Search results for: proprieties elastic

Authors: Bummo Ahn

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Palpation is widely used to measure soft tissue firmness or stiffness in the living condition in order to apply detection, diagnosis, and treatment of tumors, scar tissue, abnormal muscle tone, or muscle spasticity. Since these methods are subjective and depend on the proficiency level, it is concluded that there are other diagnoses depending on the condition of the experts and the results are not objective. The mechanical property obtained by using the elasticity of the tissue is important to calculate a predictive variable for monitoring abnormal tissues. If the mechanical load such as reaction force on the foot increases in the same region under the same conditions, the mechanical property of the tissue is changed. Therefore, objective diagnosis is possible not only for experts but also for patients using this quantitative information. Furthermore, the portable system also allows non-experts to easily diagnose at home, not in hospitals or institutions. In this paper, we introduce a portable palpation system that can be used to measure the mechanical properties of human tissue, which can be applied to monitor diabetic foot ulceration patients with measuring the mechanical property change of foot tissue. The system was designed to be smaller and portable in comparison with the conventional palpation systems. It is consists of the probe, the force sensor, linear actuator, micro control unit, the display module, battery, and housing. Using this system, we performed validation experiments by applying different palpations (3 and 5 mm) to soft tissue (silicone rubber) and measured reaction forces. In addition, we estimated the elastic moduli of the soft tissue against different palpations and compare the estimated elastic moduli that show similar value even if the palpation depths are different.

Keywords: palpation probe, portable, diabetic foot ulceration, monitoring, mechanical property

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Authors: Tai Yuan Yu, Pei-Jen Wang

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A simulation scheme of rotational motions for predictions of bump-type gas foil bearings operating at steady-state is proposed; and, the scheme is based on multi-physics coupling computer aided engineering packages modularized with computational fluid dynamic model and structure elasticity model to numerically solve the dynamic equation of motions of a hydrodynamic loaded shaft supported by an elastic bump foil. The bump foil is assumed to be modelled as infinite number of Hookean springs mounted on stiff wall. Hence, the top foil stiffness is constant on the periphery of the bearing housing. The hydrodynamic pressure generated by the air film lubrication transfers to the top foil and induces elastic deformation needed to be solved by a finite element method program, whereas the pressure profile applied on the top foil must be solved by a finite element method program based on Reynolds Equation in lubrication theory. As a result, the equation of motions for the bearing shaft are iteratively solved via coupling of the two finite element method programs simultaneously. In conclusion, the two-dimensional center trajectory of the shaft plus the deformation map on top foil at constant rotational speed are calculated for comparisons with the experimental results.

Keywords: computational fluid dynamics, fluid structure interaction multi-physics simulations, gas foil bearing, load capacity

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Authors: Bernd Engel, Sara Salman Hassan Al-Maeeni

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A substantial amount of natural resources are nowadays consumed at a growing rate, as humans all over the world used materials obtained from the Earth. Machinery manufacturing industry is one of the major resource consumers on a global scale. Even though the incessant finding out of the new material, metals, and resources, it is urgent for the industry to develop methods to use the Earth's resources intelligently and more sustainable than before. Re-engineering of machine tools regarding design and failure analysis is an approach whereby out-of-date machines are upgraded and returned to useful life. To ensure the reliable future performance of the used machine components, it is essential to investigate the machine component failure through the material, design, and surface examinations. This paper presents an experimental approach aimed at inspecting the shaft of the rotary draw bending machine as a case to study. The testing methodology, which is based on the principle of the three-point bending test, allows assessing the shaft elastic behavior under loading. Furthermore, the shaft elastic characteristics include the maximum linear deflection, and maximum bending stress was determined by using an analytical approach and finite element (FE) analysis approach. In the end, the results were compared with the ones obtained by the experimental approach. In conclusion, it is seen that the measured bending deflection and bending stress were well close to the permissible design value. Therefore, the shaft can work in the second life cycle. However, based on previous surface tests conducted, the shaft needs surface treatments include re-carburizing and refining processes to ensure the reliable surface performance.

Keywords: deflection, FE analysis, shaft, stress, three-point bending

Procedia PDF Downloads 133

Authors: Dicko Ali Hamadi, Tong-Yette Nicolas, Gilles Benjamin, Faure Francois, Palombi Olivier

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A novel hybrid model of the lumbar spine, allowing fast static and dynamic simulations of the disc pressure and the spine mobility, is introduced in this work. Our contribution is to combine rigid bodies, deformable finite elements, articular constraints, and springs into a unique model of the spine. Each vertebra is represented by a rigid body controlling a surface mesh to model contacts on the facet joints and the spinous process. The discs are modeled using a heterogeneous tetrahedral finite element model. The facet joints are represented as elastic joints with six degrees of freedom, while the ligaments are modeled using non-linear one-dimensional elastic elements. The challenge we tackle is to make these different models efficiently interact while respecting the principles of Anatomy and Mechanics. The mobility, the intradiscal pressure, the facet joint force and the instantaneous center of rotation of the lumbar spine are validated against the experimental and theoretical results of the literature on flexion, extension, lateral bending as well as axial rotation. Our hybrid model greatly simplifies the modeling task and dramatically accelerates the simulation of pressure within the discs, as well as the evaluation of the range of motion and the instantaneous centers of rotation, without penalizing precision. These results suggest that for some types of biomechanical simulations, simplified models allow far easier modeling and faster simulations compared to usual full-FEM approaches without any loss of accuracy.

Keywords: hybrid, modeling, fast simulation, lumbar spine

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Authors: Fatemeh Abbasi, Arne Hofemeier, Timo Betz

