Search results for: Hirota Bilinear Method

Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

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In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

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Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

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The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

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Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Anthony Usoro

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In this paper, two classes of bilinear time series model are obtained under certain conditions from the general bilinear autoregressive moving average model. Bilinear Autoregressive (BAR) and Bilinear Moving Average (BMA) Models have been identified. From the general bilinear model, BAR and BMA models have been proved to exist for q = Q = 0, => j = 0, and p = P = 0, => i = 0 respectively. These models are found useful in modelling most of the economic and financial data.

Keywords: autoregressive model, bilinear autoregressive model, bilinear moving average model, moving average model

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Authors: Abdullah Eqal Al Mazrooei

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In this paper, we introduce a mathematical algorithm which is used for estimating the states in the bilinear systems. This algorithm uses a special linearization of the second-order term by using the best available information about the state of the system. This technique makes our algorithm generalizes the well-known Kalman estimators. The system which is used here is of the bilinear class, the evolution of this model is linear-bilinear in the state of the system. Our algorithm can be used with linear and bilinear systems. We also here introduced a real application for the new algorithm to prove the feasibility and the efficiency for it.

Keywords: estimation algorithm, bilinear systems, Kakman filter, second order linearization

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Authors: Abdullah E. Al-Mazrooei

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In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real measurements is introduced to illustrate the efficiency of the proposed algorithm.

Keywords: bilinear systems, state space model, Kalman filter, application, models

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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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: Zeyu Zhou, Xiaojun Bi

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Due to the limited environmental parameters and the limited resolution of the sensor, the universal existence of the mixed pixels in the process of remote sensing images restricts the spatial resolution of the remote sensing images. Sub-pixel mapping technology can effectively improve the spatial resolution. As the bilinear interpolation algorithm inevitably produces the edge blur effect, which leads to the inaccurate sub-pixel mapping results. In order to avoid the edge blur effect that affects the sub-pixel mapping results in the interpolation process, this paper presents a new edge-directed interpolation algorithm which uses the covariance adaptive interpolation algorithm on the edge of the low-resolution image and uses bilinear interpolation algorithm in the low-resolution image smooth area. By using the edge-directed interpolation algorithm, the super-resolution of the image with low resolution is obtained, and we get the percentage of each sub-pixel under a certain type of high-resolution image. Then we rely on the probability value as a soft attribute estimate and carry out sub-pixel scale under the ‘hard classification’. Finally, we get the result of sub-pixel mapping. Through the experiment, we compare the algorithm and the bilinear algorithm given in this paper to the results of the sub-pixel mapping method. It is found that the sub-pixel mapping method based on the edge-directed interpolation algorithm has better edge effect and higher mapping accuracy. The results of the paper meet our original intention of the question. At the same time, the method does not require iterative computation and training of samples, making it easier to implement.

Keywords: remote sensing images, sub-pixel mapping, bilinear interpolation, edge-directed interpolation

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Authors: Phuoc Si Nguyen

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Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: frequency transformation, bilinear z-transformation, pre-warping frequency, digital filters, analog filters, pascal’s triangle

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Authors: Yulong Jia, Xiang Zhang, Ziyuan Wu, Shiji Hu

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The calculation of bilinear pairing is the core of the SM9 algorithm, which relies on the underlying prime domain algorithm and the quadratic extension domain algorithm. Among the field algorithms, modular multiplication operation is the most time-consuming part. Therefore, the underlying modular multiplication algorithm is optimized to maximize the operation speed of bilinear pairings. This paper uses a modular multiplication method based on non-least positive (NLP) combined with Karatsuba and schoolbook multiplication to improve the Montgomery algorithm. At the same time, according to the characteristics of multiplication operation in the quadratic extension domain, a quadratic extension domain FP2-NLP modular multiplication algorithm for bilinear pairings is proposed, which effectively reduces the operation time of modular multiplication in the quadratic extension domain. The sub-expanded domain Fp₂ -NLP modular multiplication algorithm effectively reduces the operation time of modular multiplication under the second-expanded domain. The multiplication unit in the quadratic extension domain is implemented using SMIC55nm process, and two different implementation architectures are designed to cope with different application scenarios. Compared with the existing related literature, The output latency of this design can reach a minimum of 15 cycles. The shortest time for calculating the (AB+CD)r⁻¹ mod form is 37.5ns, and the comprehensive area-time product (AT) is 11400. The final R-ate pairing algorithm hardware accelerator consumes 2670k equivalent logic gates and 1.8ms computing time in 55nm process.

