Search results for: elastic beam theory
6115 A Study on Application of Elastic Theory for Computing Flexural Stresses in Preflex Beam
Authors: Nasiri Ahmadullah, Shimozato Tetsuhiro, Masayuki Tai
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This paper presents the step-by-step procedure for using Elastic Theory to calculate the internal stresses in composite bridge girders prestressed by the Preflexing Technology, called Prebeam in Japan and Preflex beam worldwide. Elastic Theory approaches preflex beams the same way as it does the conventional composite girders. Since preflex beam undergoes different stages of construction, calculations are made using different sectional and material properties. Stresses are calculated in every stage using the properties of the specific section. Stress accumulation gives the available stress in a section of interest. Concrete presence in the section implies prestress loss due to creep and shrinkage, however; more work is required to be done in this field. In addition to the graphical presentation of this application, this paper further discusses important notes of graphical comparison between the results of an experimental-only research carried out on a preflex beam, with the results of simulation based on the elastic theory approach, for an identical beam using Finite Element Modeling (FEM) by the author.Keywords: composite girder, Elastic Theory, preflex beam, prestressing
Procedia PDF Downloads 2756114 Using the Nonlocal Theory of Free Vibrations Nanobeam
Authors: Ali Oveysi Sarabi
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The dimensions of nanostructures are in the range of inter-atomic spacing of the structures which makes them impossible to be modeled as a continuum. Nanoscale size-effects on vibration analysis of nanobeams embedded in an elastic medium is investigated using different types of beam theory. To this end, Eringen’s nonlocal elasticity is incorporated to various beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT). The surrounding elastic medium is simulated with both Winkler and Pasternak foundation models and the difference between them is studies. Explicit formulas are presented to obtain the natural frequencies of nanobeam corresponding to each nonlocal beam theory. Selected numerical results are given for different values of the non-local parameter, Winkler modulus parameter, Pasternak modulus parameter and aspect ratio of the beam that imply the effects of them, separately. It is observed that the values of natural frequency are strongly dependent on the stiffness of elastic medium and the value of the non-local parameter and these dependencies varies with the value of aspect ratio and mode number.Keywords: nanobeams, free vibration, nonlocal elasticity, winkler foundation model, Pasternak foundation model, beam theories
Procedia PDF Downloads 5316113 Analysis of Simply Supported Beams Using Elastic Beam Theory
Authors: M. K. Dce
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The aim of this paper is to investigate the behavior of simply supported beams having rectangular section and subjected to uniformly distributed load (UDL). In this study five beams of span 5m, 6m, 7m and 8m have been considered. The width of all the beams is 400 mm and span to depth ratio has been taken as 12. The superimposed live load has been increased from 10 kN/m to 25 kN/m at the interval of 5 kN/m. The analysis of the beams has been carried out using the elastic beam theory. On the basis of present study it has been concluded that the maximum bending moment as well as deflection occurs at the mid-span of simply supported beam and its magnitude increases in proportion to magnitude of UDL. Moreover, the study suggests that the maximum moment is proportional to square of span and maximum deflection is proportional to fourth power of span.Keywords: beam, UDL, bending moment, deflection, elastic beam theory
Procedia PDF Downloads 3836112 Vibration Analysis of Functionally Graded Engesser-Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation
Authors: M. Karami Khorramabadi, A. R. Nezamabadi
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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.Keywords: functionally graded beam, free vibration, elastic foundation, Engesser-Timoshenko beam theory
Procedia PDF Downloads 4116111 Vibration Control of a Functionally Graded Carbon Nanotube-Reinforced Composites Beam Resting on Elastic Foundation
Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati
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In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.Keywords: carbon nanotubes, vibration control, piezoelectric layers, elastic foundation
Procedia PDF Downloads 2626110 Application of the Micropolar Beam Theory for the Construction of the Discrete-Continual Model of Carbon Nanotubes
Authors: Samvel H. Sargsyan
