Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method

Since the intrinsic limitations of FEM (Finite element method) and lumped-mass method, we derive the formula of 8-node hexahedral element based on VFIFE (vector form intrinsic finite element method) method and applied it in contact analysis of gears. This paper proposed a new method to determine pure nodal deformation, which could simplify the computation compared to the traditional VFIFE method. Combining the VFIFE method and matching contact algorithm, we analyzed spiral bevel gear meshing problems. Spiral bevel models with two different mesh densities are calculated analyzed by the VFIFE method and FEM. Performance indicators of gears are extracted and compared, including contact forces, contact and bending stresses, contact stress patterns and loaded transmission errors. The results show that the VFIFE method has a stable performance and reliable accuracy under coarse or refined mesh conditions, while the FEM inaccurately calculates the contact stress of the coarse mesh model. The examples demonstrate that the proposed method could precisely analyze gear meshing problems with a coarse mesh model, which provides a new solution for gear mechanics.     

Load share and finite element stress analysis for double circular-arc helical gears

The authors analyze the tooth surface contact and stresses for double circular-arc helical gear drives. The geometry of such gear drives has been represented by the authors in their previous paper [1]. The proposed approach is based on application of (i) computerized simulation of meshing and contact of loaded gear drives, and (ii) the finite element method. Load share between the neighboring pairs of teeth is based on the analysis of position errors caused by surface mismatch and elastic deformation of teeth. The authors have investigated the conditions of load share under a load and determined the real contact ratio for aligned and misaligned gear drives, respectively. Elastic deformation of teeth and the stress analysis of the double circular-arc helical gears are accomplished by using the finite element method. The finite element models for the pinion and gear are constructed, respectively. Contact pressure is spread over elliptical area. The stress analysis for aligned and misaligned gear drives, respectively, has been performed. The numerical results have been compared with those obtained by other approaches.     

Three-dimensional simulation of flat rolling through a combined finite element–boundary element approach

This paper presents an innovative approach for analysing three-dimensional flat rolling. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the rigid–plastic numerical modelling of the workpiece allowing the estimation of the roll separating force, rolling torque and contact pressure along the surface of the rolls. The boundary element method is applied for computing the elastic deformation of the rolls. The combination of the two numerical methods is made using the finite element solution of the contact pressure along the surface of the rolls to define the boundary conditions to be applied on the elastic analysis of the rolls. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature.     

A finite element method for granular flow through a frictional boundary

A finite element method for the flow of dry granular solids through a domain involving a frictional contact boundary is formulated. The granular material is assumed as a compressible viscous-elastic–plastic continuum. Based on the principles of continuum mechanics, a complete set of equations is developed. The resulting boundary value problem is solved by the finite element method in space and by the finite difference method in time. The derivation of the finite element equations and the mathematical framework of the numerical technique are presented, together with two illustrative examples to demonstrate the validity of the technique.     

Simulation and analysis of rotary forging a ring workpiece using finite element method

The methods of dealing with some key problems in analyzing a rotary forging process with a finite element method are given. The presented mechanical model of the finite element analysis is in accordance with the actual conditions of the rotary forging process. A three-dimensional rigid–plastic finite element analysis code is developed in FORTRAN language and used to analyze the rotary forging process of a ring workpiece. Velocity fields and stress–strain fields of both contact and non-contact zones of the ring workpiece in the rotary forging are obtained. The deformation mechanism and metal flow laws of the contact zone surface of the ring workpiece in the rotary forging process are revealed. The pressure distributions of the contact surface along the radial and tangential directions and effects of rotary forging parameters on deformation characteristics are given.     

Plastic zone development in dynamic tear-type test specimens

The J-integral is a fracture criterion, which permits measurement of the fracture toughness of a specimen where fracture occurs in the elastic–plastic regime. An understanding of the ratio of plastic zone size (radius) to the crack tip blunting (stretch zone) is required to determine the upper temperature for transition curves, where elastic–plastic fracture becomes invalid and general yielding occurs. This study endeavors to acquire this ratio using finite element techniques. The development of the plastic zone in dynamic tear (DT) specimens and non-standard three-point bending fracture test specimens was the main focus of the study. The ABAQUS finite element software was used to model the elastic–plastic behaviour of the specimens. The cracks in the specimens were induced by pressing the notch followed by fatigue cracking at 30–40% of the limit loads. The shapes of these cracks were adequately modelled in the finite element analysis. The specimens were made of 350WT steel and 304 stainless steel materials and were loaded until fixed amounts of permanent deformation were recorded. Results were obtained in the form of plots, showing the progression of the plastic zone around the crack tip. For each case, mid-point plastic deflection, stretch zone width and plastic zone radius were computed.     