Keywords: sm9, hardware, NLP, Montgomery

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Authors: Abdullah Eqal Al Mazrooei

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In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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Authors: Kyeong Hoon Park, Taiji Mazuda

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High damping rubber (HDR) bearings are dissipating devices mainly used in seismic isolation systems and have a great damping performance. Although many studies have been conducted on the dynamic model of HDR bearings, few models can reflect phenomena such as dependency of experienced shear strain on initial history. In order to develop a model that can represent the dependency of experienced shear strain of HDR by Mullins effect, dynamic loading test was conducted using HDR specimen. The reaction of HDR was measured by applying a horizontal vibration using a hybrid actuator under a constant vertical load. Dynamic program analysis was also performed after dynamic loading test. The dynamic model applied in program analysis is a bilinear type double-target model. This model is modified from typical bilinear model. This model can express the nonlinear characteristics related to the initial history of HDR bearings. Based on the dynamic loading test and program analysis results, equivalent stiffness and equivalent damping ratio were calculated to evaluate the mechanical properties of HDR and the feasibility of the bilinear type double-target model was examined.

Keywords: base-isolation, bilinear model, high damping rubber, loading test

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Authors: Abderrhamane Jarou, Dominique Sauter, Christophe Aubrun

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Over the past decade, the growing demand for energy efficiency in buildings has attracted the attention of the control community. Failures in HVAC (heating, ventilation and air conditioning) systems in buildings can have a significant impact on the desired and expected energy performance of buildings and on the user's comfort as well. FTC is a recent technology area that studies the adaptation of control algorithms to faulty operating conditions of a system. The application of Fault-Tolerant Control (FTC) in HVAC systems has gained attention in the last two decades. The objective is to maintain the variations in system performance due to faults within an acceptable range with respect to the desired nominal behavior. This paper considers the so-called active approach, which is based on fault and identification scheme combined with a control reconfiguration algorithm that consists in determining a new set of control parameters so that the reconfigured performance is "as close as possible, "in some sense, to the nominal performance. Thermal models of buildings and their HVAC systems are described by non-linear (usually bi-linear) equations. Most of the works carried out so far in FDI (fault diagnosis and isolation) or FTC consider a linearized model of the studied system. However, this model is only valid in a reduced range of variation. This study presents a new fault diagnosis (FD) algorithm based on a bilinear observer for the detection and accurate estimation of the magnitude of the HVAC system failure. The main contribution of the proposed FD algorithm is that instead of using specific linearized models, the algorithm inherits the structure of the actual bilinear model of the building thermal dynamics. As an immediate consequence, the algorithm is applicable to a wide range of unpredictable operating conditions, i.e., weather dynamics, outdoor air temperature, zone occupancy profile. A bilinear fault detection observer is proposed for a bilinear system with unknown inputs. The residual vector in the observer design is decoupled from the unknown inputs and, under certain conditions, is made sensitive to all faults. Sufficient conditions are given for the existence of the observer and results are given for the explicit computation of observer design matrices. Dedicated observer schemes (DOS) are considered for sensor FDI while unknown input bilinear observers are considered for actuator or system components FDI. The proposed strategy for FTC works as follows: At a first level, FDI algorithms are implemented, making it also possible to estimate the magnitude of the fault. Once the fault is detected, the fault estimation is then used to feed the second level and reconfigure the control low so that that expected performances are recovered. This paper is organized as follows. A general structure for fault-tolerant control of buildings is first presented and the building model under consideration is introduced. Then, the observer-based design for Fault Diagnosis of bilinear systems is studied. The FTC approach is developed in Section IV. Finally, a simulation example is given in Section V to illustrate the proposed method.

Keywords: bilinear systems, fault diagnosis, fault-tolerant control, multi-zones building

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Authors: P. S. Jagadeesh Kumar, Yang Yung, Wenli Hu

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Speech emotion classification is a dominant research field in finding a sturdy and profligate classifier appropriate for different real-life applications. This effort accentuates on classifying different emotions from speech signal quarried from the features related to pitch, formants, energy contours, jitter, shimmer, spectral, perceptual and temporal features. Tensor deep stacking neural networks were supported to examine the factors that influence the classification success rate. Facial electromyography signals were composed of several forms of focuses in a controlled atmosphere by means of audio-visual stimuli. Proficient facial electromyography signals were pre-processed using moving average filter, and a set of arithmetical features were excavated. Extracted features were mapped into consistent emotions using bilinear mapping. With facial electromyography signals, a database comprising diverse emotions will be exposed with a suitable fine-tuning of features and training data. A success rate of 92% can be attained deprived of increasing the system connivance and the computation time for sorting diverse emotional states.

