氯离子在混凝土中扩散传输的有限体积法模拟分析

基于氯离子在混凝土结构中的扩散传输理论,建立了氯离子扩散传输偏微分方程,讨论了边界与初始条件。根据因变量在有限大小的控制体积中满足守恒定理,建立了氯离子在混凝土中扩散传输的离散方程,编制了计算程序。算例分析表明,有限体积法可以很好地模拟氯离子在混凝土中的扩散传输,可以分析计算复杂边界条件下的混凝土内的氯离子分布,并对受氯离子侵蚀混凝土结构的使用寿命进行预测分析。     

A finite volume format for structural mechanics

A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.     

Application of the finite volume method and unstructured meshes to linear elasticity

A recent emergence of the finite volume method (FVM) in structural analysis promises a viable alternative to the well‐established finite element solvers. In this paper, the linear stress analysis problem is discretized using the practices usually associated with the FVM in fluid flows. These include the second‐order accurate discretization on control volumes of arbitrary polyhedral shape; segregated solution procedure, in which the displacement components are solved consecutively and iterative solvers for the systems of linear algebraic equations. Special attention is given to the optimization of the discretization practice in order to provide rapid convergence for the segregated solution procedure. The solver is set‐up to work efficiently on parallel distributed memory computer architectures, allowing a fast turn‐around for the mesh sizes expected in an industrial environment. The methodology is validated on two test cases: stress concentration around a circular hole and transient wave propagation in a bar. Finally, the steady and transient stress analysis of a Diesel injector valve seat in 3‐D is presented, together with the set of parallel speed‐up results. Copyright © 2000 John Wiley & Sons, Ltd.     

3D modelling of strong discontinuities in elastoplastic solids: fixed and rotating localization formulations

This paper is concerned with the incorporation of displacement discontinuities into a continuum theory of elastoplasticity for the modelling of localization processes such as cracking in brittle materials. Based on the strong discontinuity approach (SDA) (Computational Mechanics 1993; 12: 277–296) mesh objective 2D and 3D finite element formulations are developed using linear and quadratic 2D elements as well as 8‐noded 3D elements. In the formulation of the finite‐element model proposed in the paper, the analogy with standard formulations is emphasized. The parameter defining the amplitude of the displacement jump within the finite element is condensed out at the material level without employing the standard static condensation technique. This approach results in linearized constitutive equations formally identical to continuum models. Therefore, the standard return mapping algorithm is used to solve the non‐linear equations. In analogy to concepts used in continuum smeared crack models, a rotating formulation of the SDA is proposed in addition to the standard concept of fixed discontinuities. It is shown that the rotating localization approach reduces locking effects observed in analyses based on fixed localization directions. The applicability of the proposed SDA finite‐element model as well as its numerical performance is investigated by means of a three‐dimensional ultimate load analysis of a steel anchor embedded in a concrete block subjected to a shear force. Copyright © 2003 John Wiley & Sons, Ltd.     

3D mass-redistributed finite element method in structural–acoustic interaction problems

A 2D mass-redistributed finite element method (MR-FEM) for pure acoustic problems was recently proposed to reduce the dispersion error. In this paper, the 3D MR-FEM is further developed to solve more complicated structural–acoustic interaction problems. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and MR-FEM is applied in acoustic domain. The global equations of structural–acoustic interaction problems are then established by coupling the MR-FEM for the acoustic domain and the edge-based smoothed finite element method for the structure. The perfect balance between the mass matrix and stiffness matrix is able to improve the accuracy of the acoustic domain significantly. The gradient smoothing technique used in the structural domain can provide a proper softening effect to the “overly-stiff” FEM model. A number of numerical examples have demonstrated the effectiveness of the mass-redistributed method with smoothed strain.     

Parallelized FVM algorithm for three-dimensional viscoelastic flows

 A parallel implementation for the finite volume method (FVM) for three-dimensional (3D) viscoelastic flows is developed on a distributed computing environment through Parallel Virtual Machine (PVM). The numerical procedure is based on the SIMPLEST algorithm using a staggered FVM discretization in Cartesian coordinates. The final discretized algebraic equations are solved with the TDMA method. The parallelisation of the program is implemented by a domain decomposition strategy, with a master/slave style programming paradigm, and a message passing through PVM. A load balancing strategy is proposed to reduce the communications between processors. The three-dimensional viscoelastic flow in a rectangular duct is computed with this program. The modified Phan-Thien–Tanner (MPTT) constitutive model is employed for the equation system closure. Computing results are validated on the secondary flow problem due to non-zero second normal stress difference N ₂. Three sets of meshes are used, and the effect of domain decomposition strategies on the performance is discussed. It is found that parallel efficiency is strongly dependent on the grid size and the number of processors for a given block number. The convergence rate as well as the total efficiency of domain decomposition depends upon the flow problem and the boundary conditions. The parallel efficiency increases with increasing problem size for given block number. Comparing to two-dimensional flow problems, 3D parallelized algorithm has a lower efficiency owing to largely overlapped block interfaces, but the parallel algorithm is indeed a powerful means for large scale flow simulations. Received: 2 July 2002 / Accepted: 15 November 2002 This research is supported by an A^⋆STAR Grant EMT/00/011.     

