Search results for: differential actuated joints

Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf

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Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.

Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: P. Zamani, S. Mohajerzadeh, R. Masoudinejad, K. Farhangdoost

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The riveting process is one of the important ways to keep fastening the lap joints in aircraft structures. Failure of aircraft lap joints directly depends on the stress field in the joint. An important application of riveting process is in the construction of aircraft fuselage structures. In this paper, a 3D finite element method is carried out in order to optimize residual stress field in a riveted lap joint and also to estimate its fatigue life. In continue, a number of experiments are designed and analyzed using design of experiments (DOE). Then, Taguchi method is used to select an optimized case between different levels of each factor. Besides that, the factor which affects the most on residual stress field is investigated. Such optimized case provides the maximum residual stress field. Fatigue life of the optimized joint is estimated by Paris-Erdogan law. Stress intensity factors (SIFs) are calculated using both finite element analysis and experimental formula. In addition, the effect of residual stress field, geometry, and secondary bending are considered in SIF calculation. A good agreement is found between results of such methods. Comparison between optimized fatigue life and fatigue life of other joints has shown an improvement in the joint’s life.

Keywords: fatigue life, residual stress, riveting process, stress intensity factor, Taguchi method

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Authors: Mary Chriselda A

Abstract:

This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Malika Elkyal

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We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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Authors: H. Karakoc, A. Uzun, G. Kırmızı, H. Çinici, R. Çitak

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The main objective of this investigation was to apply friction welding for joining of AA7039 rods produced by powder metallurgy. Friction welding joints were carried out using a rotational friction welding machine. Friction welds were obtained under different rotational speeds between (2700 and 2900 rpm). The friction pressure of 10 MPa and friction time of 30 s was kept constant. The cross sections of joints were observed by optical microscopy. The microstructures were analyzed using scanning electron microscope/energy dispersive X-ray spectroscopy. The Vickers micro hardness measurement of the interface was evaluated using a micro hardness testing machine. Finally the results obtained were compared and discussed.

Keywords: Aluminum alloy, powder metallurgy, friction welding, microstructure

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Authors: T. Vamsee Kiran, A. Gopi

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The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

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Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Valentina Di Maria, Anton Ianakiev

Abstract:

The use of adhesive anchors for wooden constructions is an efficient technology to connect and design timber members in new timber structures and to rehabilitate the damaged structural members of historical buildings. Due to the lack of standard regulation in this specific area of structural design, designers’ choices are still supported by test analysis that enables knowledge, and the prediction, of the structural behavior of glued in rod joints. The paper outlines an experimental research activity aimed at identifying the tensile resistance capacity of several new adhesive joint prototypes made of epoxy resin, steel bar and timber, Oak and Douglas Fir species. The development of new adhesive connectors has been carried out by using epoxy to glue stainless steel bars into pre-drilled holes, characterized by smooth and rough internal surfaces, in timber samples. The realization of a threaded contact surface using a specific drill bit has led to an improved bond between wood and epoxy. The applied changes have also reduced the cost of the joints’ production. The paper presents the results of this parametric analysis and a Finite Element analysis that enables identification and study of the internal stress distribution in the proposed adhesive anchors.

Keywords: glued in rod joints, adhesive anchors, timber, epoxy, rough contact surface, threaded hole shape

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Authors: Jaskirat Singh, Roshan Lal Virdi, Khushdeep Goyal

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The purpose of this paper is to perform a microstructural analysis of Friction Stir Welded joints of aluminum alloys 6063 and 5083, also to check the properties of the weld zone by SEM analysis. FSW experiments were carried on CNC Vertical milling machine. The tools used for welding were the round cylindrical pin shape and square pin shape. It is found that Microstructure shows the uniformly distributed material with minimum heat affected zone and dense welded zone without any defect. Microstructures indicate that the weld material is defect free. The SEM shows the diffusion of material with base metal with proper bonding without any defect.

Keywords: friction stir welding, aluminum alloy, microstructure, SEM analysis

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Authors: Azadeh Jafari, Mohammad Taghi Karimi, Azadeh Nadi

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Background: Scoliosis is the lateral curvature of the spine which may influence the abilities of the subjects during standing and walking. Most of the scoliotic subjects use orthosis to reduce the curve and to decrease the risk of curve progression. There was lack of information regarding the effects of orthosis on kinematic and joint contact force. Therefore, this research was done to highlight the effects of orthosis on the aforementioned parameters. Method: 5 scoliotic subjects were recruited in this study, with single curve less than 40 (females with age 13.2 ± 1.7). They were asked to walk with and without orthosis. The kinematic of the joints, force applied on the legs, moments transmitted through the joints and joint contact forces were evaluated in this study. Moreover, the lengths of muscles were determined by use of computer muscle control approach in OpenSim. Results: There was a significant difference between the second peak of vertical ground reaction force while walking with and without orthosis (p-value < 0.05). There was no difference between spatiotemporal gait parameters while walking with and without orthosis (P-value > 0.05). The mean values of joint contact forces (vertical component) increased by the use of orthosis, but the difference was not significant (p-value > 0.05). Conclusion: Although the kinematic of most of the body joints was not influenced by the use of orthosis, the joint contact force may be increased by orthosis. The increase in joint contact force may be due to the performance of orthosis which restricts the motions of pelvic and increases compensatory mechanism used by the subjects to decrease the side effects of the orthosis.

