Search results for: elastic moduli
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 869

Search results for: elastic moduli

539 Seismic Inversion for Geothermal Exploration

Authors: E. N. Masri, E. Takács

Abstract:

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

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538 Crystalline Particles Dispersed Cu-Based Metallic Glassy Composites Fabricated by Spark Plasma Sintering

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

Abstract:

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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537 3D Numerical Simulation of Undoweled and Uncracked Joints in Short Paneled Concrete Pavements

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

Abstract:

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

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536 Assessment of Analytical Equations for the Derivation of Young’s Modulus of Bonded Rubber Materials

Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

Abstract:

The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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535 Combining the Fictitious Stress Method and Displacement Discontinuity Method in Solving Crack Problems in Anisotropic Material

Authors: Bahatti̇n Ki̇mençe, Uğur Ki̇mençe

Abstract:

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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534 Modern Seismic Design Approach for Buildings with Hysteretic Dampers

Authors: Vanessa A. Segovia, Sonia E. Ruiz

Abstract:

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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533 Viscoelastic Behavior of Human Bone Tissue under Nanoindentation Tests

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

Abstract:

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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532 Experimental Studies on Stress Strain Behavior of Expanded Polystyrene Beads-Sand Mixture

Authors: K. N. Ashna

Abstract:

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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531 Effect of Out-Of-Plane Deformation on Relaxation Method of Stress Concentration in a Plate

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 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

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530 Effect of Out-Of-Plane Deformation on Relaxation Method of Stress Concentration in a Plate with a Circular Hole

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

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529 Simulation of Concrete Wall Subjected to Airblast by Developing an Elastoplastic Spring Model in Modelica Modelling Language

Authors: Leo Laine, Morgan Johansson

Abstract:

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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528 Body Armours in Amazonian Fish

Authors: Fernando G. Torres, Donna M. Ebenstein, Monica Merino

Abstract:

Most fish are covered by a protective external armour. The characteristics of these armours depend on the individual elements that form them, such as scales, scutes or dermal plates. In this work, we assess the properties of two different types of protective elements: scales from A. gigas and dermal plates from P. pardalis. A. Gigas and P. Pardalis are two Amazonian fish with a rather prehistoric aspect. They have large scales and dermal plates that form two different types of protective body armours. Although both scales and dermal plates are formed by collagen and hydroxyapatite, their structures display remarkable differences. The structure and composition of the samples were assessed by means of X-ray diffraction (XRD), Fourier Transform Infrared spectroscopy (FTIR) and Differential Scanning Calorimetry (DSC). Morphology studies were carried out using a Scanning Electron Microscopy (SEM). Nanoindentation tests were performed to measure the reduced moduli in A. gigas scales and P. pardalis plates. The similarities and differences between scales and dermal plates are discussed based on the experimental results. Both protective armours are designed to be lightweight, flexible and tough. A. Gigas scales are are light laminated composites, while P. pardalis dermal plates show a sandwich like structure with dense outer layers and a porous inner matrix. It seems that the armour of P. pardalis is more suited for a bottom-dwelling fish and allows for protection against predators. The scales from A. Gigas are more adapted to give protection to a swimming fish. The information obtained from these studies is also important for the development of bioinspired nanocomposites, with potential applications in the biomedical field.

Keywords: pterygoplichthys pardalis, dermal plates arapaima gigas, fish scales

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527 Adaptation Mechanism and Planning Response to Resiliency Shrinking of Small Towns Based on Complex Adaptive System by Taking Wuhan as an Example

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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526 The Reliability Analysis of Concrete Chimneys Due to Random Vortex Shedding

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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525 Convergence Results of Two-Dimensional Homogeneous Elastic Plates from Truncation of Potential Energy

Authors: Erick Pruchnicki, Nikhil Padhye

Abstract:

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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524 Computer Software for Calculating Electron Mobility of Semiconductors Compounds; Case Study for N-Gan

Authors: Emad A. Ahmed

Abstract:

Computer software to calculate electron mobility with respect to different scattering mechanism has been developed. This software is adopted completely Graphical User Interface (GUI) technique and its interface has been designed by Microsoft Visual Basic 6.0. As a case study the electron mobility of n-GaN was performed using this software. The behaviour of the mobility for n-GaN due to elastic scattering processes and its relation to temperature and doping concentration were discussed. The results agree with other available theoretical and experimental data.