Coupled FEM-BEM for elastoplastic contact problems using Lagrange multipliers

The coupling of the elastoplastic finite element and elastic boundary element methods for two-dimensional frictionless contact stress analysis is presented. Interface traction matching (boundary element approach), which involves the force terms in the finite element analysis being transformed to tractions, is chosen for the coupling method. The analysis at the contact region is performed by the finite element method, and the Lagrange multiplier approach is used to apply the contact constraints. Since the analyses of elastoplastic problems are non-linear and involve iterative solution, the reduced size of the final system of equations introduced by combining the two methods is very advantageous, especially for contact problems where the nature of the problem also involves an iterative scheme.     

Nonlinear finite element reliability analysis of Concrete-Faced Rockfill (CFR) dams under static effects

The response of concrete slab on Concrete-Faced Rockfill (CFR) dams is very important. This study investigates the reliability of the concrete slab on a CFR dam by the improved Rackwitz–Fiessler method under static loads. For this purpose, ANSYS finite element analysis software and FERUM reliability analysis program are combined with direct coupled method and response surface method. Reliability index and probability of failure of the concrete are computed in the all critical points of the concrete slab by dam height. This study is also expanded for the reliability of CFR dams including different concrete slab thickness. In addition to the linear behavior, geometrically and materially non-linear responses of the dam are considered in the finite element analysis which is performed with reliability analysis. The Drucker–Prager method and the multi linear kinematic hardening method are, respectively, used for concrete slab and for rockfill and foundation rock. Finite element model used in the analyses includes dam–reservoir–foundation interaction. Reservoir water is modeled by the Lagrangian approach. Welded and friction contact based on the Coulomb’s friction law are considered in the joints of the dam. One-dimensional two noded contact elements are used to define friction. The self-weight of the dam and the hydrostatic pressure of the reservoir water are considered in the numerical solutions. According to this study, hydrostatic pressure, nonlinear response of the rockfill and the decrease in the concrete slab thickness reduce the reliability of the concrete slab of the CFR dam. Besides, the CFR dam models including friction are safer than the models including welded contact in the joints.     

Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material

Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening.     

Bi-nonlinear vibration model of tubing string in oil & gas well and its experimental verification

Fluid-induced vibration (FIV) prediction is an important prerequisite work in wear and fatigue analysis of tubing string in oil & gas well. The finite element method, energy method and Hamiltonian principle are comprehensively used to establish a single nonlinear vibration model of pipe conveying fluid, taking into account the longitudinal/lateral coupled vibration. Based on the contact/impact theory of elastic/plastic body, the nonlinear contact-impact model of tubing-casing is established and introduced into the single nonlinear vibration model to form a bi-nonlinear vibration model of tubing string in oil & gas well. The bi-nonlinear model is numerically discretized by the finite element method, solved by Newmark− β method, and verified preliminarily by a classical contact/impact example in literature in which the influence of inflow is not taken into account temporarily. A similar experiment of tubing vibration is designed and completed to further test the validity of the bi-nonlinear vibration model by comparing the frequency-domain and time-domain responses of the experiment with those from the model. The analysis shows that the bi-nonlinear model has good calculation accuracy and the vibration response law is basically consistent with the experimental results, which can provide an effective theoretical analysis tool for FIV behavior of tubing string in oil & gas well.     

A wavelet-based stochastic finite element method of thin plate bending

A wavelet-based stochastic finite element method is presented for the bending analysis of thin plates. The wavelet scaling functions of spline wavelets are selected to construct the displacement interpolation functions of a rectangular thin plate element and the displacement shape functions are expressed by the spline wavelets. A new wavelet-based finite element formulation of thin plate bending is developed by using the virtual work principle. A wavelet-based stochastic finite element method that combines the proposed wavelet-based finite element method with Monte Carlo method is further formulated. With the aid of the wavelet-based stochastic finite element method, the present paper can deal with the problem of thin plate response variability resulting from the spatial variability of the material properties when it is subjected to static loads of uncertain nature. Numerical examples of thin plate bending have demonstrated that the proposed wavelet-based stochastic finite element method can achieve a high numerical accuracy and converges fast.     

区间运算和静力区间有限元

用均值和离差两参数表征区间变量的不确定性,根据区间运算规则,论证了区间变量的运算特性.将区间分析和有限元方法相结合,提出了非概率不确定结构的一种区间有限元分析方法.将区间有限元静力控制方程中n自由度不确定位移场特征参数的求解归结为求解一2n阶线性方程组.实例分析表明文中方法是有效和可行的.     

Hybrid-conventional finite element for gradient-dependent plasticity

The hybrid-conventional finite element method is applied to the analysis of quasi-static, gradient-dependent elastoplastic problems in solid mechanics. The stresses within the element domain and the displacements on the boundary are simultaneously and independently approximated using Trefftz constraints, which lead to boundary integrals. The plastic multipliers are conventionally approximated with regard to C₀ continuity of the multiplier field of the gradient-dependent plasticity. The finite element formulation is derived using a Galerkin-weighted residual approach. The plastic boundary conditions are examined and plastic radiations are set to zero on the plastic boundaries. The effectiveness of the present method is demonstrated with three numerical applications.     

