Studies on stress concentration in tensile strips with large circular holes

The stress concentration factor K in a tensile strip with large circular hole is accurately determined using a high precision, plane stress, triangular element. The values of a/w where a is the diameter of the hole and w is the width of the strip, considered range from 0.99 to 0.999. The values of K obtained found to be very near to but greater than 2.0, when linear analysis is performed. Some discrepancies in the stress values at the outer free edge observed in the present linear analysis compared to the well documented experimental values prompted the authors to go for geometrically nonlinear analysis gave a K value which is a function of the load applied, less than 2.0 and for sufficiently large loads this value is very near but slightly greater than 1.0.     

Stress concentration around a part-through hole weakening a laminated plate

A quasi-three-dimensional-elasticity type theory, based on the assumptions of transverse inextensibility and layerwise constant shear-angle, is presented, in the context of an assumed quadratic displacement potential energy approach, for analyzing an edge-loaded laminated plate weakened by the presence of a part-through hole. Numerical results, obtained using the C°-type triangular finite element, indicate the existence of severe cross-sectional warping in the vicinity of the hole and plate boundaries. Furthermore, the three-dimensional nature of the stress concentration factor in the neighborhood of the hole boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the part-through hole. The numerical results presented should serve as bench-mark solutions for future comparisons.     

圆锥壳开孔与围栏加强力学特性分析

圆锥壳由于锥角的存在,其开孔的力学特性比圆柱壳开孔更为复杂.通过有限元方法分析圆锥壳半锥角对开孔应力集中系数的影响,认为开孔偏斜角越大,导致的应力集中系数越大;并在此基础上,研究了圆锥壳开孔大小α/R对应力集中系数的影响规律.并分析了加强围栏的长度变化对孔应力集中系数的影响,表明围栏是圆锥壳开孔加强的有效措施.     

发动机缸体线性与非线性对比分析

采用线性分析发动机缸体时,在螺栓接触和绑定的位置会出现明显的应力集中点,且计算得到疲劳安全因数远远低于合理值.在考虑材料非线性的基础上对发动机缸体进行非线性分析,发现在螺栓接触和绑定位置处的应力明显降低,计算得到的疲劳安全因数也趋于合理.通过汽油机缸体线性与非线性对比分析可以发现,缸体非线性模型的计算结果更合理.若要改善螺栓孔周边的安全因数,一定要保证螺栓绑定和接触位置接近实际情况,特别在2个面过渡的位置不能绑定,这样可以避免造成应力集中.     

材料塑性应变对某钢制车轮残余应力测试的影响

针对车轮轮辋与轮辐组合焊缝附近结构的残余应力测试通常采用盲孔法,孔边由于应力集中易产生塑性变形的问题,采用有限元仿真与测试相结合的方法分析在钢制车轮加工的不同阶段,轮辋焊缝区残余应力测试时材料塑性变形对应变释放因数和残余应力测试结果的影响,并分析由Kirsch解析解确定的应变释放因数A和B计算车轮焊缝区残余应力测试所带来的误差.发现当孔边塑性变形较大时,用Kirsch解析解确定的应变释放因数计算残余应力会产生很大误差.     

Stress analysis of an elastic plate with an opening or notches under tension based on the concept of general systems

The paper presents a method of calculation dealing with plane stress problems, based on the concept of general systems theory. The first part makes a proposal for calculating the stresses and the stress concentration factor of an elastic plate with a circular hole under tension. The remainder describes its application to similar problems, such as an elastic plate with an elliptical hole, an oval hole and semi-circular notches under tension. The stresses at any point in a plate are calculated from the effect of the stresses on the boundaries. General systems theory suggests state object evolves at discrete times. The deformation of the plate is supposed to take a few steps along the time axis, though the real deformation finishes at one step. The results were compared with analytical solutions and/or experimental results.     

Hybrid FEM/HTA analysis of friction contact in elastic and elastoplastic plane stress problems

The Hopfield–Tank neural network evolutionary equations (called for short HTA – HT Analog) were modified for the analysis of friction contact interface. The modified HTA was used for modeling a function in the hybrid program FEM/HTA and applied to the analysis of two numerical examples. The first example, taken from [Mistakidis ES, Panagiotopoulos PG. Numerical treatment of the nonmonotone (zig-zag) friction and adhesive contact problems with debounding: approximation by monotone subproblems. Comput Struct 1993;(47):33–46], is related to the analysis of nonmonotone (zig-zag) contact of elastic strips. The second example concerns the tension of elastoplastic strip with a rigid bolt inserted into a circular hole of the strip. The example generalizes the analysis performed in [Pabisek E. Neural analysis of elastoplastic plane stress problem with unilateral constraints. Comput Assis Mech Eng Sci, in press], considering Coulomb’s friction contact in the bolt–hole inference.     