Keywords: electron mobility, relaxation time, GaN, scattering, computer software, computation physics

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523 Structure and Mechanics Patterns in the Assembly of Type V Intermediate-Filament Protein-Based Fibers

Authors: Mark Bezner, Shani Deri, Tom Trigano, Kfir Ben-Harush

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Intermediate filament (IF) proteins-based fibers are among the toughest fibers in nature, as was shown by native hagfish slime threads and by synthetic fibers that are based on type V IF-proteins, the nuclear lamins. It is assumed that their mechanical performance stems from two major factors: (1) the transition from elastic -helices to stiff-sheets during tensile load; and (2) the specific organization of the coiled-coil proteins into a hierarchical network of nano-filaments. Here, we investigated the interrelationship between these two factors by using wet-spun fibers based on C. elegans (Ce) lamin. We found that Ce-lamin fibers, whether assembled in aqueous or alcoholic solutions, had the same nonlinear mechanical behavior, with the elastic region ending at ~5%. The pattern of the transition was, however, different: the ratio between -helices and -sheets/random coils was relatively constant until a 20% strain for fibers assembled in an aqueous solution, whereas for fibers assembled in 70% ethanol, the transition ended at a 6% strain. This structural phenomenon in alcoholic solution probably occurred through the transition between compacted and extended conformation of the random coil, and not between -helix and -sheets, as cycle analyses had suggested. The different transition pattern can also be explained by the different higher order organization of Ce-lamins in aqueous or alcoholic solutions, as demonstrated by introducing a point mutation in conserved residue in Ce-lamin gene that alter the structure of the Ce-lamins’ nano-fibrils. In addition, biomimicking the layered structure of silk and hair fibers by coating the Ce-lamin fiber with a hydrophobic layer enhanced fiber toughness and lead to a reversible transition between -helix and the extended conformation. This work suggests that different hierarchical structures, which are formed by specific assembly conditions, lead to diverse secondary structure transitions patterns, which in turn affect the fibers’ mechanical properties.

Keywords: protein-based fibers, intermediate filaments (IF) assembly, toughness, structure-property relationships

Procedia PDF Downloads 110
522 Performance of Fiber-Reinforced Polymer as an Alternative Reinforcement

Authors: Salah E. El-Metwally, Marwan Abdo, Basem Abdel Wahed

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Fiber-reinforced polymer (FRP) bars have been proposed as an alternative to conventional steel bars; hence, the use of these non-corrosive and nonmetallic reinforcing bars has increased in various concrete projects. This concrete material is lightweight, has a long lifespan, and needs minor maintenance; however, its non-ductile nature and weak bond with the surrounding concrete create a significant challenge. The behavior of concrete elements reinforced with FRP bars has been the subject of several experimental investigations, even with their high cost. This study aims to numerically assess the viability of using FRP bars, as longitudinal reinforcement, in comparison with traditional steel bars, and also as prestressing tendons instead of the traditional prestressing steel. The nonlinear finite element analysis has been utilized to carry out the current study. Numerical models have been developed to examine the behavior of concrete beams reinforced with FRP bars or tendons against similar models reinforced with either conventional steel or prestressing steel. These numerical models were verified by experimental test results available in the literature. The obtained results revealed that concrete beams reinforced with FRP bars, as passive reinforcement, exhibited less ductility and less stiffness than similar beams reinforced with steel bars. On the other hand, when FRP tendons are employed in prestressing concrete beams, the results show that the performance of these beams is similar to those beams prestressed by conventional active reinforcement but with a difference caused by the two tendon materials’ moduli of elasticity.