基于频率变化识别结构损伤的摄动有限元方法

在结构有限元计算模型中定义了单元的损伤识别参数,将摄动理论与振动理论相结合导出结构振动特征值的一、二阶摄动方程,并由此建立了结构的一、二次损伤识别方程,给出了两种方程在欠定情况下求解损伤识别参数的优化算法。该方法仅使用在役结构固有频率测量值就能识别出结构的损伤位置和损伤程度,以及结构的老化程度,避免了使用模态振型识别结构损伤,因测量精度不高或自由度不足带来的误差。通过一座连续梁桥损伤识别的数值仿真结果,证明了该方法的有效性和实用性。该方法可用于大型结构的损伤识别或健康监测。     

Recursive approach for random response analysis using non-orthogonal polynomial expansion

Using non-orthogonal polynomial expansions, a recursive approach is proposed for the random response analysis of structures under static loads involving random properties of materials, external loads, and structural geometries. In the present formulation, non-orthogonal polynomial expansions are utilized to express the unknown responses of random structural systems. Combining the high-order perturbation techniques and finite element method, a series of deterministic recursive equations is set up. The solutions of the recursive equations can be explicitly expressed through the adoption of special mathematical operators. Furthermore, the Galerkin method is utilized to modify the obtained coefficients for enhancing the convergence rate of computational outputs. In the post-processing of results, the first- and second-order statistical moments can be quickly obtained using the relationship matrix between the orthogonal and the non-orthogonal polynomials. Two linear static problems and a geometrical nonlinear problem are investigated as numerical examples in order to illustrate the performance of the proposed method. Computational results show that the proposed method speeds up the convergence rate and has the same accuracy as the spectral finite element method at a much lower computational cost, also, a comparison with the stochastic reduced basis method shows that the new method is effective for dealing with complex random problems.     

成层介质中平面内自由波场的一维化时域算法

提出了一种弹性水平成层半空间中平面内波动斜入射时自由波场时域计算的一维化有限元方法。首先,基于弹性波在斜入射情形下的传播特点对计算区域进行自动虚拟网格划分。然后将集中质量有限元法和中心差分法相结合建立节点的二维运动方程组,并根据采用的离散化准则和显式有限元法的特点将其转化为一维方程组。求解此方程组,即得到自由场中竖向一列节点的运动。最后根据行波的传播规律得到全部自由波场。以P波为例给出了理论分析和数值算例。结果表明,该方法不仅简单实用,而且具有较高的精度和良好的稳定性。     

A domain decomposition method for a two‐phase transport model of polymer electrolyte fuel cell containing micro‐porous layer

In this paper, a nonlinear Dirichlet–Robin iteration‐by‐subdomain domain decomposition method is studied for a multidimensional, multiphysics, and multiphase model of polymer electrolyte fuel cell (PEFC) containing micro‐porous layer (MPL). Across the interface of gas diffusion layer and MPL in PEFC, it is well known that the capillary pressure is continuous, whereas liquid saturation is discontinuous, by which the liquid‐water removal in the porous electrodes can be significantly enhanced. We design a type of non‐overlapping domain decomposition method to deal with water transport in such multi‐layer diffusion media, where Kirchhoff transformation and its inverse techniques are employed to conquer the discontinuous and degenerate water diffusivity in the coexisting single‐phase and two‐phase regions. In addition, the conservation equations of mass, momentum, charge, and hydrogen and oxygen transport are also solved by the combined finite element–upwind finite volume method (FEM/FVM) to overcome the dominated convection effect in gas channels. Numerical simulations demonstrate that the presented techniques are effective in obtaining a fast and convergent nonlinear iteration for such a 3D PEFC model within around 50 steps, in contrast with the oscillatory and nonconvergent iteration conducted by standard FEM/FVM. A series of numerical convergence tests are also carried out to verify the efficiency and accuracy of the present numerical techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

A wall boundary treatment using analytical volume integrations in a particle method

Numerical treatment of complicated wall geometry has been one of the most important challenges in particle methods for computational fluid dynamics. In this study, a novel wall boundary treatment using analytical volume integrations has been developed for two-dimensional (2D) incompressible flow simulations with the moving particle semi-implicit method. In our approach, wall geometry is represented by a set of line segments in 2D space. Thus, arbitrary-shaped boundaries can easily be handled without auxiliary boundary particles. The wall's contributions to the spatial derivatives as well as the particle number density are formulated based on volume integrations over the solid domain. These volume integrations are analytically solved. Therefore, it does not entail an expensive calculation cost nor compromise accuracy. Numerical simulations have been carried out for several test cases including the plane Poiseuille flow, a hydrostatic pressure problem with complicated shape, a high viscous flow driven by a rotating screw, a free-surface flow driven by a rotating cylinder and a dam break in a tank with a wedge. The results obtained using the proposed method agreed well with analytical solutions, experimental observations or calculation results obtained using finite volume method (FVM), which confirms that the proposed wall boundary treatment is accurate and robust.     

