A comparative study on algorithms of boundary element solution for free torsional vibration of bodies of revolution

In this paper the functionu=rsin in cylindrical coordinates (r,,z) is introduced into the equation for free torsional vibration of bodies of revolution (where=v / r represents the angle of twist). With the static fundamental solution (–1 /R) a mixed BEM / FEM equation is derived. The domain integral term in the equation is discretized by Serendipity elements instead of commonly used constant value finite elements in the literature. The equation is an algebraic eigenvalue one. The dynamic fundamental solution (e ^1R /R) is also used for deriving the other mixed BEM / FEM equation. An appropriate iterative solution procedure is described. An algebraic eigenvalue equation can be obtained and its solution accuracy is almost interior meshing independent. A number of examples are studied. The results show the good economy and high accuracy of the algorithms proposed.The Project is Supported by National Natural Science Foundation of China.     

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.     

An improvement of the Prandtl-Reuss theory and the hybrid / mixed vari-stiffness method of finite element analysis

The common Prandtl-Reuss theory has been improved in this paper. A quasi-flow law of the isotropic hardening Mises materials has been proposed as well, on the basis of which, an efficient iterative algorithm of finite element analysis, hybrid / mixed vari-stiffness method, has been obtained. The numerical examples calculated by the plane stress / strain element model are given. Compared with the common initial stress method, the hybrid / mixed vari-stiffness method shows its advantages in the convergent speed, calculating accuracy and treatment scheme of the incompressibility of materials.     

An efficient edge‐based level set finite element method for free surface flow problems

We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit solution scheme is proposed. A custom data structure, obtained by blending node‐based and edge‐based approaches is presented so to allow a good parallel performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples. Copyright © 2012 John Wiley & Sons, Ltd.     

A combined programming and iteration algorithm for finite element analysis of three-dimensional contact problems

Comparing with two-dimensional contact problems, three-dimensional frictional contact problems are more difficult to deal with, because of the unknown slip direction of the tangential force and enormous computing time. In order to overcome these difficulties, a combined PQP (Parametric Quadratic Programming) and iteration method is derived in this paper. The iteration algorithm, which alleviates the difficulty of unknown slip direction, is used along with the PQP method to cut down computing costs. Numerical example is given to demonstrate the validity of the present algorithm. The project supported by the Machinary and Electronics Ministry of China     

偶应力问题的杂交／混合元分析

将弹性力学中Hellinger—Reissner交分原理推广到偶应力理论中，并以罚函数的形式引入其约束条件，提出了一种有效的杂交／混合单元。文中分别分析了带中心小孔平板在轴向均匀加载时的应力集中情况，以及含中问裂纹的无限平板单轴拉伸时的位移场和应力场。算例表明，该单元计算效率高，精度好，即使在材料本征长度很小时，仍然能够得到相当理想的结果。     

基于微分求积有限元法的双层微板系统振动特性研究

基于修正的偶应力理论和两变量精化的剪切变形理论,建立了由Winkler-Pasternak连续弹性夹层连接的双层微板系统的自由振动模型,着重推导了系统异步振动的运动微分方程和势能泛函。融合Gauss-Lobatto求积准则和微分求积准则构造了具有C¹连续性的微分求积有限元。通过与已有文献进行对比,验证了数值方法的有效性。详细讨论了各种因素对系统同步和异步振动特性的影响。结果表明,系统的自由振动特性对材料尺度参数、长宽比、长厚比以及边界条件呈现出依赖性;弹性夹层刚度仅对系统异步振动产生作用;随着模态阶次的增大,材料尺度参数和弹性夹层刚度对异步振动频率和模态的影响变得显著。     

求解不连续中厚板自由振动的微分容积单元法

基于区域叠加原理和微分容积法,发展了一种新型的数值方法——微分容积单元法,用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元,在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程．在相邻的单元连接处应用位移连续条件和平衡条件,引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程,由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程,并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。     

Introduction of turbulent model in a mixed finite volume/finite element method

The aim of this work is to present a new numerical method to compute turbulent flows in complex configurations. With this in view, a k-? model with wall functions has been introduced in a mixed finite volume/finite element method. The numerical method has been developed to deal with compressible flows but is also able to compute nearly incompressible flows. The physical model and the numerical method are first described, then validation results for an incompressible flow over a backward-facing step and for a supersonic flow over a compression ramp are presented. Comparisons are performed with experimental data and with other numerical results. These simulations show the ability of the present method to predict turbulent flows, and this method will be applied to simulate complex industrial flows (flow inside the combustion chamber of gas turbine engines). The main goal of this paper is not to test turbulence models, but to show that this numerical method is a solid base to introduce more sophisticated turbulence model.     