Keywords: reinforced concrete, prestressed concrete, nonlinear finite element analysis, fiber-reinforced polymer, ductility

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521 Dynamic Response around Inclusions in Infinitely Inhomogeneous Media

Authors: Jinlai Bian, Zailin Yang, Guanxixi Jiang, Xinzhu Li

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The problem of elastic wave propagation in inhomogeneous medium has always been a classic problem. Due to the frequent occurrence of earthquakes, many economic losses and casualties have been caused, therefore, to prevent earthquake damage to people and reduce damage, this paper studies the dynamic response around the circular inclusion in the whole space with inhomogeneous modulus, the inhomogeneity of the medium is reflected in the shear modulus of the medium with the spatial position, and the density is constant, this method can be used to solve the problem of the underground buried pipeline. Stress concentration phenomena are common in aerospace and earthquake engineering, and the dynamic stress concentration factor (DSCF) is one of the main factors leading to material damage, one of the important applications of the theory of elastic dynamics is to determine the stress concentration in the body with discontinuities such as cracks, holes, and inclusions. At present, the methods include wave function expansion method, integral transformation method, integral equation method and so on. Based on the complex function method, the Helmholtz equation with variable coefficients is standardized by using conformal transformation method and wave function expansion method, the displacement and stress fields in the whole space with circular inclusions are solved in the complex coordinate system, the unknown coefficients are solved by using boundary conditions, by comparing with the existing results, the correctness of this method is verified, based on the superiority of the complex variable function theory to the conformal transformation, this method can be extended to study the inclusion problem of arbitrary shapes. By solving the dynamic stress concentration factor around the inclusions, the influence of the inhomogeneous parameters of the medium and the wavenumber ratio of the inclusions to the matrix on the dynamic stress concentration factor is analyzed. The research results can provide some reference value for the evaluation of nondestructive testing (NDT), oil exploration, seismic monitoring, and soil-structure interaction.

Keywords: circular inclusions, complex variable function, dynamic stress concentration factor (DSCF), inhomogeneous medium

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520 Experimental and Theoratical Methods to Increase Core Damping for Sandwitch Cantilever Beam

Authors: Iyd Eqqab Maree, Moouyad Ibrahim Abbood

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The purpose behind this study is to predict damping effect for steel cantilever beam by using two methods of passive viscoelastic constrained layer damping. First method is Matlab Program, this method depend on the Ross, Kerwin and Unger (RKU) model for passive viscoelastic damping. Second method is experimental lab (frequency domain method), in this method used the half-power bandwidth method and can be used to determine the system loss factors for damped steel cantilever beam. The RKU method has been applied to a cantilever beam because beam is a major part of a structure and this prediction may further leads to utilize for different kinds of structural application according to design requirements in many industries. In this method of damping a simple cantilever beam is treated by making sandwich structure to make the beam damp, and this is usually done by using viscoelastic material as a core to ensure the damping effect. 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. 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. There is a very good agreement of the experimental results with the theoretical findings. The main ideas of this thesis are to find the transition region for damped steel cantilever beam (4mm and 8mm thickness) from experimental lab and theoretical prediction (Matlab R2011a). Experimentally and theoretically proved that the transition region for two specimens occurs at modal frequency between mode 1 and mode 2, which give the best damping, maximum loss factor and maximum damping ratio, thus this type of viscoelastic material core (3M468) is very appropriate to use in automotive industry and in any mechanical application has modal frequency eventuate between mode 1 and mode 2.

