A concise finite element model for three-layered straight wire rope strand

A concise finite element model (FEM) of three-layered straight helical wire rope strand under axial loads (tensile and torsional) is presented in this paper. Three-dimensional solid elements were used for structural discretization. The helical symmetry of the strand was used to establish accurate boundary conditions. Contact, friction and plastic yielding were also taken into account. For the global behaviour of wire rope strand, i.e. load vs. strain and load vs. torque (fixed-end) or load vs. strand twist rate (free-end), the finite element results showed better agreement with the experimental results of Utting and Jones (Journal of Strain Analysis for Engineering Design 1988;23(2):79–86) than those calculated using the analytical strand model of Costello (Theory of Wire Rope, 2nd ed. New York: Springer, 1997). In addition, the FE model allows the localised stress distribution to be determined. In particular, this model reveals the non-uniform stress distribution in the outer layer helical wires caused by the trellis point contact. This is particularly relevant in the fixed-end case, where the present analysis predicts an axial tensile rigidity in good agreement with the experimental observations (Utting and Jones), whereas Costello’s model predicts a significantly higher rigidity.     

An efficient approach for shape optimization of components

The optimization problem of finding the optimal shape of a mechanical component is investigated with the aim of presenting a simple and efficient numerical approach for minimizing stress concentration factor. The proposed approach is based on finite element method in conjunction with the widely used fully stressed design criterion (or the axiom of uniform stress), i.e. for structural shape optimization, an essential requirement for optimality is the achievement of constant tangential stresses along a section of the boundary to be optimized. The design boundary is modeled by using cubic splines, which are determined by a number of control points. The optimal shape of the design boundary with constant stress is achieved iteratively by adjusting the design boundary shape based on a simple logic and algorithm. The result quality in terms of accuracy and efficiency are tested and discussed with finite element analysis examples. The approach presented has the attractive properties that it can be very simply implanted into standard finite element codes.     

Implementation of Hertz theory and validation of a finite element model for stress analysis of gear drives with localized bearing contact

An analytical approach for stress analysis of gear drives with localized bearing contact based on the Hertz theory is proposed. The proposed approach provides a complete and effective solution of the contact problem but satisfaction of the hypotheses for application of the Hertz theory is its main drawback. On the other hand, a finite element model has been developed and validated in terms of the contact area, maximum contact pressure, pressure distribution, maximum Tresca stress, and Tresca stress distribution underneath the contacting surfaces. Validation of the finite element model is provided for those cases wherein the Hertz theory can be applied. The obtained results confirm the applicability of the proposed approach for gear drives with localized bearing contact wherein edge contact is avoided by surface modifications and whole crowning of tooth surfaces is provided.     

用边界元法分析前后张力对板带轧制过程的影响

建立了弹塑性有限形变接触(考虑摩擦)问题的多重非线性边界元方程,用此方法分析了前后张力对板带轧制过程的影响,计算结果与有限元法和试验结果都有很好的一致性。为板带轧制过程求解提供了新颖、简单且准确的方法。     

A direct shape optimization approach for contact problems with boundary stress concentration

The paper presents a direct shape optimization approach that minimizes both boundary stress concentration and peak contact pressure of multi-body contact systems. This approach is centered on the direct shape modification of boundary regions of stress concentration measured by von Mises stresses and contact surfaces measured by contact pressure. Without requiring sensitivity data for shape modification, shape optimization is made directly on nodal positions through an iterative computational scheme. Therefore, this approach is simple to implement using either commercial finite element software or in-house programs. An adjustable weighting factor is used to ensure stable and accelerated convergence in shape optimization. To evaluate the proposed approach, three case problems are presented, and the results show that this direct shape optimization approach can be especially applicable to the design and analysis of multi-body systems where boundary stress concentration and contact pressure distribution are an important consideration.     

板材成形回弹数值分析的静力隐式方法

给出了板材成形加载过程，卸载过程数值模拟的静力隐式有限元方法，通过平衡迭代求解有限元方程，并采用隐式算法进行应力积分及接触压力计算，这种方法应力计算准确，因而回弹计算结果具有较高的精度，数值计算表明，纯弹性板大变形卸载后能够完全恢复到原始形状，说明该方法对几何非线性问题的分析是非常准确的，最后对板材柱面、球面成形的回弹进行了分析。     

Improved flexural–torsional stability analysis of thin-walled composite beam and exact stiffness matrix

A simple but efficient method to evaluate the exact element stiffness matrix is newly presented in order to perform the spatially coupled stability analysis of thin-walled composite beams with symmetric and arbitrary laminations subjected to a compressive force. For this, the general bifurcation-type buckling theory of thin-walled composite beam is developed based on the energy functional, which is consistently obtained corresponding to semitangential rotations and semitangential moments. A numerical procedure is proposed by deriving a generalized eigenvalue problem associated with 14 displacement parameters, which produces both complex eigenvalues and multiple zero eigenvalues. Then the exact displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently exact element stiffness matrices are evaluated by applying member force–displacement relationships to these displacement functions. As a special case, the analytical solutions for buckling loads of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, the numerical, analytical, and the finite element solutions using the Hermitian beam elements are presented and compared with those from ABAQUS's shell elements. The effects of fiber orientation and the Wagner effect on the coupled buckling loads are also investigated intensively.     