A potential-hybrid/mixed finite element scheme for analysis of plates and cylindrical shells

Based on the potential-hybrid/mixed finite element scheme,4-node quadrilateralplate-bending elements MP4,MP4a and cylindrical shell element MCS4 are derived with,the inclusion of splitting rotations.All these elements demonstrate favorable convergencebehavior over the existing counterparts,free from spurious kinematic modes and do notexhibit locking phenomenon in thin plate/shell limit.Inter-connections between the existingmodified variational functionals for the use of formulating C~0-and C~1-continuous elementsare also indicated.Important particularizations of the present scheme include Prathap’sconsistent field formulation,the RIT/SRIT-compatible displacement model and so on.     

Improving the robustness of the control volume finite element method with application to multiphase porous media flow

Control volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models.     

An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.     

基于边光滑有限元法的加筋板静力和自由振动分析

运用边光滑有限元法,研究分析了加筋板结构的静力和自由振动问题。在边光滑有限元法中,将基于边的应变光滑技术用于对原来的应变场进行光滑操作;由于应变光滑技术能够适当地软化原来过刚的有限元模型,从而能够得到更加接近于系统准确刚度的光滑有限元模型;鉴于三角形单元良好的适用性,选用三角形单元对模型进行网格划分;同时,为了解决低阶Reissner-Mindlin板单元弯曲过程中的横向剪切自锁问题,采用了一种新型的离散剪切间隙技术。算例的数值计算结果表明,与传统的有限元法相比,边光滑有限元法能够得到精度更高的计算结果,且收敛更快,计算效率更佳。     

Extension of domain‐free discretization method to simulate compressible flows over fixed and moving bodies

This paper is the first endeavour to present the local domain‐free discretization (DFD) method for the solution of compressible Navier–Stokes/Euler equations in conservative form. The discretization strategy of DFD is that for any complex geometry, there is no need to introduce coordinate transformation and the discrete form of governing equations at an interior point may involve some points outside the solution domain. The functional values at the exterior dependent points are updated at each time step to impose the wall boundary condition by the approximate form of solution near the boundary. Some points inside the solution domain are constructed for the approximate form of solution, and the flow variables at constructed points are evaluated by the linear interpolation on triangles. The numerical schemes used in DFD are the finite element Galerkin method for spatial discretization and the dual‐time scheme for temporal discretization. Some numerical results of compressible flows over fixed and moving bodies are presented to validate the local DFD method. Copyright © 2006 John Wiley & Sons, Ltd.     

Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

The linear and nonlinear torsional free vibration analyses of functionally graded micro/nano-tubes (FGMTs) are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton’s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method (HAM). This method is based on the Taylor series with an embedded parameter, and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.     

无单元法求解欧拉梁及梁系的自由振动问题

双变量无单元法以广义移动最小二乘法为理论基础,同时考虑挠度和转角双变量.采用双变量无单元法建立了欧拉粱的质量矩阵和刚度矩阵,并进行自由振动的计算.不同边界条件欧拉梁动力特性的算例表明:双变量无单元法比与只考虑挠度的单变量无单元法具有更高的插值精度,并能在高阶振型计算中获得明显优于有限元的计算精度.通过试算法对影响半径中的scale乘子进行了讨论,认为在动力计算中Scale取3.5较合理.最后在欧拉粱的基础上,将无单元法应用于梁系模型的自由振动计算,显示了该法在复杂模型中的精确性.     

Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

The complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher‐order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural–acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural–acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

Design sensitivity and finite element analysis of free surface flows with application to optimal design of casting rigging systems

A novel, fully-analytical design sensitivity formulation for transient, turbulent, free surface flows is derived and implemented in the context of finite element analysis. The time-averaged, turbulent form of the Navier–Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free surface movement. The design derivatives of these governing equations are computed and solved to find the analytical sensitivities of the fluid position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sensitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The results produce runner shapes which eliminate mold-gas aspiration. © 1998 John Wiley & Sons, Ltd.     

Some applications of semi-analytical finite element method in static and dynamic analysis of structures

In this paper a kind of semi-analytical finite element method based on the transfer matrix analysis of shells of revolution is briefly formulated. Some recent investigations on its application are presented: (1) a reanalysis algorithm for improving the accuracy of free vibration analysis; (2) a kind of semi-analytical ring element for the stress analysis of a curved pipe of the slender torus shell type.