Nodeless variable finite element method for stress analysis using flux-based formulation

A nodeless variable element is combined with an adaptive meshing technique to improve solution accuracy of the finite element method for analyzing two-dimensional elasticity problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without requiring additional actual nodes. The fluxbased formulation is developed for the nodeless variable finite element to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The superconvergent patch recovery procedure is implemented to compute accurate stresses from the nodeless variable finite element solutions. The effectiveness of the combined procedure for providing higher solution convergence rate from the proposed formulation is evaluated by two well-known examples.     

Interaction of high-speed compressible viscous flow and structure by adaptive finite element method

Interaction behaviors of high-speed compressible viscous flow and thermal-structural response of structure are presented. The compressible viscous laminar flow behavior based on the Navier-Stokes equations is predicted by using an adaptive cell-centered finite-element method. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite-element method. The finite-element formulation and computational procedure are described. The performance of the combined method is evaluated by solving Mach 4 flow past a flat plate and comparing with the solution from the finite different method. To demonstrate their interaction, the highspeed flow, structural heat transfer, and deformation phenomena are studied by applying the present method to Mach 10 flow past a flat plate.     

A novel meshing algorithm for dynamic finite element analysis

This paper describes a new algorithm to handle problems in dynamic finite element analysis and run-time simulation, where mesh re-generation or dynamic adjustment is required. Based on a concept called coded box cell (CBC) substitution, this algorithm can be applied to both initial mesh generation and dynamic mesh adjustment along the border zones of multiple primitives that form an entire model. During the initial mesh generation, appropriate labels are assigned to the nodes and the faces of each finite element. These labels are used to facilitate decision-making in dynamic mesh adjustment. A mapping technique is adopted to transform curved surfaces to plain surfaces for the ease of automatic mesh adjustment while still using the same algorithm. The results of a case study show that a finite element mesh can be adjusted dynamically and locally around its border zone; and the algorithm can be utilized effectively to simulate the thermal behavior of a device under real operating conditions.     

Contact finite element method for dynamic meshing characteristics analysis of continuous engaged gear drives

The dynamic meshing characteristics of gear drives have been a major concern in the design of power transmission systems as they affect vibration, acoustic noise, durability and efficiency. Gaining a more comprehensive understanding of the dynamic meshing characteristics of continuous engaged gear drives is a key to the development of power transmission systems. In this paper, a dynamic contact finite element analysis method, considering the variation of the engaged teeth pairs, the loaded elastic and contact deformations, and the sliding friction, is presented for the dynamic meshing characteristics analysis of continuous and elastic engaged gear drives. Various kinds of continuous engaged gear models under low and high speed condition are simulated and compared using the presented method. The tooth profile modification was designed based on the simulation results. Moreover, the effects of the tooth profile modification, the sliding friction and the time-varying meshing stiffness upon the dynamic meshing characteristics of continuous engaged gear drives are discussed in detail. The results show that the method is not only effective in designing and evaluating the tooth profile modification, but also in studying the dynamic meshing characteristics of continuous engaged gear drives with realistic time-varying meshing stiffness and tooth sliding friction. The present method could provide an effective tool for vibration mechanism study and dynamic design of the continuous engaged gear drives considering more influence factors.     

A second-order time-accurate finite element method for analysis of conjugate heat transfer between solid and unsteady viscous flow

A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind Petrov-Galerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Five test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder, forced convection cooling across rectangular blocks, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the method presented. This paper was recommended for publication in revised form by Associate Editor Kyung-Soo Yang Atipong Malatip received his B.S. degree in Mechanical Engineering from King Mongkut’s University of Technology North Bangkok, Thailand, in 2002. He then received his M.S. degree in Mechanical Engineering Chulalongkorn University, Thailand, in 2005. He is currently pursuing a Ph.D. degree in Mechanical Engineering at Chulalongkorn University. His research interests include computational fluid dynamics and fluid-thermal-structural interaction. Niphon Wansophark received his B.S., M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 1996, 2000, and 2007, respectively. He is an Assistant Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods and finite element method. Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chula-longkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis.     

