主动约束层阻尼梁的数值模型

为对主动约束层阻尼结构建立精确完善的数学模型，采用有限元建模，并考虑到压电材料的机电耦合效应和粘弹性材料的本构关系随温度、频率的变化而变化的特点，将有限元方法与粘弹性材料的GHA模型相结合，从而避免因粘弹性材料导致的非线性微分方程，能直接求解模态频率、模态阻尼及结构响应。为进一步设计控制器，先在物理空间进行动力缩聚，将系统降至适当的维数，然后在状态空间用鲁棒防阶的方法进一步降阶。这样既能大大降低系统维数，又能保证降阶后系统稳定、可控、可观。这对于重量轻、柔度大、低频密集的大型空间柔性结构尤其重要。     

主动约束层阻尼部分覆盖圆柱壳耦合振动控制

采用分布参数建模,从Ham ilton变分原理出发推导了主动约束层阻尼(ACLD)覆盖圆柱壳耦合振动的运动微分方程和边界条件,并扩展适合一维连续结构分析的基于解析解的谱传递矩阵法(STMM)用于ACLD部分覆盖圆柱壳。通过数值计算,研究了ACLD的长度和位置对固有频率和模态耗散因子的影响。STMM能有效克服有限元法单元数目多、动力学方程阶数高及ACLD长度和位置变化时须重复建模的缺点,以最少的单元数目建立低阶控制方程。典型算例显示了STMM的有效性和精确性。     

主动约束层阻尼结构的数值分析方法

采用板的一阶剪切理论（ＦＯＳＴ），利用Ｈａｍｉｌｔｏｎ原理推导了分布式主动约束层阻尼结构的有限元控制方程。作为算例，应用模态应变能（ＭＳＥ）方法研究了一边固支板的主动约束层阻尼振动控制，分析了控制系统中阻尼层厚度及反馈增益对振动控制效果的影响。     

局部约束阻尼开口柱壳的减振分析及优化

为了缩减开口柱壳结构的振动,本文基于Lagrange方程以及Sanders薄壳理论建立了局部约束阻尼开口柱壳的动力学模型,分析了粘弹性单元分段数和厚度、阻尼单元占空比以及约束层敷设角和厚度对结构前三阶模态损耗因子和固有频率的影响,得到了各参数对结构振动特性的影响规律.并以前三阶损耗因子为目标,应用NSGA-Ⅱ遗传算法对...     

Dispersion error reduction for acoustic problems using the smoothed finite element method (SFEM)

The smoothed finite element method (SFEM), which was recently introduced for solving the mechanics and acoustic problems, uses the gradient smoothing technique to operate over the cell‐based smoothing domains. On the basis of the previous work, this paper reports a detailed analysis on the numerical dispersion error in solving two‐dimensional acoustic problems governed by the Helmholtz equation using the SFEM, in comparison with the standard finite element method. Owing to the proper softening effects provided naturally by the cell‐based gradient smoothing operations, the SFEM model behaves much softer than the standard finite element method model. Therefore, the SFEM can significantly reduce the dispersion error in the numerical solution. Results of both theoretical and numerical experiments will support these important findings. It is shown clearly that the SFEM suits ideally well for solving acoustic problems, because of the crucial effectiveness in reducing the dispersion error. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupling finite difference method with finite particle method for modeling viscous incompressible flows

A hybrid approach to couple finite difference method (FDM) with finite particle method (FPM) (ie, FDM-FPM) is developed to simulate viscous incompressible flows. FDM is a grid-based method that is convenient for implementing multiple or adaptive resolutions and is computationally efficient. FPM is an improved smoothed particle hydrodynamics (SPH), which is widely used in modeling fluid flows with free surfaces and complex boundaries. The proposed FDM-FPM leverages their advantages and is appealing in modeling viscous incompressible flows to balance accuracy and efficiency. In order to exchange the interface information between FDM and FPM for achieving consistency, stability, and convergence, a transition region is created in the particle region to maintain the stability of the interface between two methods. The mass flux algorithm is defined to control the particle creation and deletion. The mass is updated by N-S equations instead of the interpolation. In order to allow information exchange, an overlapping zone is defined near the interface. The information of overlapping zone is obtained by an FPM-type interpolation. Taylor-Green vortices and lid-driven shear cavity flows are simulated to test the accuracy and the conservation of the FDM-FPM hybrid approach. The standing waves and flows around NACA airfoils are further simulated to test the ability to deal with free surfaces and complex boundaries. The results show that FDM-FPM retains not only the high efficiency of FDM with multiple resolutions but also the ability of FPM in modeling free surfaces and complex boundaries.     