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Muscle growth and regeneration critically depend on satellite cells (SCs) which are muscle stem cells located between the basal lamina and myofibres. Upon damage, SCs become activated, enter the cell cycle, and give rise to myoblasts that form new myofibres, while a sub-population self-renew and re-populate the muscle stem cell niche. In aged muscle as well as in certain muscle diseases such as muscular dystrophy, some of the SCs lose their regenerative ability. Although it is demonstrated that the chemical composition of SCs quiescent niche is different from the activated niche, the mechanism initially activated in the SCs remains unknown. While extensive research efforts focused on potential chemical activation, no such factor has been identified to the author’s best knowledge. However, it is substantiated that niche mechanics affects SCs behaviors, such as stemness and engraftment. We hypothesize that mechanical stress in the healthy niche (homeostasis) is different from the regenerative niche and that this difference could serve as an early signal activating SCs upon fiber damage. To investigate this hypothesis, we develop a biomimetic system to reconstitute both, the mechanical and the chemical environment of the SC niche. Cells will be confined between two elastic polyacrylamide (PAA) hydrogels with controlled elastic moduli and functionalized surface chemistry. By controlling the distance between the PAA hydrogel surfaces, we vary the compression forces exerted by the substrates on the cells, while the lateral displacement of the upper hydrogel will create controlled shear forces. To establish such a system, a simplified system is presented. We engineered a sandwich-like configuration of two elastic PAA layer with stiffnesses between 1 and 10 kPa and confined a precursor myoblast cell line (C2C12) in between these layers. Our initial observations in this sandwich model indicate that C2C12 cells show different behaviors under mechanical compression if compared to a control one-layer gel without compression. Interestingly, this behavior is stiffness-dependent. While the shape of C2C12 cells in the sandwich consisting of two stiff (10 kPa) layers was much more elongated, showing almost a neuronal phenotype, the cell shape in a sandwich situation consisting of one stiff and one soft (1 kPa) layer was more spherical. Surprisingly, even in proliferation medium and at very low cell density, the sandwich situation stimulated cell differentiation with increased striation and myofibre formation. Such behavior is commonly found for confluent cells in differentiation medium. These results suggest that mechanical changes in stiffness and applied pressure might be a relevant stimulation for changes in muscle cell behavior.

Keywords: C2C12 cells, compression, force, satellite cells, skeletal muscle

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Authors: Rishab Das, Arnab Banerjee, Bappaditya Manna

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Mono-pile foundations are often used in soft soils in order to support heavy mega-structures, whereby often these deep footings may undergo dynamic excitation due to many causes like earthquake, wind or wave loads acting on the superstructure, blasting, and unbalanced machines, etc. A comprehensive analytical study is performed to study the dynamics of the mono-pile system embedded in cohesion-less soil. The soil is considered homogeneous and visco-elastic in nature and is analytically modeled using complex springs. Considering the N number of the elements of the pile, the final global stiffness matrix is obtained by using the theories of the spectral element matrix method. Further, statically condensing the intermediate internal nodes of the global stiffness matrix results to a smaller sub matrix containing the nodes experiencing the external translation and rotation, and the stiffness and damping functions (impedance functions) of the embedded piles are determined. Proper plots showing the variation of the real and imaginary parts of these impedance functions with the dimensionless frequency parameter are obtained. The plots obtained from this study are validated by that provided by Novak,1974. Further, the dynamic analysis of the resonator impregnated pile is proposed within this study. Moreover, with the aid of Wood's 1g laboratory scaling law, a proper scaled-down resonator-pile model is 3D printed using PLA material. Dynamic analysis of the scaled model is carried out in the time domain, whereby the lateral loads are imposed on the pile head. The response obtained from the sensors through the LabView software is compared with the proposed theoretical data.

Keywords: mono-pile, visco-elastic, impedance, LabView

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Authors: Houda Haddad, Radhia Mejri, , Alyne Rodrigues de Araujo, Amira Zairi

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Nosocomial infections represent one of the biggest health problems nowadays. Acinetobacter baumannii is known as an opportunistic pathogen in humans, affecting people with compromised immune systems, and is becoming increasingly important as a hospital-derived infection. It is known that in recent years, more and more bacteria have become multidrug-resistant (MDR), and for this reason, the development of new drugs is a priority. However, these products must not affect the human body, and therefore, cytotoxicity studies are mandatory. In this context, antimicrobial peptides with potential antibacterial proprieties could be an alternative. In this research, we describe the synthesis and the bioactivity of dermaseptins and their derivatives against Acinetobacter baumannii. The cytotoxicity of these dermaseptins was investigated on the HEp-2 cell line by the MTT cell viability assay. Thereafter, we studied morphological alterations caused by the action of one of the active peptides on the bacterial membrane using atomic force microscopy (AFM). The cytotoxicity of dermaseptins was concentration-dependent at microgram concentrations. It was observed that all tested analogs exhibit antibacterial activity with Minimum Inhibitory Concentrations (MICs) ranging from 3.125 to 12.5 μg/mL and Minimum Bactericidal Concentrations (MBCs) ranging from 6.25 to 25 μg/mL. Microscopic images obtained by AFM revealed morphological changes on the surface of treated bacteria caused by K4S4(1-16), as well as significant surface alterations. Overall, these findings demonstrate that dermaseptins might constitute new lead structures for the development of potent antibacterial agents against Acinetobacter baumannii infections.

Keywords: dermaseptin B2, dermaseptin S4, analogs, Acinetobacter baumannii, healthcare-associated infections, antibacterial activity

Procedia PDF Downloads 35

Authors: S. M. Abdul Khader, Anurag Ayachit, Raghuvir Pai, K. A. Ahmed, V. R. K Rao, S. Ganesh Kamath

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The numerical simulation has made tremendous advances in investigating the blood flow phenomenon through elastic arteries. Such study can be useful in demonstrating the disease progression and haemodynamics of cardiovascular diseases such as atherosclerosis. In the present study, patient specific case diagnosed with partially stenosed complete right ICA and normal left carotid bifurcation without any atherosclerotic plaque formation is considered. 3D patient specific carotid bifurcation model is generated based on CT scan data using MIMICS-4.0 and numerical analysis is performed using FSI solver in ANSYS-14.5. The blood flow is assumed to be incompressible, homogenous and Newtonian, while the artery wall is assumed to be linearly elastic. The two-way sequentially-coupled transient FSI analysis is performed using FSI solver for three pulse cycles. The haemodynamic parameters such as flow pattern, Wall Shear Stress, pressure contours and arterial wall deformation are studied at the bifurcation and critical zones such as stenosis. The variation in flow behavior is studied throughout the pulse cycle. Also, the simulation results reveals that there is a considerable increase in the flow behavior in stenosed carotid in contrast to the normal carotid bifurcation system. The investigation also demonstrates the disturbed flow pattern especially at the bifurcation and stenosed zone elevating the haemodynamics, particularly during peak systole and later part of the pulse cycle. The results obtained agree well with the clinical observation and demonstrates the potential of patient specific numerical studies in prognosis of disease progression and plaque rupture.

Keywords: fluid-structure interaction, arterial stenosis, wall shear stress, carotid artery bifurcation

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Authors: Francisco Velez, Juan David Gomez

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Dispersion effects on the Scattering for a semicircular canyon in a micropolar continuum are analyzed, by using a computational finite element scheme. The presence of microrotational waves and the dispersive SV waves affects the propagation of elastic waves. Here, a contrast with the classic model is presented, and the dependence with the micropolar parameters is studied.