基于FLAC~(3D)的引水隧洞主、支洞交叉部位的围岩变形分析

圆形洞室开挖后,岩体中形成一个自由空间,使原来处于挤压状态的围岩,由于失去了支撑而发生向洞内松动变形;如果这种变形超过了围岩本身所能承受的能力,则围岩就会发生破坏。本文应用有限差分法数值模拟软件FLAC3D对主、支洞交叉部位的隧洞围岩变形进行模拟分析。模拟结果表明,隧洞开挖后,围岩各部分的位移量较大,围岩应力集中在主、支洞交叉部位。     

Stress analysis of holes in angle-ply laminates: An efficient assumed stress “special-hole-element” approach and a simple estimation method

In the present paper, the development of “special hole-elements”, to enable an efficient and accurate analysis of stress concentration around through-thickness holes in angle-ply laminates, is presented. In these “hole-elements”, the development of which is based on a modified complementary energy principle, the analytical asymptotic solutions for the stress-state near the hole are embedded. The fully 3-D stress-state in the laminate is accounted for, and the interlaminar traction reciprocity is satisfied a priori, while the interelement reciprocity condition is satisfied a posteriori through a Lagrange multiplier method. In addition, a simple method of estimation of stress concentration factors is also given.Results obtained from the present “special-hole-element” procedure are compared with the solutions by the present simple estimation method as well as other available solutions in literature.     

Design study of hole positions and hole shapes for crack tip stress releasing

The method of hole drilling near or at the crack tip is often used in fatigue damage repair. From a design optimization point of view, two questions are posed: Where should the hole(s) be drilled? And is there a better shape of the hole than a circular one? For the first question, we extend earlier results for isotropic material and in general study the influence of having orthotropic material. Optimal shapes are by no means circular, and we focus on the shape of a single hole centered at (or in front of) the crack tip. It is shown that the stress field at the crack boundary can be significantly improved by noncircular shapes. As a byproduct, an alternative method for extracting the stress intensity factor from a finite element analysis is presented.     

Finite element analysis of static and dynamic stresses around suddenly punched holes in plates and shells

The magnitude and distribution of stresses around suddenly punched holes in initially stressed plates and shells is of interest to insure that cracks will not precipitate from stress concentration. This problem is of practical interest to pressure vessel designers to preclude catastrophic failure when holes are punched in vessels to release gas. This paper presents a finite element analysis of several problems investigating static and dynamic stress fields around suddenly punched circular holes.

The first problem deals with the investigation of the radial and tangential stress fields in the vicinity of a suddenly punched hole in a stretched, elastic, isotropic plate subjected to an initial hydrostatic stress field. The wave propagation from a punched hole in the plate under a hydrostatic state of stress was solved analytically, using transform techniques, by Miklowitz; the finite element analysis of this problem presented in this paper confirms the analytical solution. Two grid meshes were investigated and results are presented to show the effect of grid mesh on solution accuracy and the power of finite element techniques for solving stress unloading problems. A formula for determining integration step size is found to be a function of the minimum element length and the wave propagation velocity. A similar investigation into the stress effects around a suddenly punched hole in the plate subjected to an initial uniaxial state of stress was also carried out as a prerequisite for the final problem studied.

The last problem is an anisotropic composite shell of varying thickness under an initial stress field due to internal pressure. The static and dynamic stress fields are computed from an unloading wave that radiates outward from a reinforced circular hole that is cut in the shell in 20 μs. A finite-element model of the shell is developed using quadrilateral and triangular plate elements and both in-plane and bending stiffness is included in the analysis as is nonlinear differential stiffening incorporated into the analysis as a single step approximation. Both bending and in-plane waves radiate outward from the cut hole and the dynamic stresses around the hole edge are computed for both unloading waves. The effects of the unloading waves are temporally spaced due to different wave velocities.

