Search results for: Stress Distribution.

Authors: M. H. Kargarnovin, K. Momeni

Abstract:

The study of the stress distribution on a hollow cylindrical fiber placed in a composite material is considered in this work and an analytical solution for this stress distribution has been constructed. Finally some parameters such as fiber-s thickness and fiber-s length are considered and their effects on the distribution of stress have been investigated. For finding the governing relations, continuity equations for the axisymmetric problem in cylindrical coordinate (r,o,z) are considered. Then by assuming some conditions and solving the governing equations and applying the boundary conditions, an equation relates the stress applied to the representative volume element with the stress distribution on the fiber has been found.

Keywords: Axial Loading, Composite, Hollow CylindricalFiber, Stress Distribution.

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Authors: Ali Baladi, Alireza Fallahi Arezoodar

Abstract:

in dissimilar material joints, failure often occurs along the interface between two materials due to stress singularity. Stress distribution and its concentration depend on materials and geometry of the junction. Inhomogenity of stress distribution at the interface of junction of two materials with different elastic modules and stress concentration in this zone are the main factors resulting in rupture of the junction. Effect of joining angle in the interface of aluminum-polycarbonate will be discussed in this paper. Computer simulation and finite element analysis by ABAQUS showed that convex interfacial joint leads to stress reduction at junction corners in compare with straight joint. This finding is confirmed by photoelastic experimental results.

Keywords: Elastic Modules, Stress Concentration, JoiningAngle, Photoelastic.

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Authors: N. Ruangkajonmathee, R. Thiamsri, B. Marungsri

Abstract:

This paper presents the experimental results on space charge distribution in cross-linked polyethylene (XLPE) insulating material for 22 kV power distribution system cable by using pulse electroacoustic measurement technique (PEA). Numbers of XLPE insulating material ribbon having thickness 60 μm taken from unused 22 kV high voltage cable were used as specimen in this study. DC electric field stress was applied to test specimen at room temperature (25°C). Four levels of electric field stress, 25 kV/mm, 50 kV/mm, 75 kV/mm and 100 kV/mm, were used. In order to investigate space charge distribution characteristic, space charge distribution characteristics were measured after applying electric field stress 15 min, 30 min and 60 min, respectively. The results show that applied time and magnitude of dc electric field stress play an important role to the formation of space charge.

Keywords: Space charge distribution, pulsed electroacoustic(PEA) technique, cross-linked polyethylene (XLPE), DC electrical fields stress.

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Authors: Kaman M. O., Celik N.

Abstract:

In this study, stress distributions on dental implants made of functionally graded biomaterials (FGBM) are investigated numerically. The implant body is considered to be subjected to axial compression loads. Numerical problem is assumed to be 2D, and ANSYS commercial software is used for the analysis. The cross section of the implant thread varies as varying the height (H) and the width (t) of the thread. According to thread dimensions of implant and material properties of FGBM, equivalent stress distribution on the implant is determined and presented with contour plots along with the maximum equivalent stress values. As a result, with increasing material gradient parameter (n), the equivalent stress decreases, but the minimum stress distribution increases. Maximum stress values decrease with decreasing implant radius (r). Maximum von Mises stresses increases with decreasing H when t is constant. On the other hand, the stress values are not affected by variation of t in the case of H = constant.

Keywords: Functionally graded biomaterials, dental implant finite element method.

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Authors: A. Derardja, L. Baroura, M. Brioua

Abstract:

The nanotechnology based on epitaxial systems includes single or arranged misfit dislocations. In general, whatever is the type of dislocation or the geometry of the array formed by the dislocations; it is important for experimental studies to know exactly the stress distribution for which there is no analytical expression [1, 2]. This work, using a numerical analysis, deals with relaxation of epitaxial layers having at their interface a periodic network of edge misfit dislocations. The stress distribution is estimated by using isotropic elasticity. The results show that the thickness of the two sheets is a crucial parameter in the stress distributions and then in the profile of the two sheets. A comparative study between the case of single dislocation and the case of parallel network shows that the layers relaxed better when the interface is covered by a parallel arrangement of misfit. Consequently, a single dislocation at the interface produces an important stress field which can be reduced by inserting a parallel network of dislocations with suitable periodicity.