Keywords: 3M-468 material core, loss factor and frequency, domain method, bioinformatics, biomedicine, MATLAB

Procedia PDF Downloads 271
519 Vibration Damping Properties of Electrorheological Materials Based on Chitosan/Perlite Composite

Authors: M. Cabuk, M. Yavuz, T. A. Yesil, H. I. Unal

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Electrorheological (ER) fluids are a class of smart materials exhibiting reversible changes in their rheological and mechanical properties under an applied electric field (E). ER fluids generally are composed of polarisable solid particles dispersed in non-conducting oil. ER fluids are fluids which exhibit. The resistance to motion of the ER fluid can be controlled by adjusting the applied E, due to their fast and reversible changes in their rheological properties presence of E. In this study, a series of chitosan/expanded perlite (CS/EP) composites with different chitosan mass fractions (10%, 20%, and 50%) was used. Characterizations of the composites were carried out by Fourier Transform Infrared (FTIR), X-ray diffraction (XRD) and Scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM-EDX) techniques. Antisedimentation stability and dielectric properties of the composites were also determined. The effects of volume fraction, electric field strength, shear rate, shear stress, and temperature onto ER properties of the CS/EP composite particles dispersed in silicone oil (SO) were investigated in detail. Vibration damping behavior of the CS/EP composites were determined as a function of frequence, storage (Gʹ) and loss (Gʹ ʹ) moduli. It was observed that ER response of the CS/EP/SO ER fluids increased with increasing electric field strength and exhibited the typical shear thinning non-Newtonian viscoelastic behaviors with increasing shear rate. The maximum yield stress was obtained with 1250 Pa under E = 3 kV/mm. Further, the CS/EP/SO ER fluids were observed to sensitive to vibration control by showing reversible viscosity enhancements (Gʹ > Gʹ ʹ). Acknowledgements: The authors thank the TÜBİTAK (214Z199) for the financial support of this work.

Keywords: chitosan, electrorheology, perlite, vibration control

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518 Wireless Gyroscopes for Highly Dynamic Objects

Authors: Dmitry Lukyanov, Sergey Shevchenko, Alexander Kukaev

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Modern MEMS gyroscopes have strengthened their position in motion control systems and have led to the creation of tactical grade sensors (better than 15 deg/h). This was achieved by virtue of the success in micro- and nanotechnology development, cooperation among international experts and the experience gained in the mass production of MEMS gyros. This production is knowledge-intensive, often unique and, therefore, difficult to develop, especially due to the use of 3D-technology. The latter is usually associated with manufacturing of inertial masses and their elastic suspension, which determines the vibration and shock resistance of gyros. Today, consumers developing highly dynamic objects or objects working under extreme conditions require the gyro shock resistance of up to 65 000 g and the measurement range of more than 10 000 deg/s. Such characteristics can be achieved by solid-state gyroscopes (SSG) without inertial masses or elastic suspensions, which, for example, can be constructed with molecular kinetics of bulk or surface acoustic waves (SAW). Excellent effectiveness of this sensors production and a high level of structural integration provides basis for increased accuracy, size reduction and significant drop in total production costs. Existing principles of SAW-based sensors are based on the theory of SAW propagation in rotating coordinate systems. A short introduction to the theory of a gyroscopic (Coriolis) effect in SAW is provided in the report. Nowadays more and more applications require passive and wireless sensors. SAW-based gyros provide an opportunity to create one. Several design concepts incorporating reflective delay lines were proposed in recent years, but faced some criticism. Still, the concept is promising and is being of interest in St. Petersburg Electrotechnical University. Several experimental models were developed and tested to find the minimal configuration of a passive and wireless SAW-based gyro. Structural schemes, potential characteristics and known limitations are stated in the report. Special attention is dedicated to a novel method of a FEM modeling with piezoelectric and gyroscopic effects simultaneously taken into account.