The paper demonstrates that fast response stress problems are readily amenable to finite-element analysis. For holes other than circular, the power of finite-element methods is apparent since these shapes lead to mathematically intractable problems if closed form solutions are attempted.     

Dynamic response of a rigid strip on an elastic half-space

Numerical results for the vertical, horizontal and rocking vibrations of a rigid strip foundation on the surface of the elastic half-space are presented. The solutions are obtained over wider ranges of the frequency parameter than those considered hitherto. The rigid strip is infinite in one direction so that the elastic theory used is that for plane-strain. The mixed boundary-value problems, treated by superposition based on the solution for a stress-boundary-value problem, are considered for “exact” and simplified models. Elements of the dynamic interaction stiffness matrix are evaluated. Dynamic contact stress distributions at the interface between a rigid strip and the half-space are presented.     

电镀镍铁合金中糖精对磁通门噪声的影响

由于糖精有利于减小铁磁薄膜的内应力,而这种内应力在镍铁合金的许多应用中是不利的,故在镍铁镀液中,糖精是常用的添加剂.在镀液其他成份不变的基础上,研究了仅当糖精浓度2.5~20 g/L变化时,内置电镀长条形铁芯磁通门噪声的变化情况.对以上长条形铁芯构成的磁通门,进行了噪声功率谱密度测试,结果表明:当糖精浓度从2.5 g/L增加到20 g/L时,1 Hz噪声功率谱密度从9.387槡nT/ Hz非线性地减小到了1.386槡nT/ Hz;同时也表明为了使磁通门的噪声最小时,最常用的糖精浓度(5 g/L)并不是最好的浓度,而应是更大的糖精浓度.     

Damage tolerance based design optimisation of a fuel flow vent hole in an aircraft structure

This paper investigates the design optimisation of a fuel flow vent hole (FFVH) located in the wing pivot fitting (WPF) of an F-111 aircraft assuming a damage tolerance design philosophy. The design of the vent hole shape is undertaken considering the basic durability based design objectives of stress, residual (fracture) strength, and fatigue life. Initially, a stress based optimised shape is determined. Damage tolerance based design optimisation is then undertaken to determine the shape of the cutout so as to maximise its residual strength and fatigue life. For stress optimisation, the problem is analysed using the gradient-less biological algorithm and the gradient-based nonlinear programming methods. The optimum designs predicted by the two fundamentally different optimisation algorithms agree well. The optimum shapes of the vent hole are subsequently determined considering residual strength and fatigue life as the distinct design objectives in the presence of numerous 3D cracks located along the vent hole boundary. A number of crack cases are considered to investigate how the crack size affects the optimal shapes. A semi-analytical method is employed for computation of the stress intensity factors (SIF), and an analytical crack closure model is subsequently used to evaluate the fatigue life. The 3D biological algorithm is used for designing the cutout profiles that optimise residual strength and fatigue life of the component. An improved residual strength/fatigue life (depending on the optimisation objective) is achieved for the optimal designs. The variability in SIF/fatigue life around the cutout boundary is reduced, thereby making the shape more evenly fracture/fatigue critical. The vent hole shapes optimised for stress, residual strength, and fatigue life are different from each other for a given nature and size of the flaws. This emphasises the need to consider residual strength and/or fatigue life as the explicit design objective. The durability based optimal vent hole shapes depend on the initial and final crack sizes. It is also shown that a damage tolerance optimisation additionally produces a reduced weight WPF component, which is highly desirable for aerospace industries. The design space near the ‘optimal’ region is found to be flat. This allows us to achieve a considerable enhancement in fatigue performance without precisely identifying the local/global optimum solution, and also enables us to select a reduced weight ‘near optimal’ design rather than the precise optimal shape.     

Stress concentration in an infinite plate containing an ovaloid hole

In this paper the stress concentration problem in the case of an infinite plate containing an ovaloid hole is discussed. Ling's conformal mapping is improved by us, and the improved conformal mapping is more suitable to meet the geometry of the ovaloid hole. Using the Muskhelishvili's method, we can easily solve the proposed problem. Several numerical results are given.     