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Together with the study of electron-optical properties of nanostructures and proceeding from experiment-based data, the study of the mechanical properties of nanostructures has become quite actual. For the study of the mechanical properties of fullerene, carbon nanotubes, graphene and other nanostructures one of the crucial issues is the construction of their adequate mathematical models. Among all mathematical models of graphene or carbon nano-tubes, this so-called discrete-continuous model is specifically important. It substitutes the interactions between atoms by elastic beams or springs. The present paper demonstrates the construction of the discrete-continual beam model for carbon nanotubes or graphene, where the micropolar beam model based on the theory of moment elasticity is accepted. With the account of the energy balance principle, the elastic moment constants for the beam model, expressed by the physical and geometrical parameters of carbon nanotube or graphene, are determined. By switching from discrete-continual beam model to the continual, the models of micropolar elastic cylindrical shell and micropolar elastic plate are confirmed as continual models for carbon nanotube and graphene respectively.Keywords: carbon nanotube, discrete-continual, elastic, graphene, micropolar, plate, shell
Procedia PDF Downloads 1506109 Numerical Study on Ultimate Capacity of Bi-Modulus Beam-Column
Authors: Zhiming Ye, Dejiang Wang, Huiling Zhao
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Development of the technology demands a higher-level research on the mechanical behavior of materials. Structural members made of bi-modulus materials have different elastic modulus when they are under tension and compression. The stress and strain states of the point effect on the elastic modulus and Poisson ratio of every point in the bi-modulus material body. Accompanied by the uncertainty and nonlinearity of the elastic constitutive relation is the complicated nonlinear problem of the bi-modulus members. In this paper, the small displacement and large displacement finite element method for the bi-modulus members have been proposed. Displacement nonlinearity is considered in the elastic constitutive equation. Mechanical behavior of slender bi-modulus beam-column under different boundary conditions and loading patterns has been simulated by the proposed method. The influence factors on the ultimate bearing capacity of slender beam and columns have been studied. The results show that as the ratio of tensile modulus to compressive modulus increases, the error of the simulation employing the same elastic modulus theory exceeds the engineering permissible error.Keywords: bi-modulus, ultimate capacity, beam-column, nonlinearity
Procedia PDF Downloads 4036108 Transverse Vibration of Elastic Beam Resting on Variable Elastic Foundation Subjected to moving Load
Authors: Idowu Ibikunle Albert, Atilade Adesanya Oluwafemi, Okedeyi Abiodun Sikiru, Mustapha Rilwan Adewale
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These present-day all areas of transport have experienced large advances characterized by increases in the speeds and weight of vehicles. As a result, this paper considered the Transverse Vibration of an Elastic Beam Resting on a Variable Elastic Foundation Subjected to a moving Load. The beam is presumed to be uniformly distributed and has simple support at both ends. The moving distributed moving mass is assumed to move with constant velocity. The governing equations, which are fourth-order partial differential equations, were reduced to second-order partial differential equations using an analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). Results show that an increase in the values of beam parameters, moving Mass M, and k-stiffness K, significantly reduces the deflection profile of the vibrating beam. In the results, it was equally found that moving mass is greater than moving force.Keywords: elastic beam, moving load, response of structure, variable elastic foundation
Procedia PDF Downloads 1136107 Forced Vibration of a Planar Curved Beam on Pasternak Foundation
Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag
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The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.Keywords: curved beam, dynamic analysis, elastic foundation, finite element method
Procedia PDF Downloads 3366106 Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method
Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger
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Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model
Procedia PDF Downloads 1876105 Nonlinear Finite Element Modeling of Deep Beam Resting on Linear and Nonlinear Random Soil
Authors: M. Seguini, D. Nedjar
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An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.Keywords: finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability
Procedia PDF Downloads 4106104 The Effect of Arbitrary Support Conditions on the Static Behavior of Curved Beams Using the Finite Element Method
Authors: Hossein Mottaghi T., Amir R. Masoodi
