A non-reflecting boundary in fluid-structure interaction

A very efficient non-reflecting boundary condition is derived for the seismic response analysis of a submerged structure, such as a dam or an offshore structure, interacting with a compressible fluid domain of unbounded extent. The fluid-structure system is assumed to be two-dimensional and the analysis is conducted in the frequency domain. In the finite element discretization, pressure and displacements are considered to be the basic nodal unknowns for the fluid domain and the structure, respectively. The implementation of the proposed boundary condition in any existing finite element code, based on such a formulation, is extremely simple. Some fluid-structure systems are analysed to demonstrate the effectiveness and efficiency of the proposed method.     

Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions

The dynamic dam–fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under the assumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements, which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transient analysis of fluid–structure system. Comp Struct 1979;10:383–93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element for the dynamic analysis of fluid–solid system. Int J Numer Methods Eng 1983;19:1657–68]. The irrotational condition for inviscid fluids is imposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, and the numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analytical solution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even if the gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity is dependent on the wave frequency.For the practical analysis of the coupled dam–fluid problem the analysed region of the basin must be reduced and the use of suitable asymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layer of dampers and the analysis results are shown for the cases of sinusoidal forcing.The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate for the displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiation boundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64–100] is considered. Its implementation requires the resolution of a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integration problems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeld condition results, and with the analytical unbounded problem results.Finally, a number of finite element results are presented and their related features are discussed and critically compared.     

A finite element scheme with a high order absorbing boundary condition for elastodynamics

A high-order absorbing boundary condition (ABC) is devised on an artificial boundary for time-dependent elastic waves in unbounded domains. The configuration considered is that of a two-dimensional elastic waveguide. In the exterior domain, the unbounded elastic medium is assumed to be isotropic and homogeneous. The proposed ABC is an extension of the Hagstrom–Warburton ABC which was originally designed for acoustic waves, and is applied directly to the displacement field. The order of the ABC determines its accuracy and can be chosen to be arbitrarily high. The initial boundary value problem including this ABC is written in second-order form, which is convenient for geophysical finite element (FE) analysis. A special variational formulation is constructed which incorporates the ABC. A standard FE discretization is used in space, and a Newmark-type scheme is used for time-stepping. A long-time instability is observed, but simple means are shown to dramatically postpone its onset so as to make it harmless during the simulation time of interest. Numerical experiments demonstrate the performance of the scheme.     

考虑间隙运动副的桁架单胞等效建模与分析

本文主要研究了含间隙运动副桁架单胞的等效建模方法.主要考虑了桁架单胞的等效刚度问题以及阻尼问题.首先从间隙铰链开始研究,提出全面的铰链模型;其次提出用位移法将桁架单胞等效成板,即把桁架单胞看成是由梁元组成的钢架结构,运用平面钢架位移法得出桁架单胞的等效刚度矩阵,进而得出结构的整体固有频率和等效后的板的刚度矩阵.最后用有限元软件ANSYS对单胞结构在不同边界条件下进行了模态分析,将在自由边界条件下的固有频率和解析得出的频率做了对比,发现二者有很好的吻合度.结果表明由于间隙运动副的存在,使得桁架单胞结构的刚度降低,柔性增强.     

Consistent transmitting boundary with continued-fraction absorbing boundary conditions for analysis of soil–structure interaction in a layered half-space

A continued-fraction absorbing boundary condition (CFABC) is combined with a consistent transmitting boundary and applied to an analysis of soil–structure interaction in a layered half-space. In order to be a perfect absorber for in-plane waves with an arbitrary horizontal wavenumber in a layered half-space, it is proposed that the CFABC be used in the form of a 2-layer. A method for determination of parameters of the 2-layers was proposed for evanescent waves as well as propagating waves. Combined with consistent transmitting boundaries, the 2-layers of CFABC are applied to problems of dynamics of rigid strip and circular foundations on a layered half-space. The results demonstrate that the proposed 2-layers of the CFABC can represent a layered half-space accurately in the entire frequency range and absorb both evanescent and propagating P and S waves effectively.     

