comput. Methods Appl. Mech. Engrg. 198(5‐8):766–784, 2009, we make the observation that this scheme is stable under a hyperbolic type CFL condition, but that optimal accuracy imposes a parabolic type CFL conditions because of the splitting error. Two strategies to enhance the accuracy of the coupling scheme under the hyperbolic CFL‐condition are suggested, one using extrapolation and defect‐correction and one using a penalty‐free non‐symmetric Nitsche method. Finally, we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions. Copyright © 2013 John Wiley & Sons, Ltd.     

A coupled hp‐finite element scheme for the solution of two‐dimensional electrostrictive materials

As part of the ongoing research within the field of computational analysis for the coupled electro‐magneto‐mechanical response of smart materials, the problem of linearised electrostriction is revisited and analysed for the first time using the framework of hp‐finite elements. The governing equations modelling the physics of the dielectric are suitably modified by introducing a new total Cauchy stress tensor (A. Dorfmann and R.W. Ogden. Nonlinear electroelasticity. Acta Mechanica, 174:167–183, 2005), which includes the electrostrictive effect and a staggered partitioned scheme for the numerical solution of the coupling phenomena. With the purpose of benchmarking numerical results, the problem of an infinite electrostrictive plate with a circular/elliptical dielectric insert is revisited. The presented analytical solution is based on the theoretical framework for two‐dimensional electrostriction proposed by Knops (R.J. Knops. Two‐dimensional electrostriction. Quarterly Journal of Mechanics and Applied Mathematics, 16:377–388, 1963) and uses classical techniques of complex variable analysis. Our presentation, to the best of our knowledge, provides the first correct closed form expression for the solution to the infinite electrostrictive plate with a circular/elliptical dielectric insert, correcting the errors made in previous presentations of this problem. We use this analytical solution to assess the accuracy, efficiency and robustness of the hp‐formulation in the case of nearly incompressible electrostrictive materials. Copyright © 2012 John Wiley & Sons, Ltd.     

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

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.     

边界条件对多孔材料声学参数测试的影响研究

多孔材料声学特征参数测试前需要采用机械切割方法和样品容器匹配,然而切割后的材料边缘不能完全和样品容器匹配,因此采用加环的方式进行处理。以三聚氰胺泡沫为例,通过控制测试材料的边界条件,测试材料的流阻率,在软件中选用合适的声学模型计算得出该材料的声学特征参数。最后将阻抗管测试得到的吸声系数与AMDesigner仿真得到的吸声系数进行比较。结果显示,加两个环后仿真得到的值与测试值吻合效果较好,加一个环在低频区吻合效果较好,而直接将切割得到的材料进行测试效果最差。该研究可以为今后的声学材料测试研究提供指导。     

多孔吸声材料发展现状与展望

吸声降噪在人们日常生活、设备安全以及军事领域具有重要意义，多孔材料是一类重要的吸声材料。介绍了多孔材料的吸声原理、多孔吸声材料的种类及其特性、影响多孔吸声材料吸声性能的因素等。综述了多孔吸声材料的发展现状，并对吸声材料的发展趋势做了展望。     

Solution of FE‐BE coupled eigenvalue problems for the prediction of the vibro‐acoustic behavior of ship‐like structures

To predict the vibro‐acoustic behavior of structures, both a structural problem and an acoustic problem have to be solved. For thin structures immersed in water, a strong interaction between the structural domain and fluid domain occurs. This significantly alters the resonance frequencies. In this work, the structure is modeled by the finite element method. The exterior acoustic problem is solved by a fast boundary element method employing hierarchical matrices. An FE‐BE formulation is presented, which allows the solution of the coupled eigenvalue problem and thus the prediction of the coupled eigenfrequencies and mode shapes. It is based on a Schur complement formulation of the FE‐BE system yielding a generalized eigenvalue problem. A Krylov–Schur solver is applied for its efficient solution. Hereby, the compressibility of the fluid is neglected. The coupled eigensolution is then used for a model reduction strategy allowing fast frequency sweep calculations. The efficiency of the proposed formulations is investigated with respect to memory consumption, accuracy, and computation time. Copyright © 2011 John Wiley & Sons, Ltd.     

Improved fractional step method for simulating fluid‐structure interaction using the PFEM

Numerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid‐structure interaction. To overcome problems of mass loss on the free surface and the added‐mass effect, an improved fractional step method (FSM) that handles added‐mass terms in a mathematically exact way is developed. A further benefit is that no assumptions regarding the structural response are made in handling added‐mass terms, thus it is straightforward to incorporate material nonlinearity in fluid‐structure interaction (FSI) under this approach. Patch tests and comparisons with experimental data are presented in order to verify and validate the improved FSM for FSI applications. The computational cost of this approach is shown to be negligible compared with the other aspects of the FSM, particularly when the size of the structure and the fluid‐structure interface is small relative to the volume of fluid. Copyright © 2014 John Wiley & Sons, Ltd.     

3D‐FEM formulations of limit analysis methods for porous pressure‐sensitive materials

The first purpose of this paper is the numerical formulation of the three general limit analysis methods for problems involving pressure‐sensitive materials, that is, the static, classic, and mixed kinematic methods applied to problems with Drucker–Prager, Mises–Schleicher, or Green materials. In each case, quadratic or rotated quadratic cone programming is considered to solve the final optimization problems, leading to original and efficient numerical formulations. As a second purpose, the resulting codes are applied to non‐classic 3D problems, that is, the Gurson‐like hollow sphere problem with these materials as matrices. To this end are first presented the 3D finite element implementations of the static and kinematic classic methods of limit analysis together with a mixed method formulated to give also a purely kinematic result. Discontinuous stress and velocity fields are included in the analysis. The static and the two kinematic approaches are compared afterwards in the hydrostatic loading case whose exact solution is known for the three cases of matrix. Then, the static and the mixed approaches are used to assess the available approximate criteria for porous Drucker–Prager, Mises–Schleicher, and Green materials. Copyright © 2013 John Wiley & Sons, Ltd.