Keywords: scattering, semicircular canyon, wave dispersion, micropolar medium, FEM modeling

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Authors: Puneet Kumar, Jonnalagadda Srinivas

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The authors report here vibration and buckling analysis of functionally graded carbon nanotube-polymer composite (FG-CNTPC) beams under hygro-thermo-mechanical environments using higher order shear deformation theory. The material properties of CNT and polymer matrix are often affected by temperature and moisture content. A micromechanical model with agglomeration effect is employed to compute the elastic, thermal and moisture properties of the composite beam. The governing differential equation of FG-CNTRPC beam is developed using higher-order shear deformation theory to account shear deformation effects. The elastic, thermal and hygroscopic strain terms are derived from variational principles. Moreover, thermal and hygroscopic loads are determined by considering uniform, linear and sinusoidal variation of temperature and moisture content through the thickness. Differential equations of motion are formulated as an eigenvalue problem using appropriate displacement fields and solved by using finite element modeling. The obtained results of natural frequencies and critical buckling loads show a good agreement with published data. The numerical illustrations elaborate the dynamic as well as buckling behavior under uniaxial load for different environmental conditions, boundary conditions and volume fraction distribution profile, beam slenderness ratio. Further, comparisons are shown at different boundary conditions, temperatures, degree of moisture content, volume fraction as well as agglomeration of CNTs, slenderness ratio of beam for different shear deformation theories.

Keywords: hygrothermal effect, free vibration, buckling load, agglomeration

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Authors: Gautier Girard, Marion Martiny, Sebastien Mercier, Mohamad Jrad, Mohamed-Slim Bahi, Laurent Bodin, Francois Lechleiter, David Nevo, Sophie Dareys

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Reliability of electronic devices has always been of highest interest for Aero-MIL and space applications. In any electronic device, Printed Circuit Board (PCB), providing interconnection between components, is a key for reliability. During the last decades, PCB technologies evolved to sustain and/or fulfill increased original equipment manufacturers requirements and specifications, higher densities and better performances, faster time to market and longer lifetime, newer material and mixed buildups. From the very beginning of the PCB industry up to recently, qualification, experiments and trials, and errors were the most popular methods to assess system (PCB) reliability. Nowadays OEM, PCB manufacturers and scientists are working together in a close relationship in order to develop predictive models for PCB reliability and lifetime. To achieve that goal, it is fundamental to characterize precisely base materials (laminates, electrolytic copper, …), in order to understand failure mechanisms and simulate PCB aging under environmental constraints by means of finite element method for example. The laminates are woven composites and have thus an orthotropic behaviour. The in-plane properties can be measured by combining classical uniaxial testing and digital image correlation. Nevertheless, the out-of-plane properties cannot be evaluated due to the thickness of the laminate (a few hundred of microns). It has to be noted that the knowledge of the out-of-plane properties is fundamental to investigate the lifetime of high density printed circuit boards. A homogenization method combining analytical and numerical approaches has been developed in order to obtain the complete elastic orthotropic behaviour of a woven composite from its precise 3D internal structure and its experimentally measured in-plane elastic properties. Since the mechanical properties of the resin surrounding the fibres are unknown, an inverse method is proposed to estimate it. The methodology has been applied to one laminate used in hyperfrequency spatial applications in order to get its elastic orthotropic behaviour at different temperatures in the range [-55°C; +125°C]. Next; numerical simulations of a plated through hole in a double sided PCB are performed. Results show the major importance of the out-of-plane properties and the temperature dependency of these properties on the lifetime of a printed circuit board. Acknowledgements—The support of the French ANR agency through the Labcom program ANR-14-LAB7-0003-01, support of CNES, Thales Alenia Space and Cimulec is acknowledged.

Keywords: homogenization, orthotropic behaviour, printed circuit board, woven composites

Procedia PDF Downloads 180

Authors: B. Niez, B. Moulia, J. Dlouha, E. Badel

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Trees adjust their development to the environmental conditions they experience. Storms events of last decades showed that acclimation of trees to mechanical stresses due to wind is a very important process that allows the trees to sustain for long years. In the future, trees will experience new wind patterns, namely, more often strong winds and fewer daily moderate winds. Moreover, these patterns will go along with drought periods that may interact with the capacity of trees to adjust their growth to mechanical stresses due to wind. It is necessary to understand the mechanisms of wood functional acclimations to environmental conditions in order to predict their behaviour and in order to give foresters and breeders the relevant tools to adapt their forest management. This work aims to study how trees adjust the mechanical and hydraulic functions of their wood to environmental stresses and how this acclimation may be beneficial for the tree to resist to future stresses. In this work, young poplars were grown under controlled climatic conditions that include permanent environmental stress (daily mechanical stress of the stem by bending and/or hydric stress). Then, the properties of wood formed under these stressed conditions were characterized. First, hydraulic conductivity and sensibility to cavitation were measured at the tissue level in order to evaluate the changes in water transport capacity. Secondly, bending tests and Charpy impact tests were carried out at the millimetric scale to locally measure mechanical parameters such as elastic modulus, elastic limit or rupture energy. These experimental data allow evaluating the impacts of mechanical and water stress on the wood material. At the stem level, they will be merged in an integrative model in order to evaluate the beneficial aspect of wood acclimation for trees.

Keywords: acclimation, environmental stresses, hydraulics, mechanics, wood

Procedia PDF Downloads 185

Authors: K. Jankowski, M. Pawlikowski, A. Makuch, K. Skalski

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Depth-sensing indentation (DSI) or nanoindentation is becoming a more and more popular method of measuring mechanical properties of various materials and tissues at a micro-scale. This technique allows measurements without complicated sample preparation procedures which makes this method very useful. As a result of measurement force and displacement of the intender are obtained. It is also possible to determine three measures of hardness i.e. Martens hardness (HM), nanohardness (HIT), Vickers hardness (HV) and Young modulus EIT. In this work trabecular bone mechanical properties were investigated. The bone samples were harvested from human femoral heads during hip replacement surgery. Patients were of different age, sexes and stages of tissue degeneration caused by osteoarthritis. The specimens were divided into three groups. Each group contained samples harvested from patients of different range of age. All samples were investigated with the same measurement conditions. The maximum load was Pmax=500 mN and the loading rate was 500 mN/min. The tests were held without hold at the peak force. The tests were conducted with indenter Vickers tip and spherical tip of the diameter 0.2 mm. Each trabecular bone sample was tested 7 times in a close area of the same trabecula. The measured loading P as a function of indentation depth allowed to obtain hysteresis loop and HM, HIT, HV, EIT. Results for arbitrarily chosen sample are HM=289.95 ± 42.31 MPa, HIT=430.75 ± 45.37 MPa, HV=40.66 ± 4.28 Vickers, EIT=7.37 ± 1.84 GPa for Vickers tip and HM=115.19 ± 15.03 MPa, HIT=165.80 ± 19.30 MPa, HV=16.90 ± 1.97 Vickers, EIT=5.30 ± 1.31 GPa for spherical tip. Results of nanoindentation tests show that this method is very useful and is perfect for obtaining mechanical properties of trabecular bone. Estimated values of elastic modulus are similar. The differences between hardness are significant but it is a result of using two different types of tips. However, it has to be emphasised that the differences in the values of elastic modulus and hardness result from different testing protocols, anisotropy and asymmetry of the micro-samples and the hydration of bone.