巴克豪森励磁检测传感器设计与仿真分析

针对铁磁性材料设计了一种基于巴克豪森效应的励磁检测传感器装置.为了验证所设计的励磁检测传感器中励磁装置的可行性,利用有限元电磁场仿真分析软件Ansoft对磁化器部分进行了有限元仿真,并分析了不同激励条件下的试样磁化效果.通过仿真结果可以得出:磁化装置符合设计要求,能够对试件进行有效的励磁;通过不同参数下的仿真结果得到,励磁电流幅值以及频率是影响励磁效果的关键因素,并且对于特定分析点,随着励磁电流的幅值减小以及频率的增加,试件磁感应强度基本呈现减小的变化趋势.     

基于SPH与FEM的结构入水分析方法

建立基于光滑粒子动力学（smoothed particle hydrodynamics, SPH）、有限元法（finite element method, FEM）和无反射边界耦合的结构入水分析方法,将无限水域利用无反射边界条件截断成有限水域,将有限水域分为流体变形大的SPH区域、流体变形小的FEM区域和声学流体FEM区域,结构用FEM离散。采用通用接触算法模拟SPH与FEM的耦合,采用声固耦合方法处理FEM区域之间的耦合,建立流固耦合的SPH FEM分析方法。该方法结合SPH模拟大变形的优点和FEM的高效性,可实现含自由液面变形、液体飞溅和无限水域等特点的流固耦合问题的模拟,为结构入水分析缩小离散区域、降低自由度和SPH粒子数等提供一种有效的分析方法。     

Dynamics of gravity dam-reservoir systems

The response of a long concrete gravity dam-reservoir system for a harmonic rigid base acceleration normal to the dam axis is investigated.The hydrodynamic pressure acting on the vertical wet surface of the dam is first evaluated in closed form as a function of the unknown deflections of the dam-reservoir interface and the ground acceleration. Employing finite element techniques, the motion of the dam is investigated. The hydrodynamic pressures enter the equation of motion of the dam as loadings in excess of the inertia load.In this approach, the general flexibility of the dam cross-section and the compressibility of water are taken into account. The viscosity of water and the effect of the surface waves are neglected.The coupling between the dam and the reservoir results in changes in the mass and stiffness properties of the dam which depend on the excitation frequency. For an excitation frequency greater than the fundamental frequency of the reservoir, the damping properties of the dam are also modified.     

Topology optimization of electrode coverage of piezoelectric thin-walled structures with CGVF control for minimizing sound radiation

It is impractical to implement arbitrary-shaped piezoelectric patches from the view point of manufacturability of fragile piezoelectric ceramics, thus using designable electrode layers to deliver desired actuation forces provides a more realistic option in engineering applications. This study develops a topological design method of surface electrode distribution over piezoelectric sensors/actuators attached to a thin-walled shell structure for reducing the sound radiation in an unbounded acoustic domain. In the optimization model, the sound pressure norm at specific reference points under excitations at a certain excitation frequency or in a given frequency range is taken as the objective function. The pseudo densities for indicating absence and presence of surface electrodes at each element are taken as the design variables, and a penalized relationship between the densities and the active damping effect is employed. The vibrating structure is discretized with finite element model for the frequency response analysis and the sound radiation analysis in the unbounded acoustic domain is treated by boundary element method. The applied voltage on each actuator is determined by the constant gain velocity feedback (CGVF) control law. The technique of the complex mode superposition in the state space, in conjunction with a model reduction transformation, is adopted in the response analysis of the system characterized by a non-proportional active damping property. In this context, the adjoint-variable sensitivity analysis scheme is derived. The effectiveness and efficiency of the proposed method are demonstrated by numerical examples, and several key factors on the optimal designs are also discussed.     

