Search results for: Thermo Elastic Stress

Authors: Lenka Ševelová, Aleš Florian

Abstract:

Appropriate and progressive tool for analyzing behavior of low volume roads are probabilistic models used in reliability analyses. The necessary part of the probabilistic model is the deterministic model of structural behavior. The FE model of low volume roads is created in the ANSYS software. It is able to determine the state of stress and deformation in any point of the structure and thus generate data required for the reliability analysis. The paper compares two material constitutive models used for modeling of unbound non-homogenous materials used in low volume roads. The first model is linear elastic model according to Hook theory (H model), the second one is nonlinear elastic-plastic Drucker-Prager model (D-P model).

Keywords: FEA, FEM, geotechnical materials, low volume roads, material constitutive models, pavement.

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

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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: V. Kahya, A. Birinci, R. Erdol

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A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.

Keywords: Frictionless contact, Initial separation, Orthotropicmaterial, Singular integral equation.

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Authors: U. Mutman, S. B. Coskun

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In this study Homotopy Perturbation Method (HPM) is employed to investigate free vibration of an Euler beam with variable stiffness resting on an elastic foundation. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear problems. HPM produces analytical approximate expression which is continuous in the solution domain. This work shows that HPM is a promising method for free vibration analysis of nonuniform Euler beams on elastic foundation. Several case problems have been solved by using the technique and solutions have been compared with those available in the literature.

Keywords: Homotopy Perturbation Method, Elastic Foundation, Vibration, Beam

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Authors: H. Dehghan, E. Mahdavi, M. M. Heyhat

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In pressure vessels contain hydrogen, the role of hydrogen will be important because of hydrogen cracking problem. It is difficult to predict what is happened in metallurgical field spite of a lot of studies have been searched. The main role in controlling the mass diffusion as driving force is related to stress. In this study, finite element analysis is implemented to estimate material-s behavior associated with hydrogen embrittlement. For this purpose, one model of a pressure vessel is introduced that it has definite boundary and initial conditions. In fact, finite element is employed to solve the sequentially coupled mass diffusion with stress near a crack front in a pressure vessel. Modeling simulation intergrarnular fracture of AISI 4135 steel due to hydrogen is investigated. So, distribution of hydrogen and stress are obtained and they indicate that their maximum amounts occur near the crack front. This phenomenon is happened exactly the region between elastic and plastic field. Therefore, hydrogen is highly mobile and can diffuse through crystal lattice so that this zone is potential to trap high volume of hydrogen. Consequently, crack growth and fast fracture will be happened.

Keywords: Stress Intensity Factor, Mass Diffusion, FEM, Pressure Vessel

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Authors: K. Krizova, R. Hela

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The paper is focused on monitoring of dependencies of different composition concretes on elastic modulus values. To obtain a summary of elastic modulus development in dependence of concrete composition design variability was the objective of the experiment. Essential part of this work was initiated as a reaction to building practice when questions of elastic moduli arose at the same time and which mostly did not obtain the required and expected values from concrete constructions.

Keywords: Concrete, Compressive strength, Modulus of elasticity, EuroCode 2.

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Authors: Kyung Hyun, Choi, Minh Ngoc, Nong, M. Asif Ali, Rehmani

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This present paper proposes the modified Elastic Strip method for mobile robot to avoid obstacles with a real time system in an uncertain environment. The method deals with the problem of robot in driving from an initial position to a target position based on elastic force and potential field force. To avoid the obstacles, the robot has to modify the trajectory based on signal received from the sensor system in the sampling times. It was evident that with the combination of Modification Elastic strip and Pseudomedian filter to process the nonlinear data from sensor uncertainties in the data received from the sensor system can be reduced. The simulations and experiments of these methods were carried out.

Keywords: Collision avoidance, Avoidance obstacle, Elastic Strip, Real time collision avoidance.