Keywords: Parallel array of misfit, interface, isotropic elasticity, single crystalline substrates, coherent interface

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Authors: H. Panahi, S. Asadi

Abstract:

In this paper, the estimation of the stress-strength parameter R = P(Y < X), when X and Y are independent and both are Lomax distributions with the common scale parameters but different shape parameters is studied. The maximum likelihood estimator of R is derived. Assuming that the common scale parameter is known, the bayes estimator and exact confidence interval of R are discussed. Simulation study to investigate performance of the different proposed methods has been carried out.

Keywords: Stress-Strength model; maximum likelihoodestimator; Bayes estimator; Lomax distribution

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Authors: Maziar Ramezani, Zaidi Mohd Ripin

Abstract:

In a metal forming process, the friction between the material and the tools influences the process by modifying the stress distribution of the workpiece. This frictional behaviour is often taken into account by using a constant coefficient of friction in the finite element simulations of sheet metal forming processes. However, friction coefficient varies in time and space with many parameters. The Stribeck friction model is investigated in this study to predict springback behaviour of AA6061-T4 sheets during V-bending process. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The plane-strain bending process is simulated in ABAQUS/Standard. We compared the computed punch load-stroke curves and springback related to the constant coefficient of friction with the defined friction model. The results clearly showed that the new friction model provides better agreement between experiments and results of numerical simulations. The influence of friction models on stress distribution in the workpiece is also studied numerically

Keywords: Friction model, Stress distribution, V-bending.

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Authors: A. Chellil, A. Nour, S. Lecheb, H. Mechakra, L. Addar, H. Kebir

Abstract:

This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems.

Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: Aluminium alloys, plate, crack, failure.

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Authors: H.Panahi, S.Asadi

Abstract:

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.

Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.

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Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

Abstract:

We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: Indentation, contact problem, stress distribution, coating materials, layer-substrate body.

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Authors: Tejeet Singh, Harmanjit Singh

Abstract:

Creep behavior of thick-walled functionally graded cylinder consisting of AlSiC and subjected to internal pressure and high temperature has been analyzed. The functional relationship between strain rate with stress can be described by the well known threshold stress based creep law with a stress exponent of five. The effect of imposing non-linear particle gradient on the distribution of creep stresses in the thick-walled functionally graded composite cylinder has been investigated. The study revealed that for the assumed non-linear particle distribution, the radial stress decreases throughout the cylinder, whereas the tangential, axial and effective stresses have averaging effect. The strain rates in the functionally graded composite cylinder could be reduced to significant extent by employing non-linear gradient in the distribution of reinforcement.

Keywords: Functionally Graded Material, Pressure, Steady State Creep, Thick-Cylinder.

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Authors: Ş. Aksoy, A. Kurşun, E. Çetin, M. R. Haboğlu

Abstract:

In this study, thermo elastic stress analysis is  performed on a cylinder made of laminated isotropic materials under  thermomechanical loads. Laminated cylinders have many  applications such as aerospace, automotive and nuclear plant in the  industry. These cylinders generally performed under  thermomechanical loads. Stress and displacement distribution of the  laminated cylinders are determined using by analytical method both  thermal and mechanical loads. Based on the results, materials  combination plays an important role on the stresses distribution along  the radius. Variation of the stresses and displacements along the  radius are presented as graphs. Calculations program are prepared  using MATLAB® by authors.

 

Keywords: Isotropic materials, laminated cylinders, thermoelastic stress, thermomechanical load.

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Authors: E. A. Azrulhisham, Y. M. Asri, A. W. Dzuraidah, A. H. Hairul Fahmi

Abstract:

The aim of this paper is to introduce a parametric distribution model in fatigue life reliability analysis dealing with variation in material properties. Service loads in terms of responsetime history signal of Belgian pave were replicated on a multi-axial spindle coupled road simulator and stress-life method was used to estimate the fatigue life of automotive stub axle. A PSN curve was obtained by monotonic tension test and two-parameter Weibull distribution function was used to acquire the mean life of the component. A Pearson system was developed to evaluate the fatigue life reliability by considering stress range intercept and slope of the PSN curve as random variables. Considering normal distribution of fatigue strength, it is found that the fatigue life of the stub axle to have the highest reliability between 10000 – 15000 cycles. Taking into account the variation of material properties associated with the size effect, machining and manufacturing conditions, the method described in this study can be effectively applied in determination of probability of failure of mass-produced parts.