3D contact analysis of conjugate spur gears by a complete mating process

Instead of applying fixed boundary conditions to constrain and simplify material behavior in 2D models, the point and line contact of tooth surfaces are substituted by a face-contact model of teeth in this study. The inaccurate prediction of load, deformation, and stress in 3D contacts are solved. Most research uses one pair to three pairs of meshing teeth to simulate the mating process. However, describing the entire process of three contact zones during each mating pair is insufficient. By implementing a combined 3D face contact and finite element method, the contact stress analyses between two spur gear teeth are conducted in 11 different contact positions during a full mating process. The proposed approach provides a complete and effective solution to the contact problem in a quasi-dynamic manner. This model not only determines the load-sharing prediction but also verifies the applied boundary conditions.     

Prediction of fretting wear using boundary element method

The simulation method of the fretting wear prediction using boundary element method is developed. The contact pressure and the contact width which is the first step to predict fretting wear are obtained from contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. The geometrical updating is based on nodal wear depths computed using Archard’s equation for sliding wear. The prediction of fretting wear for two cases of contact problems is performed; one is two-dimensional cylinder on flat contact which is for the comparison with a previous model by finite element method; the other is three-dimensional spherical contact. It is observed that for two-dimensional cylindrical contact the boundary element method developed in this study reduced the calculation time by 1/48 compared to FE method. We also showed the use of developed simulation technique is efficient to predict the fretting wear for three-dimensional spherical contact.     

Design of interference fits via finite element method

Studies of interference fits in ring gear-wheel connections show that the traditional design method based on thick-wall cylinder theory has some limitations. Application of the finite element method (FEM) for the three-dimensional stress analysis of interference fitted connections gives more complete and accurate results than the traditional method. An improved design method utilizes two safety factors, λ_s and λ_p, providing a new approach for evaluating the quality of interference fits. A tolerancing method utilizing the I_max and I_min curves provides a quantitative guideline for interference fit design. The selective assembly method combined with the FEM-based method for interference fit design provides an effective approach to achieve more reliable interference-fitted connections and more precise assembly with lower manufacturing cost.     

大型旋转机械转子离心应力有限元分析

为解决大型旋转机械转子离心应力有限元计算过程中精度和效率难以兼得的问题，采用了先去除零部件微小几何特征，再通过计算不同网格密度的全局模型得到应力分布规律，最后再用子模型算得精确解的方法加以解决。研究表明，运用此法不仅可以得到转子各部件离心应力分布规律，而且计算精度更高，计算时间大幅减少，可为此类大型复杂结构件高效、精确的有限元分析提供参考。     

An enriched finite element algorithm for numerical computation of contact friction problems

In this paper, the extended finite element method (XFEM) is employed to model the presence of discontinuities caused by frictional contact. The method is used in modeling strong discontinuity within a standard finite element framework. In extended finite element method (XFEM) technique, the special functions are included in standard FEM to simulate discontinuity without considering the boundary conditions in meshing the domain. In this study, the classical finite element approximation is enriched by applying additional terms to simulate the frictional behavior of contact between two bodies. These terms, which are included for enrichment of nodal displacements, depend on the contact condition between two surfaces. The partition of unity method is applied to discretize the contact area with triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, numerical examples are presented to demonstrate the applicability of the XFEM in modeling of frictional contact behavior.     

多层U形波纹管的疲劳寿命有限元分析

应用非线性有限元法,综合考虑几何非线性、材料非线性和边界非线性等因素,采用平面轴对称单元和柔性的面-面接触对,建立了多层U形波纹管的非线性有限元模型,较好地解决了层间的接触问题.借助ANSYS软件对多层波纹管在轴向载荷与内压组合作用下的应力分布规律进行了探讨,利用结构的局部应力应变状态对波纹管的疲劳寿命进行了预测,同时考虑了波纹管的层数、壁厚减薄效应以及内压大小对于计算结果的影响,为波纹管的疲劳设计提供了依据.     