Keywords: scoliosis, joint contact force, kinetic, kinematic

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Authors: Zachary Cooper-Baldock, Paulo E. Santos, Russell S. A. Brinkworth, Karl Sammut

Abstract:

In recent years, large unmanned underwater vehicles such as the Boeing Voyager and Anduril Ghost Shark have been developed. These vessels can be structured to contain onboard internal payload bays. These payload bays can serve a variety of purposes – including the launch and recovery (LAR) of smaller underwater vehicles. The LAR of smaller vessels is extremely important, as it enables transportation over greater distances, increased time on station, data transmission and operational safety. The larger vessel and its payload bay structure complicate the LAR of UUVs in contrast to static docks that are affixed to the seafloor, as they actively impact the local flow field. These flow field impacts require analysis to determine if UUV vessels can be safely launched and recovered inside the motherships. This research seeks to determine the hydrodynamic forces exerted on a vertically over-actuated, small, unmanned underwater vehicle (OUUV) during an internal LAR manoeuvre and compare this to an under-actuated vessel (UUUV). In this manoeuvre, the OUUV is navigated through the stern wake region of the larger vessel to a set point within the internal payload bay. The manoeuvre is simulated using ANSYS Fluent computational fluid dynamics models, covering the entire recovery of the OUUV and UUUV. The analysis of the OUUV is compared against the UUUV to determine the differences in the exerted forces. Of particular interest are the drag, pressure, turbulence and flow field effects exerted as the OUUV is driven inside the payload bay of the larger vessel. The hydrodynamic forces and flow field disturbances are used to determine the feasibility of making such an approach. From the simulations, it was determined that there was no significant detrimental physical forces, particularly with regard to turbulence. The flow field effects exerted by the OUUV are significant. The vertical thrusters exert significant wake structures, but their orientation ensures the wake effects are exerted below the UUV, minimising the impact. It was also seen that OUUV experiences higher drag forces compared to the UUUV, which will correlate to an increased energy expenditure. This investigation found no key indicators that recovery via a mothership payload bay was not feasible. The turbulence, drag and pressure phenomenon were of a similar magnitude to existing static and towed dock structures.

Keywords: underwater vehicles, submarine, autonomous underwater vehicles, AUV, computational fluid dynamics, flow fields, pressure, turbulence, drag

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Authors: Zachary Cooper-Baldock, Paulo E. Santos, Russell S. A. Brinkworth, Karl Sammut

Abstract:

- In recent years, large unmanned underwater vehicles such as the Boeing Voyager and Anduril Ghost Shark have been developed. These vessels can be structured to contain onboard internal payload bays. These payload bays can serve a variety of purposes – including the launch and recovery (LAR) of smaller underwater vehicles. The LAR of smaller vessels is extremely important, as it enables transportation over greater distances, increased time on station, data transmission and operational safety. The larger vessel and its payload bay structure complicate the LAR of UUVs in contrast to static docks that are affixed to the seafloor, as they actively impact the local flow field. These flow field impacts require analysis to determine if UUV vessels can be safely launched and recovered inside the motherships. This research seeks to determine the hydrodynamic forces exerted on a vertically over-actuated, small, unmanned underwater vehicle (OUUV) during an internal LAR manoeuvre and compare this to an under-actuated vessel (UUUV). In this manoeuvre, the OUUV is navigated through the stern wake region of the larger vessel to a set point within the internal payload bay. The manoeuvre is simulated using ANSYS Fluent computational fluid dynamics models, covering the entire recovery of the OUUV and UUUV. The analysis of the OUUV is compared against the UUUV to determine the differences in the exerted forces. Of particular interest are the drag, pressure, turbulence and flow field effects exerted as the OUUV is driven inside the payload bay of the larger vessel. The hydrodynamic forces and flow field disturbances are used to determine the feasibility of making such an approach. From the simulations, it was determined that there was no significant detrimental physical forces, particularly with regard to turbulence. The flow field effects exerted by the OUUV are significant. The vertical thrusters exert significant wake structures, but their orientation ensures the wake effects are exerted below the UUV, minimising the impact. It was also seen that OUUV experiences higher drag forces compared to the UUUV, which will correlate to an increased energy expenditure. This investigation found no key indicators that recovery via a mothership payload bay was not feasible. The turbulence, drag and pressure phenomenon were of a similar magnitude to existing static and towed dock structures.