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This study presents a finite curved element for analyzing the static behavior of curved beams within the elastic range. The objective is to enhance accuracy while reducing the number of elements by incorporating first-order shear deformations of Timoshenko beams. Initially, finite element formulations are developed by considering polynomial initial functions for axial, shear, and rotational deformations for a three-node element. Subsequently, nodal interpolation functions for this element are derived, followed by the construction of the element stiffness matrix. To enable the utilization of the stiffness matrix in the static analysis of curved beams, the constructed matrix in the local coordinates of the element is transformed to the global coordinate system using the rotation matrix. A numerical benchmark example is investigated to assess the accuracy and effectiveness of this method. Moreover, the influence of spring stiffness on the rotation of the endpoint of a clamped beam is examined by substituting each support reaction of the beam with a spring. In the parametric study, the effect of the central angle of the beam on the rotation of the beam's endpoint in a cantilever beam under a concentrated load is examined. This research encompasses various mechanical, geometrical, and boundary configurations to evaluate the static characteristics of curved beams, thus providing valuable insights for their analysis and examination.Keywords: curved beam, finite element method, first-order shear deformation theory, elastic support
Procedia PDF Downloads 446103 Elastic Stress Analysis of Composite Cantilever Beam Loaded Uniformly
Authors: Merve Tunay Çetin, Ali Kurşun, Erhan Çetin, Halil Aykul
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In this investigation an elastic stress analysis is carried out a woven steel fiber reinforced thermoplastic cantilever beam loaded uniformly at the upper surface. The composite beam material consists of low density polyethylene as a thermoplastic (LDFE, f.2.12) and woven steel fibers. Granules of the polyethylene is put into the moulds and they are heated up to 160°C by using electrical resistance. Subsequently, the material is held for 5min under 2.5 MPa at this temperature. The temperature is decreased to 30°C under 15 MPa pressure in 3 min. Closed form solution is found satisfying both the governing differential equation and boundary conditions. We investigated orientation angle effect on stress distribution of composite cantilever beams. The results show that orientation angle play an important role in determining the responses of a woven steel fiber reinforced thermoplastic cantilever beams and an optimal design of these structures.Keywords: cantilever beam, elastic stress analysis, orientation angle, thermoplastic
Procedia PDF Downloads 4956102 Self-Action Effects of a Non-Gaussian Laser Beam Through Plasma
Authors: Sandeep Kumar, Naveen Gupta
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The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing.Keywords: non-Gaussian beam, collisional plasma, variational theory, self-focusing
Procedia PDF Downloads 1896101 Nonlocal Beam Models for Free Vibration Analysis of Double-Walled Carbon Nanotubes with Various End Supports
Authors: Babak Safaei, Ahmad Ghanbari, Arash Rahmani
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In the present study, the free vibration characteristics of double-walled carbon nanotubes (DWCNTs) are investigated. The small-scale effects are taken into account using the Eringen’s nonlocal elasticity theory. The nonlocal elasticity equations are implemented into the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT) to analyze the free vibrations of DWCNTs in which each wall of the nanotubes is considered as individual beam with van der Waals interaction forces. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations of each nonlocal beam model along with four commonly used boundary conditions. Then molecular dynamics (MD) simulation is performed for a series of armchair and zigzag DWCNTs with different aspect ratios and boundary conditions, the results of which are matched with those of nonlocal beam models to extract the appropriate values of the nonlocal parameter corresponding to each type of chirality, nonlocal beam model and boundary condition. It is found that the present nonlocal beam models with their proposed correct values of nonlocal parameter have good capability to predict the vibrational behavior of DWCNTs, especially for higher aspect ratios.Keywords: double-walled carbon nanotubes, nonlocal continuum elasticity, free vibrations, molecular dynamics simulation, generalized differential quadrature method
Procedia PDF Downloads 2896100 Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions
Authors: Gholamreza Koochaki
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This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam
Procedia PDF Downloads 3876099 Estimation of Effective Mechanical Properties of Linear Elastic Materials with Voids Due to Volume and Surface Defects
Authors: Sergey A. Lurie, Yury O. Solyaev, Dmitry B. Volkov-Bogorodsky, Alexander V. Volkov