Keywords: FEM simulation, gyroscope, OOFELIE, surface acoustic wave, wireless sensing

Procedia PDF Downloads 365
517 Analysis of Elastic-Plastic Deformation of Reinforced Concrete Shear-Wall Structures under Earthquake Excitations

Authors: Oleg Kabantsev, Karomatullo Umarov

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The engineering analysis of earthquake consequences demonstrates a significantly different level of damage to load-bearing systems of different types. Buildings with reinforced concrete columns and separate shear-walls receive the highest level of damage. Traditional methods for predicting damage under earthquake excitations do not provide an answer to the question about the reasons for the increased vulnerability of reinforced concrete frames with shear-walls bearing systems. Thus, the study of the problem of formation and accumulation of damages in the structures reinforced concrete frame with shear-walls requires the use of new methods of assessment of the stress-strain state, as well as new approaches to the calculation of the distribution of forces and stresses in the load-bearing system based on account of various mechanisms of elastic-plastic deformation of reinforced concrete columns and walls. The results of research into the processes of non-linear deformation of structures with a transition to destruction (collapse) will allow to substantiate the characteristics of limit states of various structures forming an earthquake-resistant load-bearing system. The research of elastic-plastic deformation processes of reinforced concrete structures of frames with shear-walls is carried out on the basis of experimentally established parameters of limit deformations of concrete and reinforcement under dynamic excitations. Limit values of deformations are defined for conditions under which local damages of the maximum permissible level are formed in constructions. The research is performed by numerical methods using ETABS software. The research results indicate that under earthquake excitations, plastic deformations of various levels are formed in various groups of elements of the frame with the shear-wall load-bearing system. During the main period of seismic effects in the shear-wall elements of the load-bearing system, there are insignificant volumes of plastic deformations, which are significantly lower than the permissible level. At the same time, plastic deformations are formed in the columns and do not exceed the permissible value. At the final stage of seismic excitations in shear-walls, the level of plastic deformations reaches values corresponding to the plasticity coefficient of concrete , which is less than the maximum permissible value. Such volume of plastic deformations leads to an increase in general deformations of the bearing system. With the specified parameters of the deformation of the shear-walls in concrete columns, plastic deformations exceeding the limiting values develop, which leads to the collapse of such columns. Based on the results presented in this study, it can be concluded that the application seismic-force-reduction factor, common for the all load-bearing system, does not correspond to the real conditions of formation and accumulation of damages in elements of the load-bearing system. Using a single coefficient of seismic-force-reduction factor leads to errors in predicting the seismic resistance of reinforced concrete load-bearing systems. In order to provide the required level of seismic resistance buildings with reinforced concrete columns and separate shear-walls, it is necessary to use values of the coefficient of seismic-force-reduction factor differentiated by types of structural groups.1

Keywords: reinforced concrete structures, earthquake excitation, plasticity coefficients, seismic-force-reduction factor, nonlinear dynamic analysis

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516 A Superposition Method in Analyses of Clamped Thick Plates

Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

Procedia PDF Downloads 597
515 Experimental Damping Performance of Composite Materials with Different Fibre Orientations

Authors: Ferhat Kadioglu

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A clamped-free vibrating beam technique was used to evaluate dynamic properties of glass fiber reinforced polymer matrix composite. In the experiment, an electromagnetic shaker and a non-contact laser head were used to vibrate and to take the response of the specimens, respectively. Test results showed that damping and elastic modulus of the material, as dynamic properties, could be obtained successfully using this technique. It was found that the balanced and symmetric specimens with 45 degrees are the best for damping performance. It is believed that such results could be used for the modal design of aerospace structures.

Keywords: composite materials, damping values, dynamic properties, non-contact measurements

Procedia PDF Downloads 348
514 Test Procedures for Assessing the Peel Strength and Cleavage Resistance of Adhesively Bonded Joints with Elastic Adhesives under Detrimental Service Conditions