Keywords: Stub axle, Fatigue life reliability, Stress-life, PSN curve, Weibull distribution, Pearson system

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Authors: Soo-yeon Seo, Seol-ki Kim, Su-jin Jung

Abstract:

In the construction of a building, it is necessary to minimize construction period and secure enough work space for stacking of materials during the construction especially in city area. In this manner, various top-down construction methods have been developed and widely used in Korea. This paper investigates the stress variation of underground structure of a building constructed by using SPS (Strut as Permanent System) known as a top-down method in Korea through an analytical approach. Various types of earth pressure distribution related to ground condition were considered in the structural analysis of an example structure at each step of the excavation. From the analysis, the most high member force acting on beams was found when the ground type was medium sandy soil and a stress concentration was found in corner area.

Keywords: Construction of building, top-down construction method, earth pressure distribution, member force, stress concentration.

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Authors: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

Abstract:

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

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Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: Stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear.

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Authors: Parveen K. Saini, Tarun Agarwal

Abstract:

An investigation into the effect of countersunk depth, plate thickness, countersunk angle and plate width on the stress concentration around countersunk hole is carried out with the help of finite element analysis. The variation of stress concentration with respect to these parameters is studied for three types of loading viz. uniformly distributed load, uniformly varying load and functionally distributed load. The results of the finite element analysis are interpreted and some conclusions are drawn. The distribution of stress concentration around countersunk hole in isotropic plates simply supported at all the edges is found similar and is independent of loading. The maximum stress concentration also occurs at a particular point irrespective of the loading conditions.

Keywords: Stress Concentration Factor, Countersunk hole, Finite element, ANSYS.

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Authors: Essam A. Al-Bahkali, Mahir H. Es-saheb, Jonny Herwan

Abstract:

In this study the elastic-plastic stress distribution in weld-bonded joint, fabricated from austenitic stainless steel (AISI 304) sheet of 1.00 mm thickness and Epoxy adhesive Araldite 2011, subjected to axial loading is investigated. This is needed to improve design procedures and welding codes, and saving efforts in the cumbersome experiments and analysis. Therefore, a complete 3-D finite element modelling and analysis of spot welded, bonded and weld-bonded joints under axial loading conditions is carried out. A comprehensive systematic experimental program is conducted to determine many properties and quantities, of the base metals and the adhesive, needed for FE modelling, such like the elastic – plastic properties, modulus of elasticity, fracture limit, the nugget and heat affected zones (HAZ) properties, etc. Consequently, the finite element models developed, for each case, are used to evaluate stresses distributions across the entire joint, in both the elastic and plastic regions. The stress distribution curves are obtained, particularly in the elastic regions and found to be consistent and in excellent agreement with the published data. Furthermore, the stresses distributions are obtained in the weld-bonded joint and display the best results with almost uniform smooth distribution compared to spot and bonded cases. The stress concentration peaks at the edges of the weld-bonded region, are almost eliminated resulting in achieving the strongest joint of all processes.

Keywords: Spot Welded, Weld-Bonded, Load-Displacement curve, Stress distribution

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Authors: Isa Ahmadi, Ramin Khamedi

Abstract:

In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C¹ continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: Cyclic Loading, Finite Element Analysis, Prager Kinematic Hardening Model, Torsion of shaft.

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Authors: L. Sandu, F. Topalâ, S. Porojan

Abstract:

Knowledge of factors, which influence stress and its distribution, is of key importance to the successful production of durable restorations. One of this is the marginal geometry. The objective of this study was to evaluate, by finite element analysis (FEA), the influence of different marginal designs on the stress distribution in teeth prepared for cast metal crowns. Five margin designs were taken into consideration: shoulderless, chamfer, shoulder, sloped shoulder and shoulder with bevel. For each kind of preparation three dimensional finite element analyses were initiated. Maximal equivalent stresses were calculated and stress patterns were represented in order to compare the marginal designs. Within the limitation of this study, the shoulder and beveled shoulder margin preparations of the teeth are preferred for cast metal crowns from biomechanical point of view.