基于ABAQUS的三环减速器多齿啮合效应分析

为了研究三环减速器的多齿啮合效应问题,从而找出三环减速器实际承载能力远高于理论承载能力的原因,根据相关力学理论,借助大型非线性有限元分析软件ABAQUS,合理建立了三环减速器主传动部分的平面有限元模型,并在不同工况下,对三环减速器的复杂非线性接触问题进行有限元分析,得到了传动过程中的实际啮合齿数及各啮合齿的应力情况,为充分发挥三环减速器的高承载能力提供了理论依据,并为三环减速器的设计提供指导。     

有限元的因次分析法

利用因次分析法对用有限元法所分析的结构进行分析,求得了模型和原型之间相似准则,对于同种材料的结构,当结构几何比为λl,外加动载荷之比为λl^2,振动频率之比为时1／λl,结构满足相似准则,则结构的振动加速度之比为1／λl,辐射声功率之比为λl^2。     

因次分析法在结构有限元分析中的应用

将因次分析法应用于结构的有限元分析中,求得模型和原型结构之间相似准则,并以结构的模态分析和谐响应分析为例,分析结构的相似关系,同时也验证了这种做法可行性。     

对数螺旋锥齿轮啮合模型的建立及有限元分析的基本思想

对于一种新型锥齿轮—对数螺旋锥齿轮,研究其啮合模型在Pro/E中的建立方法。由于其齿向线是圆锥对数螺旋线,提出了一种新的建模方法,包括三个创新点:利用夹角为的两条圆锥对数螺旋线来确定齿廓曲线的空间位置,使渐开线得以精确定位;将盘绕在节锥曲面上的圆锥对数螺旋线作为扫引轨迹线,保证齿形的准确性;扫描混合截面建立在扫引线的法面内,使轮齿各点法面内的齿形均是标准齿形。在此基础上应用有限元理论的基本思想对啮合模型作了一些运算研究,进一步分析对数螺旋锥齿轮啮合传动过程中的相关特性,进而为该种新型锥齿轮的设计和应用提供理论依据。     

Polyhedral smoothed finite element method for thermoelastic analysis

Thermoelastic analysis by means of three-dimensional polyhedral elements based on the Smoothed Finite elements method (S-FEM), for example nodal Cell-based S-FEM (CS-FEM), Node-based S-FEM (NS-FEM), and Edge-based S-FEM (ES-FEM), was studied. S-FEM allows implicit shape functions, making it possible to construct shape functions of S-FEM based polyhedral elements in a straightforward manner. The performance of S-FEM based polyhedral elements was compared with one another and with the conventional finite elements including hexahedral and tetrahedral element. Numerical examples show that the polyhedral elements by means of CS-FEM and ES-FEM provide better accuracy and convergence rate than conventional hexahedral finite elements, while the polyhedral elements by means of NS-FEM leads to spurious mode.

     

Modified r-method for the finite element adaptive analysis of plane elastic problems

The nodal relocation method (r-method) is used to uniformly distribute element discretization errors over an analytic model and improve the solution quality. When this r-method is performed with Zienkiewicz-Zhu’s error estimator, its converged solution can not be easily obtained without many iterative calculations. Further, this method also may deteriorate solution quality because of serious element distortion. This paper suggests a new error estimator which can evaluate the size and the distortion error of an isoparametric element separately and proposes a modified r-method based on this error estimator. Various numerical experiments show that the proposed error estimator properly evaluates the element discretization errors and the modified r-method can be easily applied to the practical analysis owing to the comparatively fast convergent characteristics.     

Numerical simulation of holes and inclusions using adaptive polygonal finite element method

Journal of Mechanical Science and Technology - An adaptive polygonal finite element method using the techniques of cut-cell and quadtree refinement is presented for modeling holes and inclusions in...     

Mathematical model and meshing analysis of internal meshing gear transmission with curve element

A new internal meshing gear transmission with curve element is put forward in this paper. The mathematical principle of tooth profile generation is described based on conjugate curves theory. For a given spatial curve, the meshing equation and its conjugated spatial curve under the motion law were derived. Considering the equidistant kinematic method, general internal tooth profiles models were established by the conjugate-curve pair. Numerical example of the internal gear pair was developed according to gear parameters and gear solid models were established by MATLAB and UG software. Motion simulation result shows that the gear pair satisfies point contact condition and design requirements. Meshing analysis of tooth profiles using FEA method was carried out. Stress analysis results of tooth profiles with single point contact and two points contact were, respectively, obtained. The conclusions lay the foundation for multi-point contact generation and tooth profile design. Also, further studies on transmission characteristics and manufacturing technology of the new gear drive will be carried out.