Authors: Johannes Barlang

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Adhesive bonding plays a pivotal role in various industrial applications, ranging from automotive manufacturing to aerospace engineering. The peel strength of adhesives, a critical parameter reflecting the ability of an adhesive to withstand external forces, is crucial for ensuring the integrity and durability of bonded joints. This study provides a synopsis of the methodologies, influencing factors, and significance of peel testing in the evaluation of adhesive performance. Peel testing involves the measurement of the force required to separate two bonded substrates under controlled conditions. This study systematically reviews the different testing techniques commonly applied in peel testing, including the widely used 180-degree peel test and the T-peel test. Emphasis is placed on the importance of selecting an appropriate testing method based on the specific characteristics of the adhesive and the application requirements. The influencing factors on peel strength are multifaceted, encompassing adhesive properties, substrate characteristics, environmental conditions, and test parameters. Through an in-depth analysis, this study explores how factors such as adhesive formulation, surface preparation, temperature, and peel rate can significantly impact the peel strength of adhesively bonded joints. Understanding these factors is essential for optimizing adhesive selection and application processes in real-world scenarios. Furthermore, the study highlights the role of peel testing in quality control and assurance, aiding manufacturers in maintaining consistent adhesive performance and ensuring the reliability of bonded structures. The correlation between peel strength and long-term durability is discussed, shedding light on the predictive capabilities of peel testing in assessing the service life of adhesive bonds. In conclusion, this study underscores the significance of peel testing as a fundamental tool for characterizing adhesive performance. By delving into testing methodologies, influencing factors, and practical implications, this study contributes to the broader understanding of adhesive behavior and fosters advancements in adhesive technology across diverse industrial sectors.

Keywords: adhesively bonded joints, cleavage resistance, elastic adhesives, peel strength

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513 Mechanical Characterization of Banana by Inverse Analysis Method Combined with Indentation Test

Authors: Juan F. P. Ramírez, Jésica A. L. Isaza, Benjamín A. Rojano

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This study proposes a novel use of a method to determine the mechanical properties of fruits by the use of the indentation tests. The method combines experimental results with a numerical finite elements model. The results presented correspond to a simplified numerical modeling of banana. The banana was assumed as one-layer material with an isotropic linear elastic mechanical behavior, the Young’s modulus found is 0.3Mpa. The method will be extended to multilayer models in further studies.

Keywords: finite element method, fruits, inverse analysis, mechanical properties

Procedia PDF Downloads 358
512 A Problem in Microstretch Thermoelastic Diffusive Medium

Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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511 Approximate Solution of Some Mixed Boundary Value Problems of the Generalized Theory of Couple-Stress Thermo-Elasticity

Authors: Manana Chumburidze, David Lekveishvili

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We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: the couple-stress thermoelasticity, boundary value problems, dynamic problems, approximate solution

Procedia PDF Downloads 506
510 Long Wavelength Coherent Pulse of Sound Propagating in Granular Media

Authors: Rohit Kumar Shrivastava, Amalia Thomas, Nathalie Vriend, Stefan Luding

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A mechanical wave or vibration propagating through granular media exhibits a specific signature in time. A coherent pulse or wavefront arrives first with multiply scattered waves (coda) arriving later. The coherent pulse is micro-structure independent i.e. it depends only on the bulk properties of the disordered granular sample, the sound wave velocity of the granular sample and hence bulk and shear moduli. The coherent wavefront attenuates (decreases in amplitude) and broadens with distance from its source. The pulse attenuation and broadening effects are affected by disorder (polydispersity; contrast in size of the granules) and have often been attributed to dispersion and scattering. To study the effect of disorder and initial amplitude (non-linearity) of the pulse imparted to the system on the coherent wavefront, numerical simulations have been carried out on one-dimensional sets of particles (granular chains). The interaction force between the particles is given by a Hertzian contact model. The sizes of particles have been selected randomly from a Gaussian distribution, where the standard deviation of this distribution is the relevant parameter that quantifies the effect of disorder on the coherent wavefront. Since, the coherent wavefront is system configuration independent, ensemble averaging has been used for improving the signal quality of the coherent pulse and removing the multiply scattered waves. The results concerning the width of the coherent wavefront have been formulated in terms of scaling laws. An experimental set-up of photoelastic particles constituting a granular chain is proposed to validate the numerical results.

Keywords: discrete elements, Hertzian contact, polydispersity, weakly nonlinear, wave propagation

Procedia PDF Downloads 204