Keywords: finite element, marginal geometry, metal crown

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Authors: E. Çetin, A. Kurşun, Ş. Aksoy, M. Tunay Çetin

Abstract:

The closed form study deals with elastic stress analysis of annular bi-material discs with variable thickness subjected to the mechanical and thermomechanical loads. Those discs have many applications in the aerospace industry, such as gas turbines and gears. Those discs normally work under thermal and mechanical loads. Their life cycle can increase when stress components are minimized. Each material property is assumed to be isotropic. The results show that material combinations and thickness of profiles play an important role in determining the responses of bi-material discs and an optimal design of those structures. Stress distribution is investigated and results are shown as graphs.

Keywords: Bi-material discs, elastic stress analysis, mechanical loads, rotating discs.

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Authors: O. Takakuwa, Y. Mano, H. Soyama

Abstract:

This paper reveals the interaction between hydrogen and surface stress in austenitic stainless steel by X-ray diffraction stress measurement and thermal desorption analysis before and after being charged with hydrogen. The surface residual stress was varied by surface finishing using several disc polishing agents. The obtained results show that the residual stress near surface had a significant effect on hydrogen absorption behavior, that is, tensile residual stress promoted the hydrogen absorption and compressive one did opposite. Also, hydrogen induced equi-biaxial stress and this stress has a linear correlation with hydrogen content.

Keywords: Hydrogen embrittlement, Residual stress, Surface finishing, Stainless steel.

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Authors: K. Chalernpon, P. Aroonjarattham, K. Aroonjarattham

Abstract:

Total hip replacement had been one of the most successful operations in hip arthritis surgery. The purpose of this research had been to develop a dynamic hip contact of Thai femoral bone to analyze the stress distribution on the implant and the strain distribution on the bone model under daily activities and compared with the static load simulation. The results showed the different of maximum von Mises stress 0.14 percent under walking and 0.03 percent under climbing stair condition and the different of equivalent total strain 0.52 percent under walking and 0.05 percent under climbing stair condition. The muscular forces should be evaluated with dynamic condition to reduce the maximum von Mises stress and equivalent total strain.

Keywords: Dynamic loading, Static Load, Hip prosthesis, Thai femur, Femoral bone, Finite Element Analysis.

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Authors: Zohreh Sheikh Khozani, Wan Hanna Melini Wan Mohtar, Mojtaba Porhemmat

Abstract:

Prediction of wall shear stress in a rectangular channel, with non-homogeneous roughness distribution, was studied. Estimation of shear stress is an important subject in hydraulic engineering, since it affects the flow structure directly. In this study, the Genetic Algorithm Artificial (GAA) neural network is introduced as a hybrid methodology of the Artificial Neural Network (ANN) and modified Genetic Algorithm (GA) combination. This GAA method was employed to predict the wall shear stress. Various input combinations and transfer functions were considered to find the most appropriate GAA model. The results show that the proposed GAA method could predict the wall shear stress of open channels with high accuracy, by Root Mean Square Error (RMSE) of 0.064 in the test dataset. Thus, using GAA provides an accurate and practical simple-to-use equation.

Keywords: Artificial neural network, genetic algorithm, genetic programming, rectangular channel, shear stress.

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Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Hamad, H. Kebir

Abstract:

The work involves develops attended by a numerical execution of the eXtend Finite Element Method premises a measurement by the fracture process cracked so many cracked plates an application will be processed for the calculation of the stress intensity factor SIF. In the first we give in statically part the distribution of stress, displacement field and strain of composite plate in two cases uncrack/edge crack, also in dynamical part the first six modes shape. Secondly, we calculate Stress Intensity Factor SIF for different orientation angle θ of central crack with length (2a=0.4mm) in plan strain condition, KI and KII are obtained for mode I and mode II respectively using X-FEM method. Finally from crack inclined involving mixed modes results, the comparison we chose dangerous inclination and the best crack angle when K is minimal.