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Authors: Taewon Seo

Abstract:

The characteristics of physiological blood flow in human carotid arterial bifurcation model have been numerically studied using a fully coupled fluid-structure interaction (FSI) analysis. This computational model with the fluid-structure interaction is constructed to investigate the flow characteristics and wall shear stress in the carotid artery. As the flow begins to decelerate after the peak flow, a large recirculation zone develops at the non-divider wall of both internal carotid artery (ICA) and external carotid artery (ECA) in FSI model due to the elastic energy stored in the expanding compliant wall. The calculated difference in wall shear stress (WSS) in both Non-FSI and FSI models is a range of between 5 and 11% at the mean WSS. The low WSS corresponds to regions of carotid artery that are more susceptible to atherosclerosis.

Keywords: Carotid artery, Fluid-structure interaction, Hemodynamics, Wall shear stress.

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: Stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: Hee Jae Shin, In Pyo Cha, Min Sang Lee, Hyun Kyung Yoon, Tae Ho Kim, Yoon Sun Lee, Lee Ku Kwac, Hong Gun Kim

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Non-destructive testing and evaluation techniques for assessing the integrity of composite structures are essential to both reduce manufacturing costs and out of service time of transport means due to maintenance. In this study, Analyze into non-destructive test characterization of carbon fiber reinforced plastics (CFRP) internal and external defects using thermo-graphic camera and transient thermography method. non-destructive testing were characterized by defect size (Ø8, Ø10, Ø12, Ø14) and depth (1.2mm, 2.4mm).

Keywords: Non Destructive test (NDT), Thermal characteristic, Thermo graphic Camera, Carbon Fiber Reinforced Plastics (CFRP).

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Authors: A. Benmakhlouf, A. Bentabet

Abstract:

In this paper, we investigated the athermal pressure behavior of the structural and elastic properties of scheelite BaWO4 phase up to 7 GPa using the ab initio pseudo-potential method. The calculated lattice parameters pressure relation have been compared with the experimental values and found to be in good agreement with these results. Moreover, we present for the first time the investigation of the elastic properties of this compound using the density functional perturbation theory (DFPT). It is shown that this phase is mechanically stable up to 7 GPa after analyzing the calculated elastic constants. Other relevant quantities such as bulk modulus, pressure derivative of bulk modulus, shear modulus; Young’s modulus, Poisson’s ratio, anisotropy factors, Debye temperature and sound velocity have been calculated. The obtained results, which are reported for the first time to the best of the author’s knowledge, can facilitate assessment of possible applications of the title material.

Keywords: Pseudo-potential method, pressure, structural and elastic properties, scheelite BaWO4 phase.

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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

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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: Amin Almasi

Abstract:

Analysis of reciprocating equipment piston rod leads to nonlinear elastic-plastic deformation analysis of rod with initial imperfection under axial dynamic load. In this paper a new and effective model and analytical formulations are presented to evaluate dynamic deformation and elastic-plastic stresses of reciprocating machine piston rod. This new method has capability to account for geometric nonlinearity, elastic-plastic deformation and dynamic effects. Proposed method can be used for evaluation of piston rod performance for various reciprocating machines under different operation situations. Rod load curves and maximum allowable rod load are calculated with presented method for a refinery type reciprocating compressor. Useful recommendations and guidelines for rod load, rod load reversal and rod drop monitoring are also addressed.

Keywords: Deformation, Reciprocating Equipment, Rod.

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Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

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Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

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This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: Sh. Hamada

Abstract:

The current work aims to study the rainbow like-structure observed in the elastic scattering of alpha particles on both ¹²C and ¹⁶O nuclei. We reanalyzed the experimental elastic scattering angular distributions data for α+¹²C and α+¹⁶O nuclear systems at different energies using both optical model and double folding potential of different interaction models such as: CDM3Y1, DDM3Y1, CDM3Y6 and BDM3Y1. Potential created by BDM3Y1 interaction model has the shallowest depth which reflects the necessity to use higher renormalization factor (N_r). Both optical model and double folding potential of different interaction models fairly reproduce the experimental data.

Keywords: Nuclear rainbow, elastic scattering, optical model, double folding, density distribution.

