功能梯度压电材料壳体热残余应力

功能梯度压电材料结构成型冷却后会出现热残余现象,影响结构强度.借鉴复合材料层合结构的研究方法,将功能梯度压电材料球壳和圆柱壳沿厚度分为若干层,各层视为均匀材料,根据层间连续条件导出递推关系,得到显式的力—电—热多场耦合热残余解.统一了多层功能梯度压电材料壳体和连续功能梯度压电材料壳体热残余解.对于前者,其解为精确解;对于后者,其解为渐近解,随层数增加而收敛于精确解.其解也适用于功能梯度压电材料涂层.该方法对材料性能的变化方式(函数)没有要求,适应性强.并讨论影响热残余应力和界面强度的因素,球壳因双曲率的影响,热残余应力显著大于柱壳.     

Nonlinear transient heat transfer and thermoelastic analysis of thick-walled FGM cylinder with temperature-dependent material properties using Hermitian transfinite element

Nonlinear transient heat transfer and thermoelastic stress analyses of a thick-walled FGM cylinder with temperature-dependent materials are performed by using the Hermitian transfinite element method. Temperature-dependency of the material properties has not been taken into account in transient thermoelastic analysis, so far. Due to the mentioned dependency, the resulting governing FEM equations of transient heat transfer are highly nonlinear. Furthermore, in all finite element analysis performed so far in the field, Lagrangian elements have been used. To avoid an artificial local heat source at the mutual boundaries of the elements, Hermitian elements are used instead in the present research. Another novelty of the present paper is simultaneous use of the transfinite element method and updating technique. Time variations of the temperature, displacements, and stresses are obtained through a numerical Laplace inversion. Finally, results obtained considering the temperature-dependency of the material properties are compared with those derived based on temperature independency assumption. Furthermore, the temperature distribution and the radial and circumferential stresses are investigated versus time, geometrical parameters and index of power law. Results reveal that the temperature-dependency effect is significant.     

滑动接触中摩擦发热的数值分析

在滑动接触中，存在摩擦起热问题，运动机理对接触行为参数特性的影响不同于纯滚动接触，采用有限元方法，利用ANSYS软件，对2维滚滑模型进行分析，通过研究接触区的温度，接触应力和变形在运动学状态下的变化特性，可以看到接触状态的非稳定性必定会造成实际摩擦状态的不同，这也是形成接触表面不均匀磨损的原因之一。     

Dynamic relaxation method for nonlinear buckling analysis of moderately thick FG cylindrical panels with various boundary conditions

Using new approach proposed by Dynamic relaxation (DR) method, buckling analysis of moderately thick Functionally graded (FG) cylindrical panels subjected to axial compression is investigated for various boundary conditions. The mechanical properties of FG panel are assumed to vary continuously along the thickness direction by the simple rule of mixture and Mori-Tanaka model. The incremental form of nonlinear formulations are derived based on First-order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the incremental form of equilibrium equations. The critical mechanical buckling load is determined based on compressive load-displacement curve by adding the incremental displacements in each load step to the displacements obtained from the previous ones. A detailed parametric study is carried out to investigate the influences of the boundary conditions, rule of mixture, grading index, radius-to-thickness ratio, length-to-radius ratio and panel angle on the mechanical buckling load. The results reveal that with increase of grading index the effect of radius-to-thickness ratio on the buckling load decreases. It is also observed that effect of distribution rules on the buckling load is dependent to the type of boundary conditions.

     

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.     

混杂纤维圆筒与加强承力环共固化工艺的残余应力分析

具有加强承力环的混杂纤维圆筒在采用共固化工艺成型后,往往在加强承力环与筒身的界面附近出现分层(或开裂)。采用热传导和热弹性有限元方法研究某一混杂纤维增强筒在共固化工艺中残余应力的分布变化规律,由分析表明,采用改变加强承力环端部的几何形状与铺层顺序等措施可改善增强筒中的应力分布和防止在共固化工艺后筒身与加强承力环之间界面附近的分层(或开裂)。     

Crack growth pattern prediction in a thin walled cylinder based on closed form thermo-elastic stress intensity factors

Circumferential crack growth pattern in a thin-walled cylinder is studied. Thermo-elastic stresses in a cylinder subjected to thermomechanical loads are extracted. Closed form thermo-elastic stress intensity factor for cracked cylinder are derived using weight function method. An algorithm is developed to simulate different crack growth patterns utilizing a very high efficiency weight function method. This would lessen the taken time for the analyses compared to other numerical methods such as FEM. Results show that while the load effect on cylinder subjected to thermal load lead to the crack growth in small aspect ratio, in cylinder subjected to mechanical loads, it would lead to the growth of crack in large aspect ratio. The results show that, apart from load effects, the cylinders containing initial semi-circular crack have the longest life among the cylinders containing initial semi-elliptical crack with the same initial depth.     