Keywords: Stress Intensity Factor (SIF), Crack orientation, Glass/Epoxy, natural Frequencies, X-FEM.

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Authors: Mohammad AL Amro

Abstract:

This study will provide a brief description of the stress in Najdi Arabic dialect as well as Modern Standard Arabic. Beyond the analysis of stress patterns, this paper will also attempt to deal with two important phenomena that affect stress, namely epenthesis/insertion, vowel shortening, and consonant (the glottal stop) deletion.

Keywords: Epenthesis, Najd, stress, vowel shortening.

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Authors: Saeid Norouzi, Ali Shams, Hassan Farhangi, Alireza Darvish

Abstract:

Hot tear cracking and residual stress are two different consequences of thermal stress both of which can be considered as casting problem. The purpose of the present study is simulation of the effect of casting shape characteristic on hot tearing and residual stress. This study shows that the temperature range for simulation of hot tearing and residual stress are different. In this study, in order to study the development of thermal stress and to predict the hot tearing and residual stress of shaped casting, MAGMASOFT simulation program was used. The strategy of this research was the prediction of hot tear location using pinpointing hot spot and thermal stress concentration zones. The results shows that existing of stress concentration zone increases the hot tearing probability and consequently reduces the amount of remaining residual stress in casting parts.

Keywords: Hot tearing, residual stress, simulation, investment casting.

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Authors: Jun Peng, Johnny Ching Ming Ho

Abstract:

In order to calculate the flexural strength of normal-strength concrete (NSC) beams, the nonlinear actual concrete stress distribution within the compression zone is normally replaced by an equivalent rectangular stress block, with two coefficients of α and β to regulate the intensity and depth of the equivalent stress respectively. For NSC beams design, α and β are usually assumed constant as 0.85 and 0.80 in reinforced concrete (RC) codes. From an earlier investigation of the authors, α is not a constant but significantly affected by flexural strain gradient, and increases with the increasing of strain gradient till a maximum value. It indicates that larger concrete stress can be developed in flexure than that stipulated by design codes. As an extension and application of the authors- previous study, the modified equivalent concrete stress block is used here to produce a series of design charts showing the maximum design limits of flexural strength and ductility of singly- and doubly- NSC beams, through which both strength and ductility design limits are improved by taking into account strain gradient effect.

Keywords: Concrete beam, Ductility, Equivalent concrete stress, Normal strength, Strain gradient, Strength

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Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

When the characteristic length of an elastic solid is down to the nanometer level, its deformation behavior becomes size dependent. Surface energy /surface stress have recently been applied to explain such dependency. In this paper, the effect of strain-independent surface stress on the deformation of an isotropic elastic solid containing a nanosized elliptical hole is studied by the finite element method. Two loading cases are considered, in the first case, hoop stress along the rim of the elliptical hole induced by pure surface stress is studied, in the second case, hoop stress around the elliptical opening under combined remote tension and surface stress is investigated. It has been shown that positive surface stress induces compressive hoop stress along the hole, and negative surface stress has opposite effect, maximum hoop stress occurs near the major semi-axes of the ellipse. Under combined loading of remote tension and surface stress, stress concentration around the hole can be either intensified or weakened depending on the sign of the surface stress.

Keywords: Surface stress, finite element method, stress concentration, nanosized elliptical hole

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Authors: Jinyong Yao, Hongzhi Li, Chao Du, Jiao Li

Abstract:

Reliability of long-term storage products is related to the availability of the whole system, and the evaluation of storage life is of great necessity. These products are usually highly reliable and little failure information can be collected. In this paper, an analytical method based on data from accelerated storage life test is proposed to evaluate the reliability index of the long-term storage products. Firstly, singularities are eliminated by data normalization and residual analysis. Secondly, with the preprocessed data, the degradation path model is built to obtain the pseudo life values. Then by life distribution hypothesis, we can get the estimator of parameters in high stress levels and verify failure mechanism consistency. Finally, the life distribution under the normal stress level is extrapolated via the acceleration model and evaluation of the actual average life is available. An application example with the camera stabilization device is provided to illustrate the methodology we proposed.

Keywords: Accelerated storage life test, failure mechanism consistency, life distribution, reliability.

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