Keywords: human bone, mechanical properties, nano hardness nanoindentation, trabecular bone

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Authors: Iyd Eqqab Maree, Habil Jurgen Bast

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Vibration control of machines and structures incorporating viscoelastic materials in suitable arrangement is an important aspect of investigation. The use of viscoelastic layers constrained between elastic layers is known to be effective for damping of flexural vibrations of structures over a wide range of frequencies. The energy dissipated in these arrangements is due to shear deformation in the viscoelastic layers, which occurs due to flexural vibration of the structures. Multilayered cantilever sandwich beam like structures can be used in aircrafts and other applications such as robot arms for effective vibration control. These members may experience parametric instability when subjected to time dependant forces. The theory of dynamic stability of elastic systems deals with the study of vibrations induced by pulsating loads that are parametric with respect to certain forms of deformation. The purpose of the present work is to investigate the dynamic stability of a three layered symmetric sandwich beam (Drone Aircraft wings ) subjected to an end periodic axial force . Equations of motion are derived using finite element method (MATLAB software). It is observed that with increase in core thickness parameter fundamental buckling load increases. The fundamental resonant frequency and second mode frequency parameter also increase with increase in core thickness parameter. Fundamental loss factor and second mode loss factor also increase with increase in core thickness parameter. Increase in core thickness parameter enhances the stability of the beam. With increase in core loss factor also the stability of the beam enhances. There is a very good agreement of the experimental results with the theoretical findings.

Keywords: steel cantilever beam, viscoelastic material core, loss factor, transition region, MATLAB R2011a

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Authors: E. N. Masri, E. Takács

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Amplitude Versus Offset (AVO) and simultaneous model-based impedance inversion techniques have not been utilized for geothermal exploration commonly; however, some recent publications called the attention that they can be very useful in the geothermal investigations. In this study, we present rock physical attributes obtained from 3D pre-stack seismic data and well logs collected in a study area of the NW part of Pannonian Basin where the geothermal reservoir is located in the fractured zones of Triassic basement and it was hit by three productive-injection well pairs. The holes were planned very successfully based on the conventional 3D migrated stack volume prior to this study. Subsequently, the available geophysical-geological datasets provided a great opportunity to test modern inversion procedures in the same area. In this presentation, we provide a summary of the theory and application of the most promising seismic inversion techniques from the viewpoint of geothermal exploration. We demonstrate P- and S-wave impedance, as well as the velocity (Vp and Vs), the density, and the Vp/Vs ratio attribute volumes calculated from the seismic and well-logging data sets. After a detailed discussion, we conclude that P-wave impedance and Vp/Vp ratio are the most helpful parameters for lithology discrimination in the study area. They detect the hot water saturated fracture zone very well thus they can be very useful in mapping the investigated reservoir. Integrated interpretation of all the obtained rock-physical parameters is essential. We are extending the above discussed pre-stack seismic tools by studying the possibilities of Elastic Impedance Inversion (EII) for geothermal exploration. That procedure provides two other useful rock-physical properties, the compressibility and the rigidity (Lamé parameters). Results of those newly created elastic parameters will also be demonstrated in the presentation. Geothermal extraction is of great interest nowadays; and we can adopt several methods have been successfully applied in the hydrocarbon exploration for decades to discover new reservoirs and reduce drilling risk and cost.

Keywords: fractured zone, seismic, well-logging, inversion

Procedia PDF Downloads 106

Authors: Sandrine Cardinal, Jean-Marc Pelletier, Guang Xie, Florian Mercier, Florent Delmas

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Bulk metallic glasses exhibit several superior properties, compared to their corresponding crystalline counterpart, such as high strength, high elastic limit or good corrosion resistance. Therefore they can be considered as good candidates for structural applications in many sectors. However, they are generally brittle and do not exhibit plastic deformation at room temperature. These materials are mainly obtained by rapid cooling from a liquid state to prevent crystallization, which limits their size. To overcome these two drawbacks: fragility and limited dimensions, composite metallic glass matrix reinforced by a second phase whose role is to slow crack growth are developed. Concerning the limited size of the pieces, the proposed solution is to get the material from amorphous powders by densifying under load. In this study, Cu50Zr45Al5 bulk metallic glassy matrix composites (MGMCs) containing different volume fraction (Vf) of Zr crystalline particles were manufactured by spark plasma sintering (SPS). Microstructure, thermal stability and mechanical properties of the MGMCs were investigated. Matrix of the composites remains a fully amorphous phase after consolidation at 420°C under 600 MPa. A good dispersion of the particles in the glassy matrix is obtained. Results show that the compressive strength decreases with Vf : 1670 MPa (Vf=0%) to 1300MPa (Vf=30%), the elastic modulus decreases but only slighty respectively 97.3GPa and 94.5 GPa and plasticity is improved from 0 to 4%. Fractographic investigation indicates a good bonding between amorphous and crystalline particles. In conclusion, present study has demonstrated that SPS method is useful for the synthesis of the bulk glassy composites. Large controlled microstructure specimens with interesting ductility can be obtained compared with others methods.

Keywords: composite, mechanical properties, metallic glasses, spark plasma sintering

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Authors: K. Sridhar Reddy, M. Amaranatha Reddy, Nilanjan Mitra

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Short paneled concrete pavement (SPCP) with shorter panel size can be an alternative to the conventional jointed plain concrete pavements (JPCP) at the same cost as the asphalt pavements with all the advantages of concrete pavement with reduced thickness, less chance of mid-slab cracking and or dowel bar locking so common in JPCP. Cast-in-situ short concrete panels (short slabs) laid on a strong foundation consisting of a dry lean concrete base (DLC), and cement treated subbase (CTSB) will reduce the thickness of the concrete slab to the order of 180 mm to 220 mm, whereas JPCP was with 280 mm for the same traffic. During the construction of SPCP test sections on two Indian National Highways (NH), it was observed that the joints remain uncracked after a year of traffic. The undoweled and uncracked joints load transfer variability and joint behavior are of interest with anticipation on its long-term performance of the SPCP. To investigate the effects of undoweled and uncracked joints on short slabs, the present study was conducted. A multilayer linear elastic analysis using 3D finite element package for different panel sizes with different thicknesses resting on different types of solid elastic foundation with and without temperature gradient was developed. Surface deflections were obtained from 3D FE model and validated with measured field deflections from falling weight deflectometer (FWD) test. Stress analysis indicates that flexural stresses in short slabs are decreased with a decrease in panel size and increase in thickness. Detailed evaluation of stress analysis with the effects of curling behavior, the stiffness of the base layer and a variable degree of load transfer, is underway.