Keywords: speech emotion classification, tensor deep stacking neural networks, facial electromyography, bilinear mapping, audio-visual stimuli

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Authors: Wenjiang Deng, Tian Mou, Yudi Pawitan, Trung Nghia Vu

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Estimation of isoform-level gene expression from RNA-seq data depends on simplifying assumptions, such as uniform reads distribution, that are easily violated in real data. Such violations typically lead to biased estimates. Most existing methods provide a bias correction step(s), which is based on biological considerations, such as GC content–and applied in single samples separately. The main problem is that not all biases are known. For example, new technologies such as single-cell RNA-seq (scRNA-seq) may introduce new sources of bias not seen in bulk-cell data. This study introduces a method called XAEM based on a more flexible and robust statistical model. Existing methods are essentially based on a linear model Xβ, where the design matrix X is known and derived based on the simplifying assumptions. In contrast, XAEM considers Xβ as a bilinear model with both X and β unknown. Joint estimation of X and β is made possible by simultaneous analysis of multi-sample RNA-seq data. Compared to existing methods, XAEM automatically performs empirical correction of potentially unknown biases. XAEM implements an alternating expectation-maximization (AEM) algorithm, alternating between estimation of X and β. For speed XAEM utilizes quasi-mapping for read alignment, thus leading to a fast algorithm. Overall XAEM performs favorably compared to other recent advanced methods. For simulated datasets, XAEM obtains higher accuracy for multiple-isoform genes, particularly for paralogs. In a differential-expression analysis of a real scRNA-seq dataset, XAEM achieves substantially greater rediscovery rates in an independent validation set.

Keywords: alternating EM algorithm, bias correction, bilinear model, gene expression, RNA-seq

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Authors: R. Saini, R. Lal

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The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords: rectangular, non-homogeneous, bilinear thickness, generalized differential quadrature (GDQ)

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Authors: Hertzog Clara, Sakurai Sho, Hirota Koichi, Nojima Takuya

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It is common to see graphics appearing on television while watching a sports game to provide information, but it is less common to see graphics specifically aiming to boost spectators’ dynamism perception. It is even less common to see such graphics designed especially for virtual reality (VR). However, it appears that even with simple dynamic graphics, it would be possible to improve VR sports spectators’ experience. So, in this research, we explain how graphics can be used in VR to improve the dynamism of a broadcasted sports game and we provide a simple example. This example consists in a white halo displayed around the video and blinking according to the game speed. We hope to increase people’s awareness about VR sports spectating and the possibilities this display offers through dynamic graphics.

Keywords: broadcasting, graphics, sports spectating, virtual reality

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Authors: Milad Alizadeh Galdiani, Jabbar Ali Zakeri

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Lateral movement of CWR ballasted track occurs in sharp curves because of the lack of adequate lateral resistance. Several strategies have been proposed and used for increase the lateral resistance of ballasted tracks, but still there are some problems in tracks with small radius curves. In this paper, a new method has been presented for increase the lateral resistance. This method is using the lateral supports as numerical and field studies. In this paper, the field and laboratory tests have been conducted by using the single tie pressure test (STPT) and track panel loading test (LTPT). Then, their results were compared with the numerical results. The results of numerical and field tests showed that the lateral stiffness of ballasted tracks significantly increased when there were lateral supports in ballasted tracks. Also, the track structure had a bilinear behavior.

Keywords: ballasted railway, Lateral resistance, railway buckling, field and numerical studies

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Authors: Saeed Javaherzadeh, Babak Dindar Safa

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Structure, given its ductility, can depreciate significant amount of seismic energy in the form of hysteresis behavior; the amount of energy depreciation depends on the structure ductility rate. So in seismic guidelines such as ASCE7-10 code, to reduce the number of design forces and using the seismic energy dissipation capacity of structure, when entering non-linear behavior range of the materials, the response modification factor is used. Various parameters such as ductility modification factor, overstrength factor and reliability factor, are effective in determining the value of this factor. Also, gradually, energy dissipation systems, especially added dampers, have become an inseparable part of the seismic design. In this paper, in addition to reviewing of previous studies, using the response modification factor caused by using more added viscoelastic dampers, a new design method has introduced for steel moment-frame with added dampers installed. To do this, in addition to using bilinear behavior models and quick ways such as using the equivalent lateral force method and capacity spectrum method for the proposed design methodology, the results has been controlled with non-linear time history analysis for a number of structural. The analysis is done by Opensees Software.