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Authors: Sanjeev Sharma, Manoj Sahni

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Transition theory has been used to derive the elasticplastic and transitional stresses. Results obtained have been discussed numerically and depicted graphically. It is observed that the rotating disk made of incompressible material with inclusion require higher angular speed to yield at the internal surface as compared to disk made of compressible material. It is seen that the radial and circumferential stresses are maximum at the internal surface with and without edge load (for flat disk). With the increase in thickness parameter (k = 2, 4), the circumferential stress is maximum at the external surface while the radial stress is maximum at the internal surface. From the figures drawn the disk with exponentially varying thickness (k = 2), high angular speed is required for initial yielding at internal surface as compared to flat disk and exponentially varying thickness for k = 4 onwards. It is concluded that the disk made of isotropic compressible material is on the safer side of the design as compared to disk made of isotropic incompressible material as it requires higher percentage increase in an angular speed to become fully plastic from its initial yielding.

Keywords: Finite deformation, Incompressibility, Transitionalstresses, Elastic-plastic.

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Authors: Anto Antony Samy, Atefeh Golbang, Edward Archer, Alistair McIlhagger

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Fused Deposition Modelling (FDM) is one of the additive manufacturing techniques that has become highly attractive in the industrial and academic sectors. However, parts fabricated through FDM are highly susceptible to geometrical defects such as warpage, shrinkage, and delamination that can severely affect their function. Among the thermoplastic polymer feedstock for FDM, semi-crystalline polymers are highly prone to part distortion due to polymer crystallization. In this study, the influence of FDM processing conditions such as chamber temperature and print bed temperature on the induced thermal residual stress and resulting warpage are investigated using 3D transient thermal model for a semi-crystalline polymer. The thermo-mechanical properties and the viscoelasticity of the polymer, as well as the crystallization physics which considers the crystallinity of the polymer, are coupled with the evolving temperature gradient of the print model. From the results it was observed that increasing the chamber temperature from 25 °C to 75 °C leads to a decrease of 3.3% residual stress and increase of 0.4% warpage, while decreasing bed temperature from 100 °C to 60 °C resulted in 27% increase in residual stress and a significant rise of 137% in warpage. The simulated warpage data are validated by comparing it with the measured warpage values of the samples using 3D scanning.

Keywords: Finite Element Analysis, FEA, Fused Deposition Modelling, residual stress, warpage.

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Authors: H. Hosseini, B. V. Berdyshev, I. Iskopintsev

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This paper presents a rheological model for producing shape-memory thermoplastic polymers. Shape-memory occurs as a result of internal rearrangement of the structural elements of a polymer. A non-linear viscoelastic model was developed that allows qualitative and quantitative prediction of the stress-strain behavior of shape-memory polymers during heating. This research was done to develop a technique to determine the maximum possible change in size of shape-memory products during heating. The rheological model used in this work was particularly suitable for defining process parameters and constructive parameters of the processing equipment.

Keywords: Elastic deformation, heating, shape-memory polymers, stress-strain behavior.

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Authors: Chongyang Ye, Rong Liu

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Elastic compression stockings (ECSs) have been widely applied in prophylaxis and treatment of chronic venous insufficiency of lower extremities. The medical function of ECS is to improve venous return and increase muscular pumping action to facilitate blood circulation, which is largely determined by the complex interaction between the ECS and lower limb tissues. Understanding the mechanical transmission of ECS along the skin surface, deeper tissues, and vascular system is essential to assess the effectiveness of the ECSs. In this study, a three-dimensional (3D) finite element (FE) model of the leg-ECS system integrated with a 3D fluid-solid interaction (FSI) model of the leg-vein system was constructed to analyze the biomechanical properties of veins and soft tissues under different ECS compression. The Magnetic Resonance Imaging (MRI) of the human leg was divided into three regions, including soft tissues, bones (tibia and fibula) and veins (peroneal vein, great saphenous vein, and small saphenous vein). The ECSs with pressure ranges from 15 to 26 mmHg (Classes I and II) were adopted in the developed FE-FSI model. The soft tissue was assumed as a Neo-Hookean hyperelastic model with the fixed bones, and the ECSs were regarded as an orthotropic elastic shell. The interfacial pressure and stress transmission were simulated by the FE model, and venous hemodynamics properties were simulated by the FSI model. The experimental validation indicated that the simulated interfacial pressure distributions were in accordance with the pressure measurement results. The developed model can be used to predict interfacial pressure, stress transmission, and venous hemodynamics exerted by ECSs and optimize the structure and materials properties of ECSs design, thus improving the efficiency of compression therapy.