Keywords: joint behavior, short slabs, uncracked joints, undoweled joints, 3D numerical simulation

Procedia PDF Downloads 158

Authors: Bahatti̇n Ki̇mençe, Uğur Ki̇mençe

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In this study, the purpose of obtaining the influence functions of the displacement discontinuity in an anisotropic elastic medium is to produce the boundary element equations. A Displacement Discontinuous Method formulation (DDM) is presented with the aim of modeling two-dimensional elastic fracture problems. This formulation is found by analytical integration of the fundamental solution along a straight-line crack. With this purpose, Kelvin's fundamental solutions for anisotropic media on an infinite plane are used to form dipoles from singular loads, and the various combinations of the said dipoles are used to obtain the influence functions of displacement discontinuity. This study introduces a technique for coupling Fictitious Stress Method (FSM) and DDM; the reason for applying this technique to some examples is to demonstrate the effectiveness of the proposed coupling method. In this study, displacement discontinuity equations are obtained by using dipole solutions calculated with known singular force solutions in an anisotropic medium. The displacement discontinuities method obtained from the solutions of these equations and the fictitious stress methods is combined and compared with various examples. In this study, one or more crack problems with various geometries in rectangular plates in finite and infinite regions, under the effect of tensile stress with coupled FSM and DDM in the anisotropic environment, were examined, and the effectiveness of the coupled method was demonstrated. Since crack problems can be modeled more easily with DDM, it has been observed that the use of DDM has increased recently. In obtaining the displacement discontinuity equations, Papkovitch functions were used in Crouch, and harmonic functions were chosen to satisfy various boundary conditions. A comparison is made between two indirect boundary element formulations, DDM, and an extension of FSM, for solving problems involving cracks. Several numerical examples are presented, and the outcomes are contrasted to existing analytical or reference outs.

Keywords: displacement discontinuity method, fictitious stress method, crack problems, anisotropic material

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Authors: Vanessa A. Segovia, Sonia E. Ruiz

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The use of energy dissipation systems for seismic applications has increased worldwide, thus it is necessary to develop practical and modern criteria for their optimal design. Here, a direct displacement-based seismic design approach for frame buildings with hysteretic energy dissipation systems (HEDS) is applied. The building is constituted by two individual structural systems consisting of: 1) A main elastic structural frame designed for service loads and 2) A secondary system, corresponding to the HEDS, that controls the effects of lateral loads. The procedure implies to control two design parameters: A) The stiffness ratio (α=K_frame/K_(total system)), and B) The strength ratio (γ= V_damper / V_(total system)). The proposed damage-controlled approach contributes to the design of a more sustainable and resilient building because the structural damage is concentrated on the HEDS. The reduction of the design displacement spectrum is done by means of a damping factor (recently published) for elastic structural systems with HEDS, located in Mexico City. Two limit states are verified: Serviceability and near collapse. Instead of the traditional trial-error approach, a procedure that allows the designer to establish the preliminary sizes of the structural elements of both systems is proposed. The design methodology is applied to an 8-story steel building with buckling restrained braces, located in soft soil of Mexico City. With the aim of choosing the optimal design parameters, a parametric study is developed considering different values of α and γ. The simplified methodology is for preliminary sizing, design, and evaluation of the effectiveness of HEDS, and it constitutes a modern and practical tool that enables the structural designer to select the best design parameters.

Keywords: damage-controlled buildings, direct displacement-based seismic design, optimal hysteretic energy dissipation systems, hysteretic dampers

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Authors: Anna Makuch, Grzegorz Kokot, Konstanty Skalski, Jakub Banczorowski

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Cancellous bone is a porous composite of a hierarchical structure and anisotropic properties. The biological tissue is considered to be a viscoelastic material, but many studies based on a nanoindentation method have focused on their elasticity and microhardness. However, the response of many organic materials depends not only on the load magnitude, but also on its duration and time course. Depth Sensing Indentation (DSI) technique has been used for examination of creep in polymers, metals and composites. In the indentation tests on biological samples, the mechanical properties are most frequently determined for animal tissues (of an ox, a monkey, a pig, a rat, a mouse, a bovine). However, there are rare reports of studies of the bone viscoelastic properties on microstructural level. Various rheological models were used to describe the viscoelastic behaviours of bone, identified in the indentation process (e. g Burgers model, linear model, two-dashpot Kelvin model, Maxwell-Voigt model). The goal of the study was to determine the influence of creep effect on the mechanical properties of human cancellous bone in indentation tests. The aim of this research was also the assessment of the material properties of bone structures, having in mind the energy aspects of the curve (penetrator loading-depth) obtained in the loading/unloading cycle. There was considered how the different holding times affected the results within trabecular bone.As a result, indentation creep (CIT), hardness (HM, HIT, HV) and elasticity are obtained. Human trabecular bone samples (n=21; mean age 63±15yrs) from the femoral heads replaced during hip alloplasty were removed and drained from alcohol of 1h before the experiment. The indentation process was conducted using CSM Microhardness Tester equipped with Vickers indenter. Each sample was indented 35 times (7 times for 5 different hold times: t1=0.1s, t2=1s, t3=10s, t4=100s and t5=1000s). The indenter was advanced at a rate of 10mN/s to 500mN. There was used Oliver-Pharr method in calculation process. The increase of hold time is associated with the decrease of hardness parameters (HIT(t1)=418±34 MPa, HIT(t2)=390±50 MPa, HIT(t3)= 313±54 MPa, HIT(t4)=305±54 MPa, HIT(t5)=276±90 MPa) and elasticity (EIT(t1)=7.7±1.2 GPa, EIT(t2)=8.0±1.5 GPa, EIT(t3)=7.0±0.9 GPa, EIT(t4)=7.2±0.9 GPa, EIT(t5)=6.2±1.8 GPa) as well as with the increase of the elastic (Welastic(t1)=4.11∙10-7±4.2∙10-8Nm, Welastic(t2)= 4.12∙10-7±6.4∙10-8 Nm, Welastic(t3)=4.71∙10-7±6.0∙10-9 Nm, Welastic(t4)= 4.33∙10-7±5.5∙10-9Nm, Welastic(t5)=5.11∙10-7±7.4∙10-8Nm) and inelastic (Winelastic(t1)=1.05∙10-6±1.2∙10-7 Nm, Winelastic(t2) =1.07∙10-6±7.6∙10-8 Nm, Winelastic(t3)=1.26∙10-6±1.9∙10-7Nm, Winelastic(t4)=1.56∙10-6± 1.9∙10-7 Nm, Winelastic(t5)=1.67∙10-6±2.6∙10-7)) reaction of materials. The indentation creep increased logarithmically (R2=0.901) with increasing hold time: CIT(t1) = 0.08±0.01%, CIT(t2) = 0.7±0.1%, CIT(t3) = 3.7±0.3%, CIT(t4) = 12.2±1.5%, CIT(t5) = 13.5±3.8%. The pronounced impact of creep effect on the mechanical properties of human cancellous bone was observed in experimental studies. While the description elastic-inelastic, and thus the Oliver-Pharr method for data analysis, may apply in few limited cases, most biological tissues do not exhibit elastic-inelastic indentation responses. Viscoelastic properties of tissues may play a significant role in remodelling. The aspect is still under an analysis and numerical simulations. Acknowledgements: The presented results are part of the research project founded by National Science Centre (NCN), Poland, no.2014/15/B/ST7/03244.