Keywords: underwater vehicles, submarine, autonomous underwater vehicles, auv, computational fluid dynamics, flow fields, pressure, turbulence, drag

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Karim Akkouche

Abstract:

Many methods have been developed for characterizing the behavior of bolted joints. However, in the presence of a certain model of stiffeners, no orientation was given in relation to their modeling. To this end, multitude of coarse errors can arise in the reproduction of the propagation of efforts and in representation of the modes of deformations. Considering these particularities, a numerical investigation was carried out in our laboratory. In this paper we will present a comparative study between three types of assemblies. A non-linear 3D modeling was chosen, given that it takes into consideration geometric and material non-linearity, using the Finite Element calculation code ABAQUS. Initially, we evaluated the influence of the presence of each stiffener on the "global" behavior of the assemblies, this by analyzing their Moment-Rotation curves, also by referring to the classification system proposed by NF EN 1993- 1.8 which is based on the resisting moment Mj-Rd and the initial stiffness Sj.int. In a second step, we evaluated the "local" behavior of their components by referring to the stress-strain curves.

Keywords: assembly, post-beam, end plate, nonlinearity

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Authors: Vince Scolaro, Lakshman Prasad, Ted Polley, Sanjivan Deshpande

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The LH Ford Bridge, built in the 1960s, comprises 28 spans, is 800m long and crosses the Macquarie River at Dubbo, NSW. The main bridge spans comprise three spans with a 63m center span (25m drop-in section) supported by halving joints from the main cantilevers and back spans of 28m. The main bridge spans were built using complex construction staging (the first of this type in NSW). They comprise twin precast boxes, in-situ reinforced concrete infills, and cantilevered outriggers stressed both longitudinally and transversely. Since construction, this bridge has undergone significantly increased design vehicle loads and showed signs of excessive shrinkage and creep leading to significant sagging of the centre span with evidence of previous failure and remediation of the halving joints. A comprehensive load rating assessment was undertaken taking account of the original complex construction staging. Deficiencies identified included inadequate capacity of the halving joints, failure of the bearings at the halving joints, inadequate shear capacity of the girder webs and inadequate girder flexural capacity to carry B-Double design vehicles. A unique strengthening system comprising two new piers (under each of the halving joints), new bearings and installation of external prestressing to the soffit of both drop-in-span and back spans was adopted. A portion of the dead load had to be transferred from the superstructure to the new piers via innovative soft/stiff bearing combinations to reduce new locked-in stresses resulting from the new pier supports. Significant temporary works comprised a precast concrete shell beam forming the pile cap/pier structure, addition of a temporary suspended scaffold (without overstressing the existing superstructure) and the installation of jacking stays for new bearing top and bottom plates. This paper presents how this existing historic and socially important bridge was strengthened and updated to increase its design life without the need for replacement.

Keywords: strengthening, creep, construction, box girder

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Jiahe Liu, Hongyang Yu, Feng Qian, Miao Luo, Linhang Zhu

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This study proposed a 3D human body reconstruction method, which integrates multi-view joint information into a set of joints and processes it with a parametric human body template. Firstly, we obtained human body image information captured from multiple perspectives. The multi-view information can avoid self-occlusion and occlusion problems during the reconstruction process. Then, we used the MvP algorithm to integrate multi-view joint information into a set of joints. Next, we used the parametric human body template SMPL-X to obtain more accurate three-dimensional human body reconstruction results. Compared with the traditional single-view parametric human body template reconstruction, this method significantly improved the accuracy and stability of the reconstruction.

Keywords: parametric human body templates, reconstruction of the human body, multi-view, joint

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Authors: T. Teruzzi, S. Antonietti, C. Mosca, C. Paglia

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This paper discusses the causes of the structural failure in a tower crane. The structural collapse occurred at the upper joints of the extension element used to increase the height of the crane. The extension element consists of a steel lattice structure made with angular profiles and plates joined to the tower element by arc welding. Macroscopic inspection of the sections showed that the break was always observed on the angular profiles at the weld bead edge. The case study shows how, using mechanical characterization, chemical analysis of the steel and macroscopic and microscopic metallographic examinations, it was possible to obtain significant evidence that identified the mechanism causing the breakage. The analyses identified the causes of the structural failure as the use of materials that were not suitable for welding and poor performance in the welding joints.

Keywords: failure, metals, weld, microstructure

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Daniil Karzanov

Abstract:

This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Mircea I. Pastrav, Cornelia Baera, Florea Dinu

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A different concept for designing and detailing of reinforced concrete precast frame structures is analyzed in this paper. The new detailing of the joints derives from the special hybrid moment frame joints. The special reinforcements of this alternative detailing, named modified special hybrid joint, are bondless with respect to both column and beams. Full scale tests were performed on a plan model, which represents a part of 5 story structure, cropped in the middle of the beams and columns spans. Theoretical approach was developed, based on testing results on twice repaired model, subjected to lateral seismic type loading. Discussion regarding the modified special hybrid joint behavior and further on widening research needed concludes the presentation.

Keywords: modified hybrid joint, repair, seismic loading type, acceptance criteria

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Authors: Somveer Singh, Vineet Kumar Singh

Abstract:

This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Youssef Abdelli, Rachid Nasri

Abstract:

The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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