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The media with voids is considered and the method of the analytical estimation of the effective mechanical properties in the theory of elastic materials with voids is proposed. The variational model of the porous media is discussed, which is based on the model of the media with fields of conserved dislocations. It is shown that this model is fully consistent with the known model of the linear elastic materials with voids. In the present work, the generalized model of the porous media is proposed in which the specific surface properties are associated with the field of defects-pores in the volume of the deformed body. Unlike typical surface elasticity model, the strain energy density of the considered model includes the special part of the surface energy with the quadratic form of the free distortion tensor. In the result, the non-classical boundary conditions take modified form of the balance equations of volume and surface stresses. The analytical approach is proposed in the present work which allows to receive the simple enough engineering estimations for effective characteristics of the media with free dilatation. In particular, the effective flexural modulus and Poisson's ratio are determined for the problem of a beam pure bending. Here, the known voids elasticity solution was expanded on the generalized model with the surface effects. Received results allow us to compare the deformed state of the porous beam with the equivalent classic beam to introduce effective bending rigidity. Obtained analytical expressions for the effective properties depend on the thickness of the beam as a parameter. It is shown that the flexural modulus of the porous beam is decreased with an increasing of its thickness and the effective Poisson's ratio of the porous beams can take negative values for the certain values of the model parameters. On the other hand, the effective shear modulus is constant under variation of all values of the non-classical model parameters. Solutions received for a beam pure bending and the hydrostatic loading of the porous media are compared. It is shown that an analytical estimation for the bulk modulus of the porous material under hydrostatic compression gives an asymptotic value for the effective bulk modulus of the porous beam in the case of beam thickness increasing. Additionally, it is shown that the scale effects appear due to the surface properties of the porous media. Obtained results allow us to offer the procedure of an experimental identification of the non-classical parameters in the theory of the linear elastic materials with voids based on the bending tests for samples with different thickness. Finally, the problem of implementation of the Saint-Venant hypothesis for the transverse stresses in the porous beam are discussed. These stresses are different from zero in the solution of the voids elasticity theory, but satisfy the integral equilibrium equations. In this work, the exact value of the introduced surface parameter was found, which provides the vanishing of the transverse stresses on the free surfaces of a beam.Keywords: effective properties, scale effects, surface defects, voids elasticity
Procedia PDF Downloads 4046098 Influence of Hygro-Thermo-Mechanical Loading on Buckling and Vibrational Behavior of FG-CNT Composite Beam with Temperature Dependent Characteristics
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
Procedia PDF Downloads 2556097 The Continuously Supported Infinity Rail Subjected to a Moving Complex Bogie System
Authors: Vladimir Stojanović, Marko D. Petković
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The vibration of a complex bogie system that moves on along the high order shear deformable beam on a viscoelastic foundation is studied. The complex bogie system has been modeled by elastically connected rigid bars on an identical supports. Elastic coupling between bars is introduced to simulate rigidly or flexibly (transversal or/and rotational) connection. Identical supports are modeled as a system of attached spring and dashpot to the bar on one side and interact with the beam through the concentrated mass on the other side. It is assumed that the masses and the beam are always in contact. New analytically determined critical velocity of the system is presented. It is analyzed the case when the complex bogie system exceeds the minimum phase velocity of waves in the beam when the vibration of the system may become unstable. Effect of an elastic coupling between bars on the stability of the system has been analyzed. The instability regions are found for the complex bogie system by applying the principle of the argument and D-decomposition method.Keywords: Reddy-Bickford beam, D-decomposition method, principle of argument, critical velocity
Procedia PDF Downloads 3036096 Numerical Study of Elastic Performances of Sandwich Beam with Carbon-Fibre Reinforced Skins
Authors: Soukaina Ounss, Hamid Mounir, Abdellatif El Marjani