Keywords: bone, creep, indentation, mechanical properties

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Authors: K. N. Ashna

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Lightweight fills are a viable alternative where weak soils such as soft clay, peat, and loose silt are encountered. Materials such as Expanded Polystyrene (EPS) geo-foam, plastics, tire wastes, rubber wastes have been used along with soil in order to obtain a lightweight fill. Out of these, Expanded Polystyrene (EPS) geo-foam has gained wide popularity in civil engineering over the past years due to its wide variety of applications. It is extremely lightweight, durable and is available in various densities to meet the strength requirements. It can be used as backfill behind retaining walls to reduce lateral load, as a fill over soft clay or weak soils to prevent the excessive settlements and to reduce seismic forces. Geo-foam is available in block form as well as beads form. In this project Expanded Polystyrene (EPS) beads of various diameters and varying densities were mixed along with sand to study their lightweight as well as strength properties. Four types of EPS beads were used 1mm, 2mm, 3-7 mm and a mix of 1-7 mm. In this project, EPS beads were varied at .25%, .5%, .75% and 1% by weight of sand. A water content of 10% by weight of sand was added to prevent segregation of the mixture. Unconsolidated Unconfined (UU) tri-axial test was conducted at 100kPa, 200 kPa and 300 kPa and angle of internal friction, and cohesion was obtained. Unit weight of the mix was obtained for a relative density of 65%. The results showed that by increasing the EPS content by weight, maximum deviator stress, unit weight, angle of internal friction and initial elastic modulus decreased. An optimum EPS bead content was arrived at by considering the strength as well as the unit weight. The stress-strain behaviour of the mix was found to be dependent on type of bead, bead content and density of the beads. Finally, regression equations were developed to predict the initial elastic modulus of the mix.

Keywords: expanded polystyrene beads, geofoam, lightweight fills, stress-strain behavior, triaxial test

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Authors: Shingo Murakami, Shinichi Enoki

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In structures, stress concentration is a factor of fatigue fracture. Basically, the stress concentration is a phenomenon that should be avoided. However, it is difficult to avoid the stress concentration. Therefore, relaxation of the stress concentration is important. The stress concentration arises from notches and circular holes. There is a relaxation method that a composite patch covers a notch and a circular hole. This relaxation method is used to repair aerial wings, but it is not systematized. Composites are more expensive than single materials. Accordingly, we propose the relaxation method that a single material patch covers a notch and a circular hole, and aim to systematize this relaxation method. We performed FEA (Finite Element Analysis) about an object by using a three-dimensional FEA model. The object was that a patch adheres to a plate with a circular hole. And, a uniaxial tensile load acts on the patched plate with a circular hole. In the three-dimensional FEA model, it is not easy to model the adhesion layer. Basically, the yield stress of the adhesive is smaller than that of adherents. Accordingly, the adhesion layer gets to plastic deformation earlier than the adherents under the yield stress of adherents. Therefore, we propose the three-dimensional FEA model which is applied a nonlinear elastic region to the adhesion layer. The nonlinear elastic region was calculated by a bilinear approximation. We compared the analysis results with the tensile test results to confirm whether the analysis model has usefulness. As a result, the analysis results agreed with the tensile test results. And, we confirmed that the analysis model has usefulness. As a result that the three-dimensional FEA model was used to the analysis, it was confirmed that an out-of-plane deformation occurred to the patched plate with a circular hole. The out-of-plane deformation causes stress increase of the patched plate with a circular hole. Therefore, we investigate that the out-of-plane deformation affects relaxation of the stress concentration in the plate with a circular hole on this relaxation method. As a result, it was confirmed that the out-of-plane deformation inhibits relaxation of the stress concentration on the plate with a circular hole.

Keywords: stress concentration, patch, out-of-plane deformation, Finite Element Analysis

Procedia PDF Downloads 244

Authors: Shingo Murakami, Shinichi Enoki

Abstract:

In structures, stress concentration is a factor of fatigue fracture. Basically, the stress concentration is a phenomenon that should be avoided. However, it is difficult to avoid the stress concentration. Therefore, relaxation of the stress concentration is important. The stress concentration arises from notches and circular holes. There is a relaxation method that a composite patch covers a notch and a circular hole. This relaxation method is used to repair aerial wings, but it is not systematized. Composites are more expensive than single materials. Accordingly, we propose the relaxation method that a single material patch covers a notch and a circular hole, and aim to systematize this relaxation method. We performed FEA (Finite Element Analysis) about an object by using a three-dimensional FEA model. The object was that a patch adheres to a plate with a circular hole. And, a uniaxial tensile load acts on the patched plate with a circular hole. In the three-dimensional FEA model, it is not easy to model the adhesion layer. Basically, the yield stress of the adhesive is smaller than that of adherents. Accordingly, the adhesion layer gets to plastic deformation earlier than the adherents under the yield load of adherents. Therefore, we propose the three-dimensional FEA model which is applied a nonlinear elastic region to the adhesion layer. The nonlinear elastic region was calculated by a bilinear approximation. We compared the analysis results with the tensile test results to confirm whether the analysis model has usefulness. As a result, the analysis results agreed with the tensile test results. And, we confirmed that the analysis model has usefulness. As a result that the three-dimensional FEA model was used to the analysis, it was confirmed that an out-of-plane deformation occurred to the patched plate with a circular hole. The out-of-plane deformation causes stress increase of the patched plate with a circular hole. Therefore, we investigated that the out-of-plane deformation affects relaxation of the stress concentration in the plate with a circular hole on this relaxation method. As a result, it was confirmed that the out-of-plane deformation inhibits relaxation of the stress concentration on the plate with a circular hole.