The coupling method for torsion problem of the square cross-section bar with cracks

By coupling natural boundary element method (NBEM) with FEM based on domain decomposition, the torsion problem of the square cross-sections bar with cracks have been studied, the stresses of the nodes of the cross-sections and the stress intensity factors have been calculated, and some distribution pictures of the stresses have been drawn. During computing, the effect of the relaxed factors to the convergence speed of the iterative method has been discussed. The results of the computation have confirmed the advantages of the NBEM and its coupling with the FEM. Foundation item: the State Key Laboratory of Science and Engineering Computation Biography: ZHAO Hui-ming (1971-)     

一种新的有限元模型移频动力缩聚法

将矩阵幂迭代法与移频技术相结合,建立了一种新的结构动力缩聚方法.该方法首先应用矩阵幂迭代法对结构的初始有限元模型进行一次缩聚,计算初始缩聚模型的特征值,然后通过判断低阶特征值的收敛情况确定移频位置,选择合适的移频值,建立移频后的广义特征方程;再根据矩阵幂迭代法迭代计算新的广义特征方程的动力缩聚矩阵,经迭代收敛后得到精确...     

结构可靠性分析方法——AFOSM的进一步精确化

给出了结构可靠性分析方法－改进一次二阶矩法（AFOSM）一套新的计算公式，并以纤维增强复合材料层合板结构为研究对象，运用随机有限元法（SFEM）数值计算方法分析各单层板的可靠性指标β。文中算例计算结果表明，本文给出的计算公式是合理的和有效的，而且用它所得计算结果比用原AFOSM所得结果更加精确。     

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

Parallel FEM LES with one-equation subgrid-scale model for incompressible flows

This article develops a parallel large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model based on the Galerkin finite element method and three-dimensional (3D) brick elements. The governing filtered Navier–Stokes equations were solved by a second-order accurate fractional-step method, which decomposed the implicit velocity–pressure coupling in incompressible flow and segregated the solution to the advection and diffusion terms. The transport equation for the SGS turbulent kinetic energy was solved to calculate the SGS processes. This FEM LES model was applied to study the turbulence of the benchmark open channel flow at a Reynolds number Re_τ = 180 (based on the friction velocity and channel height) using different model constants and grid resolutions. By comparing the turbulence statistics calculated by the current model with those obtained from direct numerical simulation (DNS) and experiments in literature, an optimum set of model constants for the current FEM LES model was established. The budgets of turbulent kinetic energy and vertical Reynolds stress were then analysed for the open channel flow. Finally, the flow structures were visualised to further reveal some important characteristics. It was demonstrated that the current model with the optimum model constants can predict well the organised structure near the wall and free surface, and can be further applied to other fundamental and engineering applications.     

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

A wavelet-based variational multiscale method for the LES of incompressible flows in a high-order DG-FEM framework

This work focuses upon the development of a wavelet-based variant of the variational multiscale method (VMS) for accurate and efficient large eddy simulation (LES) called wavelet-based VMS-LES (WMS-LES). This approach has been incorporated within the framework of a high-order incompressible flow solver based upon the pressure-stabilized discontinuous Galerkin finite element method (DG-FEM). The VMS approach is designed to produce an a priori scale separation of the governing equations, in a manner which makes no assumptions on either the boundary conditions or the mesh uniformity. Using second-generation wavelets (SGWs) elementwise for scale separation ensures, on one hand, the preservation of the computational compactness of the DG-FEM scheme and, on the other hand, the ability to achieve scale separation in wavenumber space. The optimal space-frequency localization property of the SGW provides an improvement over the commonly used Legendre polynomials. The suitability of the elementwise SGW scale-separation operation as a tool for error indication has been demonstrated in an h-adaptive computation of the reentrant corner test case. Finally, the DG-FEM solver and the WMS-LES method have been assessed through simulations upon the three-dimensional Taylor-Green vortex test case. Our results indicate that the WMS-LES approach exhibits a distinct improvement over the monolevel LES approach. This effect is not produced by a change in the magnitude of the subgrid dissipation but rather by the redistribution of the subgrid dissipation in wavenumber space.     

An immersed boundary method for fluid flows around rigid objects

In this paper, we present an immersed boundary method for solving fluid flow problems in the presence of static and moving rigid objects. A FEM is used starting from a base mesh that does not represent exactly rigid objects (non?body?conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier–Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body?fitted meshes whenever possible. Copyright © 2014 John Wiley & Sons, Ltd.     

An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation

This paper presents a fast numerical method, based on the indirect shooting method and Proper Orthogonal Decomposition (POD) technique, for solving distributed optimal control of the wave equation. To solve this problem, we consider the first‐order optimality conditions and then by using finite element spatial discretization and shooting strategy, the solution of the optimality conditions is reduced to the solution of a series of initial value problems (IVPs). Generally, these IVPs are high‐order and thus their solution is time‐consuming. To overcome this drawback, we present a POD indirect shooting method, which uses the POD technique to approximate IVPs with smaller ones and faster run times. Moreover, in the presence of the nonlinear term, to reduce the order of the nonlinear calculations, a discrete empirical interpolation method (DEIM) is applied and a POD/DEIM indirect shooting method is developed. We investigate the performance and accuracy of the proposed methods by means of 4 numerical experiments. We show that the presented POD and POD/DEIM indirect shooting methods dramatically reduce the CPU time compared to the full indirect shooting method, whereas there is no significant difference between the accuracy of the reduced and full indirect shooting methods.     

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time‐independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi–Babuska condition. The k–l model is used to complete the turbulence closure problem. The non‐symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a ‘V‐cycling’ schedule. These methods are all compared to the non‐symmetric frontal solver. Copyright © 1999 John Wiley & Sons, Ltd.