The interdependence of hygrothermal processes and elasto-viscoplastic behavior in polymer-dominated multi-material systems

An analytical numerical method was developed to predict the time-dependent mechanical behavior of polymer-dominated multi-material systems. The method takes into account the interdependence of stress, strain, moisture diffusion and heat conduction, and it provides stress, strain, moisture and temperature distributions through the system as functions of time, when the external hygrothermal-mechanical conditions are given. In addition it requires the input of empirical stress-strain-time relationships as well as stress-diffusion coupling coefficients. Following experimental evaluation of the necessary coefficients a set of nonlinear coupled differential equations is solved numerically by the finite strip method, which was found to be efficient and accurate for the purpose.The experimental results of the deformation behavior and moisture concentration in an asymmetrical Epoxy-Aluminum model exposed to different hygrothermomechanical histories show a good correlation with analytical prediction.     

Residual Stress Measurement on a MEMS Structure With High-Spatial Resolution

A new approach to the local measurement of residual stress in microstructures is described in this paper. The presented technique takes advantage of the combined milling-imaging features of a focused ion beam (FIB) equipment to scale down the widely known hole drilling method. This method consists of drilling a small hole in a solid with inherent residual stresses and measuring the strains/displacements caused by the local stress release, that takes place around the hole. In the presented case, the displacements caused by the milling are determined by applying digital image correlation (DIC) techniques to high resolution micrographs taken before and after the milling process. The residual stress value is then obtained by fitting the measured displacements to the analytical solution of the displacement fields. The feasibility of this approach has been demonstrated on a micromachined silicon nitride membrane showing that this method has high potential for applications in the field of mechanical characterization of micro/nanoelectromechanical systems     

Interlaminar stress analysis for laminated plates containing a curvilinear hole

This study presents a variational-perturbation approach for the three-dimensional stress analysis around a curvilinear cutout in composite laminates. The solution is based on a composite expansion and assumed stress finite element methods. Stress field solutions for angleply and cross-ply laminates containing an elliptical hole have been presented. The effects of the ellipse aspect ratio and the fiber orientation on the interlaminar shear stress magnitude have been investigated. A failure criterion based on the interlaminar distortional energy function has been suggested. According to this criterion, it was found that, for angle-ply laminates containing an elliptical hole, a delamination failure initiation occurs at a point along the perpendicular to the direction of loading.     

Optimization of axisymmetric elastic modulus distributions around a hole for increased strength

Holes in engineering structures cause stress concentrations that often lead to failure. In nature, however, blood vessel holes (foramina) in load-bearing bones are not normally involved in structural failures. It has been found that this behavior is linked to the material distribution near the hole. In the present paper, we have investigated the effectiveness of optimizing the radial distribution of the isotropic elastic modulus around a circular hole to increase load-carrying capacity. Bezier curves were used to describe the radial distribution of the elastic modulus. Since changing the elastic modulus usually affects the strength, the ratio of maximum principal stress to strength was chosen as the objective function for optimization. Using non-dimensional analysis of the 2-D elasticity equations, we identified three parameters that govern the optimum design and are applicable to a wide range of materials, loading, and geometries. The first is a material parameter that describes the relationship between the strength and elastic modulus, the second is the geometric parameter given by the ratio of the optimized field to the hole radius, and the third is the biaxial load ratio. The effect of failure criterion choice on the optimum elastic modulus distribution is also investigated. Optimum elastic modulus distributions for materials whose strength increases faster than the stiffness, as density and/or composition is varied, completely eliminated the effect of the hole by locally stiffening areas that experience high stresses. When the strength lagged behind the stiffness, optimum designs were similar to those found in bones, and relied on modulus distributions that direct the loads away from the hole.     

Axisymmetric substitute structures for circular disks with noncentral holes

For economical finite element calculations of aero-engine disks it is advantageous to use an axisymmetric FE-model. However, disks often contain noncentral holes, for example bolt holes which disturb the axial symmetry. In the present article methods are described on how to find axisymmetric substitute structures for these local disturbances. The substitute structures have been constructed in such a way that the stresses they predict reproduce those in the original structure far away from the hole region. The stresses in the original structure were calculated by applying the formulas obtained by Muskhelishvili for a ring and for a hole in infinite space in an alternating way. An important asset of the substitute structures is that they allow for the prediction of the stress peaks occurring at the hole surfaces. This has been achieved by the determination of appropriate stress concentration factors which must be applied to the respective model stresses. For the practically relevant cases, the developed substitute structures are independent of the specific load conditions and only depend on a single geometric parameter characterizing the relative distance between the holes.