超声车铣圆环斜槽传振杆设计

针对超声波车铣加工,设计了一种谐振频率30 kHz的圆环斜槽传振杆,阐述了30 kHz圆环斜槽传振杆纵扭共振的基本原理。利用有限元分析方法,计算了圆环斜槽传振杆的尺寸和斜槽的位置以及力学特性,并比较了有限元分析结果和理论结果。有限元分析结果比理论值结果小,是由于将圆环斜槽传振杆作为理想的模型。用阻抗分析仪对圆环斜槽传振杆进行了测试,并比较了测试结果和有限元分析值,偏差较小,相对偏差符合要求。实验测试结果表明,测试参数和设计结果一致。     

Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM

The problem of an elastic cylinder in normal contact between transversely isotropic layered substrate surfaces is investigated using the finite element method (FEM). A two-dimensional finite element model is developed which accurately determines the normal stress, contact length, and approach distance of layered surfaces. Numerical results, which are initially verified using Hertzian theory, are obtained at 756 distinct conditions by varying coating material, coating thickness, normal load, cylinder radius, and cylinder material. The numerical results are normalized with respect to Hertzian contact theory and a dimensionless anisotropic coating material parameter, ζ, is introduced. Numerical expressions for the normalized maximum normal stress, contact length, and approach distance are subsequently determined by curve-fitting the results of the 756 simulations performed. The relevance of such expressions are ascertained and discussed by comparing predicted results to isotropic layer theory presented by Gupta and Walowit [P.K. Gupta, J.A. Walowit. Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lubrication Technol., Vol. 94 (1974) pp. 250–274.]     

离心机开孔转鼓应力模拟计算与研究

采用有限元方法模拟计算了按等边三角形排布开孔的转鼓应力,讨论了开孔直径、鼓壁厚度、孔桥宽度以及转鼓半径等因素对鼓壁环向应力的影响情况.通过进一步计算研究得到了最大薄膜应力出现时孔桥宽度与开孔直径的关系曲线,为工程实际中转鼓开孔问题提供了计算依据.     

Acoustic radiation from modal vibration of automotive brake drum

The vibro-acoustic characteristics of an automotive brake drum is studied by applying a hybrid approach, which combines a numerical vibration analysis with an analytical acoustic solution. Specifically, structural vibration of a drum is investigated with the numerical finite element analysis, and vibratory displacements of the outer surface of the drum is approximated by simple mathematical expressions. Then, radiation of sound from the drum vibration is calculated using well-known theoretical solutions based on the simplified modal displacements. Finally, the calculation results are compared with those obtained by full numerical analyses. The results show that the numerical-analytical hybrid method allows relatively accurate calculation of vibro-acoustic properties of a brake drum under realistic boundary conditions.     

Thermo-elasto–viscoplastic numerical model for metal casting processes

The finite element method is used to model the thermomechanical behaviour of ductile cast iron using metallic moulds. Heat conduction is assumed for the heat transfer analysis and an elasto-viscoplastic model is employed to predict the development of thermal stresses and strains. Special finite elements with coincident nodes are used to model the heat transfer and the mechanical contact at the metal–mould interface. The local heat transfer coefficient between the casting and the mould may be dependent on the air-gap formation. The latent heat evolution effect is modelled by the use of the enthalpy method. An iterative procedure is required to take into account the material and the contact non-linearity. A real casting has been modelled and numerical results are compared with the experimental measurements.     

A case study on the effect of thermal residual stresses on the crack-driving force in linear-elastic bimaterials

The effect of thermal residual stresses in bimaterial structure with initial crack located near a sharp interface is discussed in this paper. Bimaterial compact tension (CT) specimen is used in the analysis, and the residual stresses are introduced by cooling of the specimen. The residual stresses affect the stress and strain fields near the crack tip, and the crack-driving force is different compared with that in the homogeneous material without residual stresses. This difference can be quantitatively expressed through an additional crack-driving force term—the material inhomogeneity term, Cinh. In this paper, it is evaluated using the post-processing procedure based on the concept of configurational forces, following a finite-element analysis. The results indicate that accurate numerical analysis of pre-cracked bimaterials should include the effect of thermally induced residual stresses. This effect cannot be neglected, even for bimaterials with homogeneous mechanical properties and inhomogeneity in thermal properties only (e.g. welded joints of ferritic and austenitic steel). Based on the obtained results, data from this study can be used in engineering practice to improve integrity and work safety of various inhomogeneous structures.     