Keywords: Elastic compression stockings, fluid-solid interaction, tissue and vein properties, prediction.

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Authors: M. M. Rahman

Abstract:

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: Otávio J.U. Flores, Fernando A. Andrade, Dachamir Hotza, Hazim A. Al-Qureshi

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In the forming of ceramic materials the plasticity concept is commonly used. This term is related to a particular mechanical behavior when clay is mixed with water. A plastic ceramic material shows a permanent strain without rupture when a compressive load produces a shear stress that exceeds the material-s yield strength. For a plastic ceramic body it observes a measurable elastic behavior before the yield strength and when the applied load is removed. In this work, a mathematical model was developed from applied concepts of the plasticity theory by using the stress/strain diagram under compression.

Keywords: Plasticity, clay, modeling, coefficient of friction.

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Authors: Wagdi S. Soliman, Shu-ichi Sugiyama

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The C3 plants are frequently suffering from exposure to high temperature stress which limits the growth and yield of these plants. This study seeks to clarify the physiological mechanisms of heat tolerance in relation to oxidative stress in C3 species. Fifteen C3 species were exposed to prolonged moderately high temperature stress 36/30°C for 40 days in a growth chamber. Chlorophyll fluorescence (Fv/Fm) showed great difference among species at 40 days of the stress. The species showed decreases in Fv/Fm and increases in malondialdehyde (MDA) content under stress condition as well as negative correlation between Fv/Fm and MDA (r = -0.61*) at 40 days of the stress. Hydrogen peroxide (H2O2) content before and after stress in addition to its response under stress showed great differences among species. The results suggest that the difference in heat tolerance among C3 species is closely associated with the ability to suppress oxidative damage but not with the content of reactive oxygen species (ROS) which is regulated by complex network.

Keywords: C3 species, Fv/Fm, heat stress, oxidative stress.

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Authors: B. Saha Roy, T. Medhi, S. C. Saha

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To understand the friction stir welding process, it is very important to know the nature of the material flow in and around the tool. The process is a combination of both thermal as well as mechanical work i.e. it is a coupled thermo-mechanical process. Numerical simulations are very much essential in order to obtain a complete knowledge of the process as well as the physics underlying it. In the present work a model based approach is adopted in order to study material flow. A thermo-mechanical based CFD model is developed using a Finite Element package, Comsol Multiphysics. The fluid flow analysis is done. The model simultaneously predicts shear strain fields, shear strain rates and shear stress over the entire workpiece for the given conditions. The flow fields generated by the streamline plot give an idea of the material flow. The variation of dynamic viscosity, velocity field and shear strain fields with various welding parameters is studied. Finally the result obtained from the above mentioned conditions is discussed elaborately and concluded.

Keywords: AA6061-T6, friction stir welding, material flow, CFD modelling.

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Authors: Diriba T. Balcha, Boris Kulig, Oliver Hensel, Eyassu Woldesenbet