     

Performance of the p-version finite element method for limit analysis

In this paper, we investigate the use of the p-version finite element method in carrying out limit analysis using a mathematical programming-based static approach. An important motivation for this study is to overcome the well-known locking behavior—caused by the incompressibility constraint—that may occur in plane strain and 3D problems for such common yield criteria as von Mises’. Quadrilateral elements and plane stress or plane strain structures are specifically considered. Various examples are provided to highlight the robustness and accuracy of the approach.     

Acoustic analysis of lightweight auto-body based on finite element method and boundary element method

A lightweight automotive prototype using alternative materials and gauge thickness is studied by a numerical method. The noise, vibration, and harshness (NVH) performance is the main target of this study. In the range of 1–150 Hz, the frequency response function (FRF) of the body structure is calculated by a finite element method (FEM) to get the dynamic behavior of the auto-body structure. The pressure response of the interior acoustic domain is solved by a boundary element method (BEM). To find the most contributing panel to the inner sound pressure, the panel acoustic contribution analysis (PACA) is performed. Finally, the most contributing panel is located and the resulting structural optimization is found to be more efficient. __________ Translated from Journal of Shanghai Jiaotong University, 2006, 40(1): 177–180 [译自: 上海交通大学学报]     

Kineto-elastodynamic analysis of mechanisms by finite element method

In the present paper a systematic finite element method for kineto-elastodynamic analysis of high speed mechanisms has been presented. Effects of number of divisions have been investigated and it is found that a certain minimum number of divisions of links is necessary to yield accurate results. A new approach for eliminating the singularity in the stiffness matrices of mechanisms has been developed and it has been shown in this paper that this new approach yields improved results with negligible additional effort. Finite element expressions for the coriolis, tangential and normal components of elastic accelerations have been derived for a moving link and a new geometric stiffness matrix has been developed to include the effects of the rigid body pinforces and the distributed axial rigid body inertia forces on the transverse vibrations of the links. The method has been further extended to take into account the nonlinear elastic axial forces. Several examples have been solved.     

Combined finite volume and finite element method for convection-diffusion-reaction equation

A combined finite volume and finite element method is presented for solving the unsteady scalar convection-diffusion-reaction equation in two dimensions. The finite volume method is used to discretize the convection-diffusion-reaction equation. The higher-order reconstruction of unknown quantities at the cell faces is determined by Taylor’s series expansion. To arrive at an explicit scheme, the temporal derivative term is estimated by employing the idea of local expansion of unknown along the characteristics. The concept of the finite element technique is applied to determine the gradient quantities at the cell faces. Robustness and accuracy of the method are evaluated by using available analytical and numerical solutions of the two-dimensional pure-convection, convection-diffusion and convection-diffusion-reaction problems. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. This paper was recommended for publication in revised form by Associate Editor Dongshin Shin Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis. Sutthisak Phongthanapanich received his B.S. degree in Mechanical Engineering from Chiangmai University, Thailand in 1990. He then received his M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 2002, and 2006, respectively. He is a Lecturer of Mechanical Engineering Technology at King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand. His research interests are finite element method, finite volume method, mesh generation and adaptation, and shock wave dynamics.     

有限元法在结构分析中的应用

主要介绍了有限元法的现状及发展趋势,有限元法的技术路线及有限元分析软件ANSYS。     

隔离体法在有限元接触分析中的应用

这里针对施加初始预紧力时超高压密封容器有限元整体接触计算不收敛的情况,给出一种近似的计算思路—隔离体法。运用此方法,建立了该容器密封接触计算的等效隔离体模型,并运用有限元软件对该模型进行了计算,同时利用密封线比压判断准则对计算结果进行等效判断。经工程试验验证,计算结果合理,表明该近似方法的有效性。     

滚动轴承接触问题的有限元分析

基于ANSYS有限元分析软件,建立了滚动轴承接触分析的三维有限元模型,分析得到了轴承滚动体的径向位移、滚动体与内外圈的接触应力云图,并将接触应力结果与Hertz理论计算的结果对比,计算两者的接近度,进而说明该法分析的可行性,也为轴承的进一步研究提供了理论基础.