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Sandwich materials with composite reinforced skins are mostly required in advanced construction applications with a view to ensure resistant structures. Their lightweight, their high flexural stiffness and their optimal thermal insulation make them a suitable solution to obtain efficient structures with performing rigidity and optimal energy safety. In this paper, the mechanical behavior of a sandwich beam with composite skins reinforced by unidirectional carbon fibers is investigated numerically through analyzing the impact of reinforcements specifications on the longitudinal elastic modulus in order to select the adequate sandwich configuration that has an interesting rigidity and an accurate convergence to the analytical approach which is proposed to verify performed numerical simulations. Therefore, concerned study starts by testing flexion performances of skins with various fibers orientations and volume fractions to determine those to use in sandwich beam. For that, the combination of a reinforcement inclination of 30° and a volume ratio of 60% is selected with the one with 60° of fibers orientation and 40% of volume fraction, this last guarantees to chosen skins an important rigidity with an optimal fibers concentration and a great enhance in convergence to analytical results in the sandwich model for the reason of the crucial core role as transverse shear absorber. Thus, a resistant sandwich beam is elaborated from a face-sheet constituted from two layers of previous skins with fibers oriented in 60° and an epoxy core; concerned beam has a longitudinal elastic modulus of 54 Gpa (gigapascal) that equals to the analytical value by a negligible error of 2%.Keywords: fibers orientation, fibers volume ratio, longitudinal elastic modulus, sandwich beam
Procedia PDF Downloads 1596095 Second Harmonic Generation of Higher-Order Gaussian Laser Beam in Density Rippled Plasma
Authors: Jyoti Wadhwa, Arvinder Singh
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This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.
Procedia PDF Downloads 1756094 High-Pressure Calculations of the Elastic Properties of ZnSx Se 1−x Alloy in the Virtual-Crystal Approximation
Authors: N. Lebga, Kh. Bouamama, K. Kassali
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We report first-principles calculation results on the structural and elastic properties of ZnS x Se1−x alloy for which we employed the virtual crystal approximation provided with the ABINIT program. The calculations done using density functional theory within the local density approximation and employing the virtual-crystal approximation, we made a comparative study between the numerical results obtained from ab-initio calculation using ABINIT or Wien2k within the Density Functional Theory framework with either Local Density Approximation or Generalized Gradient approximation and the pseudo-potential plane-wave method with the Hartwigzen Goedecker Hutter scheme potentials. It is found that the lattice parameter, the phase transition pressure, and the elastic constants (and their derivative with respect to the pressure) follow a quadratic law in x. The variation of the elastic constants is also numerically studied and the phase transformations are discussed in relation to the mechanical stability criteria.Keywords: density functional theory, elastic properties, ZnS, ZnSe,
Procedia PDF Downloads 5696093 Flexural Behavior of Composite Hybrid Beam Models Combining Steel Inverted T-Section and RC Flange
Authors: Abdul Qader Melhem, Hacene Badache
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This paper deals with the theoretical and experimental study of shear connection via simple steel reinforcement shear connectors, which are steel reinforcing bars bent into L-shapes, instead of commonly used headed studs. This suggested L-shape connectors are readily available construction material in steel reinforcement. The composite section, therefore, consists of steel inverted T-section being embedded within a lightly reinforced concrete flange at the top slab as a unit. It should be noted that the cross section of these composite models involves steel inverted T-beam, replacing the steel top flange of a standard commonly employed I-beam section. The paper concentrates on the elastic and elastic-plastic behavior of these composite models. Failure modes either by cracking of concrete or shear connection be investigated in details. Elastic and elastoplastic formulas of the composite model have been computed for different locations of NA. Deflection formula has been derived, its value was close to the test value. With a supportive designing curve, this curve is valuable for both designing engineers and researchers. Finally, suggested designing curves and valuable equations will be presented. A check is made between theoretical and experimental outcomes.Keywords: composite, elastic-plastic, failure, inverted T-section, L-Shape connectors
Procedia PDF Downloads 2196092 Fem Models of Glued Laminated Timber Beams Enhanced by Bayesian Updating of Elastic Moduli
Authors: L. Melzerová, T. Janda, M. Šejnoha, J. Šejnoha