A concise finite element model for simple straight wire rope strand

Due to its complex geometry, a wire in a rope is subjected to the combined effects of tension, shear, bending, torsion, contact, friction and possible local plastic yielding when loaded. In this paper an accurate and general strand model using the finite element method (FEM) is presented. The model is capable of taking into account all the above effects and has been successfully used to predict the global behaviour of simple straight wire rope strand as well as the stress distribution within the wires under axial loads (tensile and torsional). In simplifying the finite element model, precise boundary conditions were developed. The finite element analysis results showed excellent agreement with the analytical theory of Costello and the experimental results of Utting and Jones. By using the model developed in this paper, localised highly non-linear phenomena such as contact stress, residual stress, friction and plastic deformation can be studied effectively.     

Analyses of piezoelectric plates with elliptical notches by special finite element

A novel special finite element with an elliptical notch, based on the complex potential theory and hybrid variational principle, is proposed for mechanical–electrical coupling analyses of piezoelectric plates with notches. The formulations are given and a variety of examples are analyzed. Comparisons are made with existing analytical or numerical data. It is shown that the proposed element is very efficient and accurate. Some new numerical results are given and discussed. It is found, perhaps for the first time according to the authors’ knowledge, that the relationships between the logarithm concentration factor of tangential (θ=0) stress, electrical displacement, and electrical field at the notch tip and logarithm b/a are linear. Some conclusions are drawn based on the results reported herein.     

Elastic small deflection analysis of annular sector Mindlin plates

An analytical method is developed for the bending response of annular sector Mindlin plates with two radial edges simply supported, and exact solutions are presented in the form of Levy-type series. Several different boundary conditions on the two circular edges are considered, viz. simply supported-simply supported, clamped-clamped and free-free. Numerical results for the case of uniform loading are presented to indicate the effect of shear deformation on the deflections and stress resultants at various points in the plate. Twisting stress couple and transverse shear stress resultant distributions along and near the edges of the plate are illustrated graphically, and the principal differences between the results predicted by Mindlin's plate theory and classical thin plate theory are discussed in detail. Results obtained with the present exact analysis may serve as references for approximate solutions and, especially, as a ‘shear locking’ test for thick plate finite element analysis.     

Analyse non-linéaire et dimensionnement d'une structure de bouclier automobile par couplage calculs–essais

Nonlinear analysis and development of bumper structure of vehicle with a coupled numerical and physical tests. A complete approach for the design of car bumpers loaded by small impacts is presented. It is based on nonlinear explicit dynamic finite element analysis and an experimental procedure to define behaviour laws. This approach is validated by several realistic tests on complex structures under low velocity or quasi-static loading, taking into account geometrical, contact and behaviour nonlinearities.     

A fracture mechanics life prediction methodology applied to dovetail fretting

This work evaluates a fracture mechanics based crack growth life prediction methodology for dovetail fretting fatigue laboratory experiments. The Ti–6Al–4V specimens were configured with angles of 35°, 45° and 55°. Experiments were conducted with constant amplitude loading at R of 0.1 and 0.5 with lives ranging from 100,000 to 10 million cycles. The approach included the contact loads and bulk stress calculated from the finite element method as inputs to the stress and life analysis. Contact stresses were calculated using the contact stress analysis software CAPRI. These stresses were input into a stress intensity factor calculation at the edge of contact. Crack propagation life was calculated from an assumed initial crack size. Analysis showed that propagation consumes a majority of the total life and is insensitive to a large range of initial crack sizes.     

内啮合斜齿轮高精度三维有限元自动建模方法

为提高内啮合斜齿轮有限元接触分析的建模速度和模型精度,提出了一种齿轮高精度三维有限元模型的自动建模方法。基于齿轮插刀齿廓方程,利用齿廓法线法,得到包括齿根过渡曲线的内、外斜齿轮端面齿廓,建立了内、外齿轮参数化粗网格有限元模型。开发了表层六面体网格剖分方法,自动识别齿面接触带单元,进行分级剖分细化,保证了有限元模型的建模精度和网格密度。进行了齿面接触分析,得到了内啮合斜齿轮的弯曲应力、接触应力、接触印痕、传动误差、时变啮合刚度和载荷分配率。粗细网格有限元模型计算结果对比分析表明,该方法提高了内啮合斜齿轮有限元建模效率和计算精度,缩短了计算时间,为快速准确的齿轮接触分析奠定了基础。     

Fretting fatigue strength estimation considering the fretting wear process

In fretting fatigue process the wear of contact surfaces near contact edges occur in accordance with the reciprocal micro-slippages on these contact surfaces. These fretting wear change the contact pressure near the contact edges. To estimate the fretting fatigue strength and life it is indispensable to analyze the accurate contact pressure distributions near the contact edges in each fretting fatigue process.So, in this paper we present the estimation methods of fretting wear process and fretting fatigue life using this wear process. Firstly the fretting-wear process was estimated using contact pressure and relative slippage as follows:

W=K×P×S,