Keywords: stress concentration, patch, out-of-plane deformation, Finite Element Analysis

Procedia PDF Downloads 281

Authors: Amine Rezzoug, Selsabil Rokia Laraba, Mourad Ancer, Said Abdi

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Composite materials are taking center stage in different fields thanks to their mechanical characteristics and their ease of preparation. Environmental constraints have led to the development of composite with natural reinforcements. The sandwich structure has the advantage to have good flexural proprieties for low density, which is why it was chosen in this work. The development of these materials is related to an energy saving strategy and environmental protection. The present work refers to the study of the development and characterization of sandwiches composites based on hybrids laminates with natural reinforcements (Alfa and Jute), a metal fabric was introduced into composite in order to have a compromise between weight and properties. We use different configurations of reinforcements (jute, metallic fabric) to develop laminates in order to use them as thin facings for sandwiches materials. While the core was an epoxy matrix reinforced with Alfa short fibers, a chemical treatment sodium hydroxide was cared to improve the adhesion of the Alfa fibers. The mechanical characterization of our materials was made by the tensile and bending test, to highlight the influence of jute and Alfa. After testing, the fracture surfaces are observed by scanning electron microscopy (SEM). Optical microscopy allowed us to calculate the degree of porosity and to observe the morphology of the individual layers. Laminates based on jute fabric have shown better results in tensile test as well as to bending, compared to those of the metallic fabric (100%, 65%). Sandwich Panels were also characterized in terms of bending test. Results we had provide, shows that this composite has sufficient properties for possible replacing conventional composite materials by considering the environmental factors.

Keywords: bending test, bio-composites, sandwiches, tensile test

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Authors: Leo Laine, Morgan Johansson

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To meet the civilizations future needs for safe living and low environmental footprint, the engineers designing the complex systems of tomorrow will need efficient ways to model and optimize these systems for their intended purpose. For example, a civil defence shelter and its subsystem components needs to withstand, e.g. airblast and ground shock from decided design level explosion which detonates with a certain distance from the structure. In addition, the complex civil defence shelter needs to have functioning air filter systems to protect from toxic gases and provide clean air, clean water, heat, and electricity needs to also be available through shock and vibration safe fixtures and connections. Similar complex building systems can be found in any concentrated living or office area. In this paper, the authors use a multidomain modelling language called Modelica to model a concrete wall as a single degree of freedom (SDOF) system with elastoplastic properties with the implemented option of plastic hardening. The elastoplastic model was developed and implemented in the open source tool OpenModelica. The simulation model was tested on the case with a transient equivalent reflected pressure time history representing an airblast from 100 kg TNT detonating 15 meters from the wall. The concrete wall is approximately regarded as a concrete strip of 1.0 m width. This load represents a realistic threat on any building in a city like area. The OpenModelica model results were compared with an Excel implementation of a SDOF model with an elastic-plastic spring using simple fixed timestep central difference solver. The structural displacement results agreed very well with each other when it comes to plastic displacement magnitude, elastic oscillation displacement, and response times.

Keywords: airblast from explosives, elastoplastic spring model, Modelica modelling language, SDOF, structural response of concrete structure

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Authors: M. F. Slim, A. Alhussein, F. Sanchette, M. François

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Thin films are widely used in various applications to enhance the surface properties and characteristics of materials. They are used in many domains such as: biomedical, automotive, aeronautics, military, electronics and energy. Depending on the elaboration technique, the elastic behavior of thin films may be different from this of bulk materials. This dependence on the elaboration techniques and their parameters makes the control of the elasticity constants of coated components necessary. Our work is focused on the characterization of the elasticity constants of isotropic thin films by means of Impulse Excitation Techniques. The tests rely on the measurement of the sample resonance frequency before and after deposition. In this work, a finite element model was performed with ABAQUS software. This model was then compared with the analytical approaches used to determine the Young’s and shear moduli. The best model to determine the film Young’s modulus was identified and a relation allowing the determination of the shear modulus of thin films of any thickness was developed. In order to confirm the model experimentally, Tungsten films were deposited on glass substrates by DC magnetron sputtering of a 99.99% purity tungsten target. The choice of tungsten was done because it is well known that its elastic behavior at crystal scale is ideally isotropic. The macroscopic elasticity constants, Young’s and shear moduli and Poisson’s ratio of the deposited film were determined by means of Impulse Excitation Technique. The Young’s modulus obtained from IET was compared with measurements by the nano-indentation technique. We did not observe any significant difference and the value is in accordance with the one reported in the literature. This work presents a new methodology on the determination of the elasticity constants of thin films using Impulse Excitation Technique. A formulation allowing the determination of the shear modulus of a coating, whatever the thickness, was developed and used to determine the macroscopic elasticity constants of tungsten films. The developed model was validated numerically and experimentally.

Keywords: characterization, coating, dynamical resonant method, Poisson's ratio, PVD, shear modulus, Young's modulus

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Authors: Yanqun Li, Hong Geng

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The rapid urbanization process taking big cities as the main body leads to the unequal configuration of urban and rural areas in the aspects of land supply, industrial division of labor, service supply and space allocation, and induces the shrinking characterization of service energy, industrial system and population vitality in small towns. As an important spatial unit in the spectrum of urbanization that serves, connects and couples urban and rural areas, the shrinking phenomenon faced by small towns has an important influence on the healthy development of urbanization. Based on the census of small towns in Wuhan metropolitan area, we have found that the shrinking of small towns is a passive contraction of elastic tension under the squeeze in cities. Once affected by the external forces such as policy regulation, planning guidance, and population return, small towns will achieve expansion and growth. Based on the theory of complex adaptive systems, this paper comprehensively constructs the development index evaluation system of small towns from five aspects of population, economy, space, society and ecology, measures the shrinking level of small towns, further analyzes the shrinking characteristics of small towns, and identifies whether the shrinking is elastic or not. And then this paper measures the resilience ability index of small town contract from the above-mentioned five aspects. Finally, this paper proposes an adaptive mechanism of urban-rural interaction evolution under fine division of labor to response the passive shrinking in small towns of Wuhan. Based on the above, the paper creatively puts forward the planning response measures of the small towns on the aspects of spatial layout, function orientation and service support, which can provide reference for other regions.