Keywords: added viscoelastic damper, design base shear, response modification factor, non-linear time history

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Authors: Kenichi Hirota, Jifeng Wang, Sadao Araki, Koji Endo, Hideki Yamamoto

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Zirconium (Zr) has been used as a fuel cladding tube for nuclear reactors, because of the excellent corrosion resistance and the low adsorptive material for neutron. Generally speaking, the natural resource of Zr is often containing Hf that has similar properties. The content of Hf in the Zr resources is about 2~4 wt%. In the industrial use, the content of Hf in Zr resources should be lower than the 100 ppm. However, the separation of Zr and Hf is not so easy, because of similar chemical and physical properties such as melting point, boiling point and things. Solvent extraction method has been applied for the separation of Zr and Hf from Zr natural resources. This method can separate Hf with high efficiency (Hf < 100ppm), however, it needs much amount of organic solvents for solvent extraction and the cost of its disposal treatment is high. Therefore, we attached attention for the fractional crystallization. This separation method depends on the solubility difference of Zr and Hf in the solvent. In this work, hexafluorozirconate (hafnate) (K2Zr(Hf)F6) was used as model compound. Solubility of K2ZrF6 in water showed lower than that of K2HfF6. By repeating of this treatment, it is possible to purify Zr, practically. In this case, 16-18 times of recrystallization stages were needed for its high purification. The improvement of the crystallization process was carried out in this work. Water, hydrofluoric acid (HF) and hydrofluoric acid (HF) +hydrochloric acid (HCl) mixture were chosen as solvent for dissolution of Zr and Hf. In the experiment, 10g of K2ZrF6 was added to each solvent of 100mL. Each solution was heated for 1 hour at 353K. After 1h of this operation, they were cooled down till 293K, and were held for 5 hours at 273K. Concentration of Zr or Hf was measured using ICP analysis. It was found that Hf was separated from Zr-Hf mixed compound with high efficiency, when HF-HCl solution was used for solvent of crystallization. From the comparison of the particle size of each crystal by SEM, it was confirmed that the particle diameter of the crystal showed smaller size with decreasing of Hf content. This paper concerned with purification of Zr from Zr-Hf mixture using crystallization method.

Keywords: crystallization, zirconium, hafnium, separation

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Authors: Moch Agus Choiron

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Crash box design has been developed to obtain optimum energy absorption. In this study, two-segment crash box design with holes is investigated under oblique load. The deformation behavior and crash energy absorption are observed. The analysis was performed using finite element method. The crash test components were impactor, crash box, and fixed rigid base. Impactor and the fixed base material are modelled as a rigid, and crash box material as bilinear isotropic hardening. The models consist of 2 and 4 holes laid within ¼, ½ and ¾ from first segment length. 100 mm aluminum crash box and frontal crash velocity of 16 km/jam were selected. Based on simulation results, it can be concluded that 2 holes located at ¾ has the largest crash energy absorption. This behavior associated with deformation pattern, which produces higher number of folding than other models.

Keywords: crash Box, two-segments, holes configuration, oblique load, deformation pattern

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Authors: Shingo Murakami, Shinichi Enoki

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

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

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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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Authors: Magdy G. Asaad

Abstract:

Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted.

Keywords: Pfaffian solutions, N-soliton solutions, soliton equations, Jimbo-Miwa

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Authors: S. A. Naeini, A. Mahigir

Abstract:

Naturally occurring cohesive soil deposits are inherently anisotropic with respect to different properties amongst which is the shear strength. The anisotropy is primary due to the process of sedimentation followed by predominantly one-dimensional consolidation. However, most soils in their natural states exhibit some anisotropy with respect to shear strength and some non-homogeneity with respect to depth. In this paper the standard Mohr-Coulomb yield criterion was modified to consider the anisotropic shear strength properties. The term non-homogeneity used in this paper refers to only the cohesion intercept which is assumed to vary linearly with depth. The effect of both anisotropy and deterministic non-homogeneity on bearing capacity of shallow foundation was investigated using finite difference method. Result of numerical analysis indicates that the cohesion anisotropy has a significant effect on bearing capacity of shallow foundation. Furthermore, the linear and bilinear heterogeneity affects the bearing capacity in a similar way although the anisotropy issue emerges to be more important as far as shallow foundations are considered.

Keywords: anisotropic ratio, finite difference analysis, bearing capacity, heterogeneity

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