钢丝缠绕式重型液压油缸应力和变形分析

为得到钢丝缠绕式重型液压油缸在预应力状态和工作状态的应力和变形分布情况,建立了解析计算模型和有限元数值模型并进行了模拟计算和分析。结果表明:缸体的径向变形是轴向位置的函数,半径方向的应力是径向位置的函数。基于有限元数值模拟结果与解析计算结果在数值和变化趋势上均趋于一致,充分地证明了建模的正确性。基于钢丝缠绕重型油缸的整体有限元分析方法大大地降低了设计计算难度,提高计算结果的准确性,为结构的进一步优化和设计改进提供理论依据。     

An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties

Exact closed-form solutions have been derived for stresses and the displacements in thick spherical shells made of functionally graded materials with exponential-varying properties subjected to internal and external pressure. Poisson’s ratio is assumed to be constant. The obtained results show that the inhomogeneity properties of FGMs have a significant influence on the displacement and stresses distribution along the radial direction. A numerical solution using finite element method is also presented and good agreement was found between the analytical solutions and the solutions carried out through the FEM. The values used in this study are arbitrarily chosen to demonstrate the effect of inhomogeneity on displacements and stresses distributions.     

Flat and rounded fretting contact problems incorporating elastic layers

The problem of plane elastic contact between a thin strip and symmetric flat and rounded punches is studied. This geometry has recently been used by a number of researchers to assess life of various mechanical couplings undergoing fretting fatigue. Most of the experimental fixtures used do not allow the problem to be treated using the conventional half-plane approximation. Here we propose a numerical approach, which enables the solution of configurations characterised by finite strip thickness, avoiding the use of finite element analyses. Various loading regimes and contact configurations are treated in detail and both surface tractions and internal stresses are derived.     

Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks

In this paper, a semi-analytical solution for magneto-thermo-elastic problem in functionally graded (FG) hollow rotating disks with variable thickness placed in uniform magnetic and thermal fields is presented. Stresses and perturbation of magnetic field vector in FG rotating disks are determined using infinitesimal theory of magneto-thermo-elasticity under plane stress conditions. The material properties except Poisson’s ratio are modeled as power-law distribution of volume fraction. The profile of disk thickness is assumed to be a parabolic function of radius. The non-dimensional distribution of temperature, displacement, stresses and perturbation of magnetic field vector throughout radius are shown. Effects of material grading index, geometry of the disk and magnetic field on the stress and displacement fields are investigated. The results of stresses and radial displacements for two different boundary conditions with and without the effect of magnetic field are compared for a FG rotating disk with concave thickness profile. It has been found that imposing a magnetic field significantly decreases tensile circumferential stresses. Therefore the fatigue life of the disk will be significantly improved by applying the magnetic field. Results of this investigation could be applied for optimum design of FG hollow rotating disks with variable thickness.     

Viscoelastic model to describe mechanical response of compact heat exchangers with plate-foam structure

The miniaturization of the process equipment has lead to the development of micro-chemical and thermal systems for high tech applications. With the increase of temperature and pressure, the design of the miniature components against creep failure becomes a primary concern. However, the stress analysis of the structure is highly complicated and time-consuming by general finite element methods if a network of inter-connected dodecahedral-like cells is involved. In the present paper, the short-term mechanical properties and the viscoelastic parameters are measured by uniaxial tension experiments. Based on these parameters and small deformation theory, the time-dependent deformation and stresses of the plate-foam structures are analyzed by assuming the metal foams as elastic foundation. Using the numerical inversion of Laplace transform and the standard linear solid model, the analytic expressions of the deformation and stresses are derived. By comparison, the results show that the time-dependent deflection and bending stress along the normalized distance from the analytical method were consistent with those from the finite element method. It indicates that the proposed analytical method was feasible and accurate. Additionally the effect of the viscoelasticity on the deflection will disappear gradually if λ is much larger than 600 GPa.     

Monoblock cylinder internally pressurised under asymmetric end constraints—Some aspects of design

The finite element method is used to analyse stresses and displacements in a monoblock cylinder open at one end only. The cylinder is internally pressurised. The analysis shows that the minimum pressure required to cause yield in the cylinder decreases rapidly with increasing cylinder height until the height is about the same as the outer radius of the cylinder, beyond which the decrease is marginal. Introduction of a fillet at the internal corner enhances the design pressure substantially while a fillet at the outer corner affects this pressure only marginally.     

颗粒增强复合材料弹性结构的双尺度有限元分析

颗粒增强方法是实现材料高性能化的重要手段。预测颗粒增强复合材料的细观结构与力学性能的关系是实现材料增强增韧的基础。为更好地分析、设计和优化复合材料,需要引入多尺度计算模型来考察细观结构对宏观力学性能的影响。基于均匀化理论,采用Voronoi有限元法对颗粒增强复合材料进行细观数值模拟,从而预测材料的宏观等效弹性常数,并直接得到材料的细观应力场。在细观尺度,首先假设满足平衡条件的应力场,采用Voronoi应力单元建立余能泛函并得到细观控制方程,最终形成可直接求解的线性代数方程组,从而求得应力系数并得到细观应力场。在宏观尺度,利用商业有限元软件ANSYS来进行宏观结构分析。通过均匀化方法求得弹性模量的宏观平均值,将其输入ANSYS系统即可进行计算,由此把宏细观两个尺度耦合起来,可以对颗粒增强复合材料构成的结构体进行有效的力学分析。