固体力学问题数值解的一种验证方法

给出了固体力学几何非线性动态问题数值解的一种精度验证方法。通过假定初始构形和现时构形之间的映射关系,利用固体力学的控制方程即可求得产生这种构形的体积力,则假定构形和所得到的体积力就构成了问题的解析解。在这些解析解的基础上,提出了一种检验数值方法精度的标准试验,可用于二维和三维问题、隐式算法和显式算法、小变形和大变形分析、弹性材料和超弹性材料。在线性位移场的情况下本文方法是和传统的分片检验(patchtest)一致的。文中给出了无网格迦辽金法(EFGM)精度检验的几个算例。     

A block iterative finite element algorithm for numerical solution of the steady–state,compressible Navier–Stokes equations

An iterative method for numerically solving the time independent Navier–Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss–Seidel principle in block form to the systems of the non-linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C⁰-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.     

Three dimensional elasticity solution for static and dynamic analysis of multi-directional functionally graded thick sector plates with general boundary conditions

In this study, the three dimensional static and dynamic behavior of a thick sector plate made of two-directional functionally graded materials (2D-FGMs) is investigated. Material properties are assumed to be graded in both radial and thickness directions according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the 3D theory of elasticity. Employing 3D graded finite element method (GFEM) based on the Hamilton’s principle and Rayleigh–Ritz energy method, the equations are solved in space and time domains. In the case of static analysis, the sector plate is subjected to a uniform pressure load and for dynamic analysis is subjected to an impact loading. The effects of material gradient index, boundary condition and thickness to radius ratio of the sector plate on the static and dynamic responses are presented and discussed.     

基于CFD/CSD耦合的二维壁板颤振特性研究

该文基于CFD/CSD(计算流体动力学/计算结构动力学)耦合方法,在时域内对二维壁板的颤振进行了分析.采用D'Alembert原理和有限元方法,建立了壁板在超声速流作用下的非线性动力学模型.采用Von Karman非线性应变位移关系来描述结构大变形,用Euler方程计算了非定常气动力.应用载荷参数空间插值传递方法,实现...     

等温黑体空腔积分发射率响应面法研究

高性能黑体辐射源是高精度复现辐射温度的关键装置。采用有限体积法模拟计算了黑体空腔积分发射率,其结果与Monte-Carlo法计算结果吻合良好,且在高发射率时较Monte-Carlo法能更准确地模拟空腔积分发射率的变化趋势。基于响应面试验设计,模拟了圆锥-圆柱黑体空腔长径比L/D、光阑开孔直径比Da/D、圆锥顶角θ和腔壁材料发射率ε及其交互作用对空腔积分发射率εe的影响。结果表明:Da/D和ε对εe影响显著;L/D和θ对εe的影响不显著。研究结果可为高性能黑体辐射源的研制和研究提供借鉴。     

Fast variation method for elastic strip calculation

A new, fast, variation method (FVM) for determining an elastic strip response to stresses arbitrarily distributed on the flat side of the strip is proposed. The remaining surface of the strip may have an arbitrary form, and it is free of stresses. The FVM, as well as the wellknown finite element method, starts with the variational principle. However, it does not use the meshing of the strip. A comparison of FVM results with the exact analytical solution in the special case of shear stresses and a rectangular strip demonstrates an excellent agreement     

The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

This article deals with the implementation of the lattice Boltzmann method (LBM) in conjunction with the finite volume method (FVM) for the solution of conduction–radiation problems with heat flux and temperature boundary conditions. Problems in 1‐D planar and 2‐D rectangular geometries have been considered. The radiating–conducting participating medium is absorbing, emitting and scattering. In the 1‐D planar geometry, the south boundary is subjected to constant heat flux, while in the 2‐D geometry the south and/or the north boundary is at constant heat flux condition. The remaining boundaries are at prescribed temperatures. The energy equation is solved using the LBM and the radiative information for the same is computed using the FVM. In the direct method, by prescribing temperatures at the boundaries, the temperature profile and heat flux are calculated. The computed heat flux values are imposed at the boundaries to establish the correctness of the numerical code in the inverse method. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction–radiation parameter, the boundary emissivity and the total heat flux and boundary temperatures are studied on the distributions of temperature, radiative and conductive heat fluxes. The results of the LBM in conjunction with the FVM have been found to compare very well with those available in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite calculus formulation for incompressible solids using linear triangles and tetrahedra

Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective–diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi‐implicit and explicit 2D and 3D non‐linear transient dynamic analysis of an impact problem and a bulk forming process are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

A scaled boundary finite element based explicit topology optimization approach for three-dimensional structures

This article proposes an efficient approach for solving three-dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the moving morphable component (MMC)-based topology optimization framework. In the proposed method, accurate response analysis in the boundary region dictates the accuracy of the entire analysis. In this regard, an adaptive refinement scheme is developed where the refined mesh is only used in the boundary region while relating coarse mesh is used away from the boundary. Numerical examples demonstrate that the computational efficiency of 3D topology optimization can be improved effectively by the proposed approach.