Keywords: complex adaptive systems, resiliency shrinking, adaptation mechanism, planning response

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Authors: Saba Rahman, Arvind K. Jain, S. D. Bharti, T. K. Datta

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Chimneys are generally tall and slender structures with circular cross-sections, due to which they are highly prone to wind forces. Wind exerts pressure on the wall of the chimneys, which produces unwanted forces. Vortex-induced oscillation is one of such excitations which can lead to the failure of the chimneys. Therefore, vortex-induced oscillation of chimneys is of great concern to researchers and practitioners since many failures of chimneys due to vortex shedding have occurred in the past. As a consequence, extensive research has taken place on the subject over decades. Many laboratory experiments have been performed to verify the theoretical models proposed to predict vortex-induced forces, including aero-elastic effects. Comparatively, very few proto-type measurement data have been recorded to verify the proposed theoretical models. Because of this reason, the theoretical models developed with the help of experimental laboratory data are utilized for analyzing the chimneys for vortex-induced forces. This calls for reliability analysis of the predictions of the responses of the chimneys produced due to vortex shedding phenomena. Although several works of literature exist on the vortex-induced oscillation of chimneys, including code provisions, the reliability analysis of chimneys against failure caused due to vortex shedding is scanty. In the present study, the reliability analysis of chimneys against vortex shedding failure is presented, assuming the uncertainty in vortex shedding phenomena to be significantly more than other uncertainties, and hence, the latter is ignored. The vortex shedding is modeled as a stationary random process and is represented by a power spectral density function (PSDF). It is assumed that the vortex shedding forces are perfectly correlated and act over the top one-third height of the chimney. The PSDF of the tip displacement of the chimney is obtained by performing a frequency domain spectral analysis using a matrix approach. For this purpose, both chimney and random wind forces are discretized over a number of points along with the height of the chimney. The method of analysis duly accounts for the aero-elastic effects. The double barrier threshold crossing level, as proposed by Vanmarcke, is used for determining the probability of crossing different threshold levels of the tip displacement of the chimney. Assuming the annual distribution of the mean wind velocity to be a Gumbel type-I distribution, the fragility curve denoting the variation of the annual probability of threshold crossing against different threshold levels of the tip displacement of the chimney is determined. The reliability estimate is derived from the fragility curve. A 210m tall concrete chimney with a base diameter of 35m, top diameter as 21m, and thickness as 0.3m has been taken as an illustrative example. The terrain condition is assumed to be that corresponding to the city center. The expression for the PSDF of the vortex shedding force is taken to be used by Vickery and Basu. The results of the study show that the threshold crossing reliability of the tip displacement of the chimney is significantly influenced by the assumed structural damping and the Gumbel distribution parameters. Further, the aero-elastic effect influences the reliability estimate to a great extent for small structural damping.

Keywords: chimney, fragility curve, reliability analysis, vortex-induced vibration

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Authors: Maira C. M. Fonseca, Maria Aparecida N. Sediyama, Rosana Goncalves R. das Dores, Sanzio Mollica Vidigal, Alberto C. P. Dias

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Among Brazilian plant diversity, many species are used as food and considered minor crops (non-conventional plant foods) (NCPF). Arrowroot (Maranta arundinacea) is a NCPF from which starch is extracted from rhizome do not have gluten. Thus, arrowroot flower starch can be consumed by celiac people. Additional, some medicinal and functional proprieties are assigned to arrowroot leaves which currently are underutilized. In Brazil, it’s cultivated mainly by small scale farmers and there is no specific recommendation for fertilization. This work aimed to determinate the best fertilization for rhizome production and to verify its influence in phenolic composition and antioxidant activity of leaf extracts. Two arrowroot varieties, “Common” and “Seta”, were cultivated in organic system at state of Minas Gerais, Brazil, using cattle manure with three levels of nitrogen (N) (0, 300 and 900 kg N ha-1). The experiment design was in randomized block with four replicates. The highest production of rhizomes in both varieties, “Common” (38198.24 kg ha-1) and “Seta” (43567.71 kg ha-1), were obtained with the use of 300 kg N ha-1. With this fertilization, the total aerial part, petiole and leaf production in the varieties were respectively: “Common” (190.312 kg ha-1; 159.312 kg ha-1; 31.100 kg ha-1) and “Seta” (207.656 kg ha-1; 180.539 kg ha-1; 27.062 kg ha-1). Methanolic leaf extracts were analysed by HPLC-DAD. The major phenolic compounds found were caffeioylquinic acids, p-coumaric derivatives and flavonoids. In general, the production of these compounds significantly decreases with the increase levels of nitrogen (900 kg N ha-1). With 300 kg N ha-1 the phenolic production was similar to control. The antioxidant activity was evaluated using DPPH method and was detected around 60% of radical scavenging when 0.1 mg/mL of plant extracts were used. We concluded that fertilization with 300 kg N ha-1 increased arrowroot rhizome production, maintaining phenolic compounds yield at leaves.

Keywords: antioxidant activity, non-conventional plants, organic fertilization, phenolic compounds

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Authors: Erick Pruchnicki, Nikhil Padhye

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Plates are important engineering structures which have attracted extensive research since the 19th century. The subject of this work is statical analysis of a linearly elastic homogenous plate under small deformations. A 'thin plate' is a three-dimensional structure comprising of a small transverse dimension with respect to a flat mid-surface. The general aim of any plate theory is to deduce a two-dimensional model, in terms of mid-surface quantities, to approximately and accurately describe the plate's deformation in terms of mid-surface quantities. In recent decades, a common starting point for this purpose is to utilize series expansion of a displacement field across the thickness dimension in terms of the thickness parameter (h). These attempts are mathematically consistent in deriving leading-order plate theories based on certain a priori scaling between the thickness and the applied loads; for example, asymptotic methods which are aimed at generating leading-order two-dimensional variational problems by postulating formal asymptotic expansion of the displacement fields. Such methods rigorously generate a hierarchy of two-dimensional models depending on the order of magnitude of the applied load with respect to the plate-thickness. However, in practice, applied loads are external and thus not directly linked or dependent on the geometry/thickness of the plate; thus, rendering any such model (based on a priori scaling) of limited practical utility. In other words, the main limitation of these approaches is that they do not furnish a single plate model for all orders of applied loads. Following analogy of recent efforts of deploying Fourier-series expansion to study convergence of reduced models, we propose two-dimensional model(s) resulting from truncation of the potential energy and rigorously prove the convergence of these two-dimensional plate models to the parent three-dimensional linear elasticity with increasing truncation order of the potential energy.

Keywords: plate theory, Fourier-series expansion, convergence result, Legendre polynomials

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