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Enset fiber is agricultural waste and available in a surplus amount in Ethiopia. However, the hypothesized variation in properties of this fiber due to diversity of its plant source breed, fiber position within plant stem and chemical treatment duration had not proven that its application for the development of composite products is problematic. Currently, limited data are known on the functional properties of the fiber as a potential functional fiber. Thus, an effort is made in this study to narrow the knowledge gaps by characterizing it. The experimental design was conducted using Design-Expert software and the tensile test was conducted on Enset fiber from 10 breeds: Dego, Dirbo, Gishera, Itine, Siskela, Neciho, Yesherkinke, Tuzuma, Ankogena, and Kucharkia. The effects of 5% Na-OH surface treatment duration and fiber location along and across the plant pseudostem was also investigated. The test result shows that the rupture stress variation is not significant among the fibers from 10 Enset breeds. However, strain variation is significant among the fibers from 10 Enset breeds that breed Dego fiber has the highest strain before failure. Surface treated fibers showed improved rupture strength and elastic modulus per 24 hours of treatment duration. Also, the result showed that chemical treatment can deteriorate the load-bearing capacity of the fiber. The raw fiber has the higher load-bearing capacity than the treated fiber. And, it was noted that both the rupture stress and strain increase in the top to bottom gradient, whereas there is no significant variation across the stem. Elastic modulus variation both along and across the stem was insignificant. The rupture stress, elastic modulus, and strain result of Enset fiber are 360.11 ± 181.86 MPa, 12.80 ± 6.85 GPa and 0.04 ± 0.02 mm/mm, respectively. These results show that Enset fiber is comparable to other natural fibers such as abaca, banana, and sisal fibers and can be used as alternatives natural fiber for composites application. Besides, the insignificant variation of properties among breeds and across stem is essential for all breeds and all leaf sheath of the Enset fiber plant for fiber extraction. The use of short natural fiber over the long is preferable to reduce the significant variation of properties along the stem or fiber direction. In conclusion, Enset fiber application for composite product design and development is mechanically feasible.

Keywords: Agricultural waste, chemical treatment, fiber characteristics, natural fiber.

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Authors: Georgios C. Dogiamis, Bedrich J. Hosticka, Anton Grabmaier

Abstract:

In this work the effects of uniaxial mechanical stress on a pixel readout circuit are theoretically analyzed. It is the effects of mechanical stress on the in-pixel transistors do not arise at the output, when a correlated double sampling circuit is used. However, mechanical stress effects on the photodiode will directly appear at the readout chain output. Therefore, compensation techniques are needed to overcome this situation. Moreover simulation technique of mechanical stress is proposed and diverse layout as well as design recommendations are put forward, in order to minimize stress related effects on the output of a circuit. he shown, that wever, Moreover, a out

Keywords: mechanical uniaxial stress, pixel readout circuit

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Authors: Mohamed Yousef, Magdy Samuel, Maha El-Meligy, Taher El-Bitar

Abstract:

The present work is dealing with 2% Si-steel alloy. The alloy contains 0.05% C as well as 0.85% Al. The alloy under investigation would be used for electrical transformation purposes. A heating (expansion) - cooling (contraction) dilation investigation was executed to detect the a, a+g, and g transformation temperatures at the inflection points of the dilation curve. On heating, primary a  was detected at a temperature range between room temperature and 687 ^oC. The domain of a+g was detected in the range between 687 ^oC and 746 ^oC. g phase exists in the closed g region at the range between 746 ^oC and 1043 ^oC. The domain of a phase appears again at a temperature range between 1043 and 1105 ^oC, and followed by secondary a at temperature higher than 1105 ^oC. A physical simulation of thermo-mechanical processing on the as-cast alloy was carried out. The simulation process took into consideration the hot flat rolling pilot plant parameters. The process was executed on the thermo-mechanical simulator (Gleeble 3500). The process was designed to include seven consecutive passes. The 1^st pass represents the roughing stage, while the remaining six passes represent finish rolling stage. The whole process was executed at the temperature range from 1100 ^oC to 900 ^oC. The amount of strain starts with 23.5% at the roughing pass and decreases continuously to reach 7.5 % at the last finishing pass. The flow curve of the alloy can be abstracted from the stress-strain curves representing simulated passes. It shows alloy hardening from a pass to the other up to pass no. 6, as a result of decreasing the deformation temperature and increasing of cumulative strain. After pass no. 6, the deformation process enhances the dynamic recrystallization phenomena to appear, where the z-parameter would be high.

Keywords: Si-steel, hot deformability, critical transformation temperature, physical simulation, thermo-mechanical processing, flow curve, dynamic softening.

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

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Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle based method, hyper-elasticity, analysis of stability.

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

Abstract:

Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model.

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