基于分层模型的复合材料耦合Lamb波频率—波数域特性研究

针对复合材料层合板中耦合Lamb波的传播问题,基于分层模型提出解析建模与有限元数值模拟相结合的方法对其进行预测和评估。利用Legendre正交多项式展开法推导多层各向异性复合材料层合板中耦合Lamb波的控制方程,并对频率-波数域频散特性曲线实现数值求解。基于平面壳单元构建复合材料层合板的有限元模型,采用波结构加载法生成单一Lamb波基本模态,设计复合材料层合板的不同纤维取向、边界和界面约束条件,并经二维傅里叶变换获得有限元模拟数据的频率-波数域频散特性曲线。通过对比验证,结果表明两种方法均有较好的吻合性。     

A combined finite and infinite element approach for modeling spherically symmetric transient subsurface flow

This paper presents a finite element-infinite element coupling approach for modeling a spherically symmetric transient flow problem in a porous medium of infinite extent. A finite element model is used to examine the flow potential distribution in a truncated bounded region close to the spherical cavity. In order to give an appropriate artificial boundary condition at the truncated boundary, a transient infinite element, that is developed to describe transient flow in the exterior unbounded domain, is coupled with the finite element model. The coupling procedure of the finite and infinite elements at their interface is described by means of the boundary integro-differential equation rather than through a matrix approach. Consequently, a Neumann boundary condition can be applied at the truncated boundary to ensure the C¹-continuity of the solution at the truncated boundary. Numerical analyses indicate that the proposed finite element-infinite element coupling approach can generate a correct artificial truncated boundary condition to the finite element model for the unbounded flow transport problem.     

Topological metallic structure design for microwave applications using a modified interpolation scheme

In structural design for microwave applications, metallic structures generate the skin effect that critically affects the performance of microwave devices. In finite element analysis (FEA), highly refined mesh generation is necessary to take the skin effect into account. To avoid the expensive fine meshing and computing process, the condition of the perfect electrical conductor (PEC) or the impedance boundary condition has been generally used in FEA based topology optimization. In this study, we proposed a modified penalization formulation using the shifted sigmoid function for the interpolation of the electric permittivity of conductive materials and applied it to microwave structural design through the phase field design method. The proposed approach is available in case of applications to structural design composed of non-ferromagnetic metals. Based on the derived optimal shape, a simple post-processing scheme is employed only once to determine the clear boundary by eliminating the gray scale area for the purpose of manufacturing feasibility. The validity of the proposed design approach is discussed in three numerical examples allowing the change of the target operation frequency.     

Non-reflecting artificial boundaries for modelling scalar wave propagation problems in two-dimensional half space

Using the operator splitting method, the non-reflecting artificial boundary condition, which has the same form as those originally presented by Hagstrom and Hariharan [Appl. Numer. Math. 27 (1998) 403] as well as Thompson et al. [Comput. Meth. Appl. Mech. Engrg. 191 (2001) 311], is re-derived in this paper to deal with transient scalar wave propagation problems in a two-dimensional homogeneous half space. In particular, the original non-reflecting artificial boundary condition is extended to approximately solve transient scalar wave propagation problems in a two-dimensional layered half space, which has a far field consisting of non-homogeneous materials. The proposed non-reflecting artificial boundary condition can be decomposed into three types of elements: physically meaningful springs and dashpots as well as the generalized energy absorbers, which represent the effects of incident waves at previous time instants on the truncated artificial boundary. Due to the meaningfulness in physics, the proposed non-reflecting artificial boundary is straightforwardly applied to the finite element analysis of wave propagation problems in infinite media. The related numerical results from three application examples have demonstrated the effectiveness, efficiency and usefulness of the proposed non-reflecting artificial boundary in dealing with scalar wave propagation problems in two-dimensional homogeneous and layered half spaces.     

基于弹性关节的二维宽频隔振结构的设计及优化

为了得到具有隔振功能的新型材料,本文对带有弹性关节的新型二维隔振结构的形状、尺寸及材料的选取进行了研究.探究了负泊松比结构实现宽频的带隙功能的作用,分析其在低频处的隔振性能.首先,文章建立了基于弹性关节单元的有限元模型,并以弹性关节的角度作为设计变量,确定角度与单元模型前三阶模态频率之间的关系,获得了最优的结构参数及单元构型.其次,对单元结构进行了动力学分析,给出了结构的动力学响应曲线,得到了隔振频带与结构参数的关系,并且确定了最优角度下的带隙深度和宽度.最后,建立了二维隔振结构有限元模型,对此二维结构进行了动力学分析,得到了在不同方向激励下的动力学响应曲线.结果表明,该二维隔振结构在低频处具有宽而深的频率带隙,实现了将弹性关节与二维隔振结构相结合的低频宽频隔振,为隔振领域的结构和材料设计提供了新思路.     