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Two finite element (FEM) models are presented in this paper to address the random nature of the response of glued timber structures made of wood segments with variable elastic moduli evaluated from 3600 indentation measurements. This total database served to create the same number of ensembles as was the number of segments in the tested beam. Statistics of these ensembles were then assigned to given segments of beams and the Latin Hypercube Sampling (LHS) method was called to perform 100 simulations resulting into the ensemble of 100 deflections subjected to statistical evaluation. Here, a detailed geometrical arrangement of individual segments in the laminated beam was considered in the construction of two-dimensional FEM model subjected to in four-point bending to comply with the laboratory tests. Since laboratory measurements of local elastic moduli may in general suffer from a significant experimental error, it appears advantageous to exploit the full scale measurements of timber beams, i.e. deflections, to improve their prior distributions with the help of the Bayesian statistical method. This, however, requires an efficient computational model when simulating the laboratory tests numerically. To this end, a simplified model based on Mindlin’s beam theory was established. The improved posterior distributions show that the most significant change of the Young’s modulus distribution takes place in laminae in the most strained zones, i.e. in the top and bottom layers within the beam center region. Posterior distributions of moduli of elasticity were subsequently utilized in the 2D FEM model and compared with the original simulations.Keywords: Bayesian inference, FEM, four point bending test, laminated timber, parameter estimation, prior and posterior distribution, Young’s modulus
Procedia PDF Downloads 2796091 Some Basic Problems for the Elastic Material with Voids in the Case of Approximation N=1 of Vekua's Theory
Authors: Bakur Gulua
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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable
Procedia PDF Downloads 1216090 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 2656089 Comparison of Two Theories for the Critical Laser Radius in Thermal Quantum Plasma
Authors: Somaye Zare
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The critical beam radius is a significant factor that predicts the behavior of the laser beam in the plasma, so if the laser beam radius is adequately greater in comparison to it, the beam will experience stable focusing on the plasma; otherwise, the beam will diverge after entering into the plasma. In this work, considering the paraxial approximation and moment theories, the localization of a relativistic laser beam in thermal quantum plasma is investigated. Using the dielectric function obtained in the quantum hydrodynamic model, the mathematical equation for the laser beam width parameter is attained and solved numerically by the fourth-order Runge-Kutta method. The results demonstrate that the stouter focusing effect is occurred in the moment theory compared to the paraxial approximation. Besides, similar to the two theories, with increasing Fermi temperature, plasma density, and laser intensity, the oscillation rate of the beam width parameter growths and focusing length reduces which means improving the focusing effect. Furthermore, it is understood that behaviors of the critical laser radius are different in the two theories, in the paraxial approximation, the critical radius after a minimum value is enhanced with increasing laser intensity, but in the moment theory, with increasing laser intensity, the critical radius decreases until it becomes independent of the laser intensity.Keywords: laser localization, quantum plasma, paraxial approximation, moment theory, quantum hydrodynamic model
Procedia PDF Downloads 676088 Analysis of Transverse Vibrations in Uniform Beams Subject to Different End Restraints
Authors: Falek Kamel
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Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory
Procedia PDF Downloads 786087 Free Vibration of Functionally Graded Smart Beams Based on the First Order Shear Deformation Theory
Authors: A. R. Nezamabadi, M. Veiskarami
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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration
Procedia PDF Downloads 4716086 Numerical Analysis of End Plate Bolted Connection with Corrugated Beam
Authors: M. A. Sadeghian, J. Yang, Q. F. Liu
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Steel extended end plate bolted connections are recommended to be widely utilized in special moment-resisting frame subjected to monotonic loading. Improper design of steel beam to column connection can lead to the collapse and fatality of structures. Therefore comprehensive research studies of beam to column connection design should be carried out. Also the performance and effect of corrugated on the strength of beam column end plate connection up to failure under monotonic loading in horizontal direction is presented in this paper. The non-linear elastic–plastic behavior has been considered through a finite element analysis using the multi-purpose software package LUSAS. The effect of vertically and horizontally types of corrugated web was also investigated.Keywords: corrugated beam, monotonic loading, finite element analysis, end plate connection
Procedia PDF Downloads 312