A new finite element model for the analysis of arbitrary stiffened shells

A new stiffened shallow shell finite element has been introduced for the static analysis of stiffened plates and shells. This approach has been presented to cater for stiffeners in which the positions and properties remain undisturbed in the formulation and the element can accomodate the stiffener anywhere within the shell element and in any direction, which introduces a considerable flexibility in the analysis. This is a distinct improvement over the existing models. Stiffened shells having various disposition of stiffeners as available in the literature, have been analysed by the proposed approach. Comparison obtained with the existing theoretical and/or experimental values have indicated good accuracy with relatively coarser mesh sizes and less CPU time.     

Multiscale damage analyis for steel structures

An approach to model the deterioration of steel structures is presented by transferring the results of a continuum damage mechanics analysis to an extended beam model which can account for the loss of structural integrity. Damage starts at the microscopic level by the initiation, growth and coalescence of voids with decreasing material resistance followed by the formation of microcracks at the mesoscale. Nevertheless, the material behavior can be sufficiently modelled on a phenomenological basis taking into account viscoplasticity, hardening effects and damage evolution. The associated model parameters are identified with the help of an evolutionary algorithm adapting numerical to experimental results. Using the finite element method a nonlocal formulation of the damage variable is required to obtain mesh-independent results by structural analysis. The maximum element size is limited by the small magnitude of the internal length. Therefore, numerical analyses of large scale 3D steel structures are computationally expensive. To reduce the effort a beam element is proposed to account for the plastic hinges and the loss of resistance in the course of damage evolution. The corresponding relationship of bending moment and curvature bases on the continuum damage mechanics model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

波形钢腹板箱梁的约束扭转剪应力分析

基于周边不变形理论,结合闭口薄壁杆件约束扭转的计算分析,研究了波形钢腹板箱梁在约束扭转时混凝土悬臂板上扭转剪应力的分布,并进行了计算.通过对悬臂板在约束扭转中剪力流计算公式的推导,进一步阐述了其自由扭转剪应力及翘曲扭转剪应力的分布,指出了相关文献在这部分计算中存在的问题.通过一个简支波形钢腹板组合箱梁算例,将该文方法计算结果与ANSYS有限元计算结果进行比较.结果表明:在波形钢腹板箱梁截面中,主要由波形钢腹板承受扭转剪应力,其次是混凝土底板,底板剪应力最大值发生在底板中心处,其数值近似等于腹板剪应力的一半,而混凝土顶板和悬臂部分的扭转剪应力很小;该文计算的扭转剪应力结果在总体上符合有限元得到的扭转剪应力分布规律,在悬臂自由端为0,随着离开悬臂自由端距离的增大,扭转剪应力逐渐增大并达到峰值.     

Modeling of viscoelastic contact-impact problems

An accurate finite element (FE) model for analyzing the response of viscoelastic structure under low-velocity impact is presented. Generalized standard linear solid (Wiechert) model is adopted to simulate the internal damping of the structure, because its capability of describing both creep and relaxation phenomena adequately. Newmark time integration scheme is proposed to transfer the problem into a static one for each time increment. The incremental convex programming method is modified to accommodate viscoelastic dynamic-contact problems. The Lagrange multiplier technique is selected to incorporate the contact condition. One, two and three-dimensional finite element model is presented to compare between the elastic and viscoelastic materials.     

Dynamic analysis of non-uniform taper bars in post-elastic regime under body force loading

This paper presents a simulation study of the free flexural vibration behavior of non-uniform taper bars of circular and rectangular cross-section under body force loading due to gravity. The loading is controlled statically to take the bar to its post-elastic state so as to predict its dynamic behavior in the presence of plastic deformation. Hence the analysis is carried out in two parts; first the static problem under axial gravity loading is solved, then the dynamic problem is solved in this loaded condition. Appropriate variational method is employed to derive the set of governing equations for both the problems. The formulation is based on unknown displacement field which is approximated by finite linear combinations of orthogonal admissible functions. The present method is validated successfully with a well-known finite element package. Results are presented to investigate the effect of shape and size on the dynamic behavior of non-uniform taper bars. The study can be extended to study the post-elastic dynamic behavior of other related problems such as rotating beams and rotating disks.     

The static shape control for intelligent structures

A finite element formulation is presented for modeling the plate structure containing distributed piezoelectric sensors and actuators (S/As). A new plate bending element for analysis of the plate with distributed piezoelectric S/As is developed. This element saves much memory and computation time. Using the bending plate element, a general method of static shape control for the intelligent structure is put forth. Two examples are given to illustrate the application of the method presented in this paper. The purpose of the first example is to check the accuracy of the finite element method presented in this paper. The second example is to study the problem of the static shape control for the intelligent structure. It is concluded that the shape of the intelligent structure can reach the desired shape through passive control or active control.     

Dynamic Stability Analysis of Shells Using a Finite Element Based Reduction Method

A finite element formulation of a reduction method for dynamic stability analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The single mode dynamic buckling analysis and its extension to parametric excitation analysis are described. The approach is available within a general purpose finite element code. Characteristic results for the parametric excitation analysis of a composite cylindrical shell are shown. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)