Topology optimization of sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems

Due to the significant difference of dynamic properties between the fluid medium and the structure, when a vibro-acoustic system is subjected to a higher frequency excitation, it may typically exhibit mid-frequency behavior which involves different wavelength deformations and is very sensitive to the uncertainties of the system. This paper deals with optimized distribution of a sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems by using hybrid boundary element analysis and statistical energy analysis. Based on the solid isotropic material with penalization approach, an artificial sound absorbing material model is suggested and the relative densities of the sound absorbing material are taken as design variables. The sound pressure level at a specified point in the acoustic cavity is to be minimized by distributing a given amount of sound absorbing material. An efficient direct differentiation scheme for the response sensitivity analysis is proposed. Then, the optimization problem is solved by using the method of moving asymptotes. A numerical example illustrates the validity and effectiveness of the present optimization model. Impact of the excitation frequency on optimized topology is also discussed.

     

A finite-element series-expansion technique for linear surface water waves

A numerical method is presented to deal with the propagation of surface water waves in the framework of the linear theory for an inviscid fluid. For particular geometrical configurations of the region in which wave propagation occurs, refraction, diffraction and reflection phenomena can arise simultaneously, so that the solution of the original Berkhoff equation with appropriate boundary conditions becomes essential to achieve an adequate picture of the resulting field. The method is based on a finite element scheme, in which the element matrices are computed by a series expansion technique. The elements are of arbitrary shape, although of constant depth, and two independent numerical approximations are given for the surface-elevation and velocity fields. An application of the method to the propagation of short water waves in a channel connecting two basins of larger dimensions shows that the method can deal with very large domains, at least when compared to the possibilities of the usual finite element approaches.     

阵列式压电模态传感器的实验研究

通过一组阵列式压电薄膜,设计未知边界条件下振动梁的模态传感器。在梁表面均匀布置一组具有相同形状的矩形聚偏氟乙烯(PVDF)薄膜,通过测量PVDF输出与激励力之间的频率响应函数,利用伪逆方法设计这组PVDF的加权系数,从而实现对结构模态坐标的测量。实验研究表明:该方法设计的模态传感器具有良好的滤波效果,非目标阶模态坐标峰值与目标阶相比,下降了12 dB以上,并且不需要预先知道结构的边界条件或者模态信息。进一步讨论了当振动梁的边界条件发生微小扰动时所设计模态传感器的鲁棒性。     

Nonlinear inelastic uniform torsion of composite bars by BEM

In this paper the elastic–plastic uniform torsion analysis of composite cylindrical bars of arbitrary cross-section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationships for the materials are assumed to be elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/elastic moment ratio in uniform inelastic torsion is demonstrated.     

Wave propagation in mechanical waveguide with curved members using wave finite element solution

In this paper, wave propagation in straight and curved mechanical waveguide is investigated. The main objective of the study is to develop a numerical model that can determine the response of the intact or damaged waveguide structure which is subjected to the incident waves. The wave finite element method, which is based on the simple development of standard finite element procedures, is used for the extraction of eigenmodes and analysis of the wave propagation properties. To make an effective use of those eigenmodes, a criterion that is based on the properties of eigensolutions is proposed to condense the mode bases. By using the reduced eigenmode bases, the high frequency wave motion due to the presence of curved part in the waveguide is examined through the wave propagation approach. Numerical analysis indicates that, in order to choose the appropriate wave modes for inspection, it is necessary to obtain both the eigenmode and wave propagation properties, thus the incident wave could be optimised for better monitoring of the structural features and detection of the local damages.