Search results for: linear algebraic method

Authors: Jay-R M. Mendoza

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In almost all mathematics classrooms, students demonstrated discrepancies in their knowledge, skills, and understanding. OECD reports predicted that this continued to aggravate as not all teachers were sufficiently trained to handle this concentration. In response, the paper explored the potential of reSolve’s professional learning module 3 (PLM3) as an affordable and accessible professional development (PD) resource. Participants’ hands-on experience and exposure to PLM3 were audio recorded. After it was transcribed and examined and their work samples were analysed, there were four issues emerged: (1) criticality of conducting preliminary data collections and increasing the validity of inferences about what students can and cannot do by addressing the probabilistic nature of their performance; (2) criticality of the conclusion: a > b and/or (a-b) ∈ Z⁺ among students’ algebraic reasoning; (3) enabling and extending prompts provided by reSolve were found useful; and (4) dynamic adaptation of reSolve PLM3 through developing transferable skills and collaboration among teachers. PLM3 provided valuable insights on assessment, teaching, and planning to include all students in mathematics experiences.

Keywords: algebraic reasoning, building teacher capacity, including all students in mathematics experiences, professional development

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Joon-Hoon Park

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The fundamental concept of observability is important in both theoretical and practical points of modern control systems. In modern control theory, a control system has criteria for determining the design solution exists for the system parameters and design objectives. The idea of observability relates to the condition of observing or estimating the state variables from the output variables that is generally measurable. To design closed-loop control system, the practical problems of implementing the feedback of the state variables must be considered and implementing state feedback control problem has been existed in this case. All the state variables are not available, so it is requisite to design and implement an observer that will estimate the state variables form the output parameters. However sometimes unknown inputs are presented in control systems as practical cases. This paper presents a design method and algorithm for observer of control system with unknown input parameters based on Rationalized Haar transform. The proposed method is more advantageous than the other numerical method.

Keywords: orthogonal functions, rationalized Haar transforms, control system observer, algebraic method

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Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Xuezhang Hou

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A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained.

Keywords: partial differential equations, flexible lamina, variable structural control, semigroup of linear operators

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Authors: Kaushalendra K. Khadanga, Lee Hee Hyol

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Passenger comfort has been paramount in the design of suspension systems of high speed cars. To analyze the effect of vibration on vehicle ride quality, a vertical model of a six degree of freedom railway passenger vehicle, with front and rear suspension, is built. It includes car body flexible effects and vertical rigid modes. A second order linear shaping filter is constructed to model Gaussian white noise into random rail excitation. The temporal correlation between the front and rear wheels is given by a second order Pade approximation. The complete track and the vehicle model are then designed. An active secondary suspension system based on a Linear Quadratic Gaussian (LQG) optimal control method is designed. The results show that the LQG control method reduces the vertical acceleration, pitching acceleration and vertical bending vibration of the car body as compared to the passive system.

Keywords: active suspension, bending vibration, railway vehicle, vibration control

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

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In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: autonomous vehicles, convoy, non-linear control, non-linear observer, sliding mode

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: K. Szymkowska, K. Mojsiewicz- Pieńkowska

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Siloxanes are a common ingredients in medicinal products used on the skin, as well as cosmetics. It is widely believed that the silicones are not capable of overcoming the skin barrier. The aim of the study was to verify the possibility of penetration and permeation of linear siloxanes through human skin and determine depth penetration limit of these compounds. Based on the results it was found that human skin is not a barrier for linear siloxanes. PDMS 50 cSt was not identified in the dermis suggests that this molecular size of silicones (3780Da) is safe when it is used in the skin formulations.

Keywords: linear siloxanes, methyl siloxanes, skin penetration, skin permeation

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Authors: Sebastian Töpfer, Marta Gilaberte Basset, Jorge Fuenzalida, Fabian Steinlechner, Juan P. Torres, Markus Gräfe

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This work introduces a combination of digital phase-shifting holography with a non-linear interferometer using undetected photons. Non-linear interferometers can be used in combination with a measurement scheme called quantum imaging with undetected photons, which allows for the separation of the wavelengths used for sampling an object and detecting it in the imaging sensor. This method recently faced increasing attention, as it allows to use of exotic wavelengths (e.g., mid-infrared, ultraviolet) for object interaction while at the same time keeping the detection in spectral areas with highly developed, comparable low-cost imaging sensors. The object information, including its transmission and phase influence, is recorded in the form of an interferometric pattern. To collect these, this work combines the method of quantum imaging with undetected photons with digital phase-shifting holography with a minimal sampling of the interference. With this, the quantum imaging scheme gets extended in its measurement capabilities and brings it one step closer to application. Quantum imaging with undetected photons uses correlated photons generated by spontaneous parametric down-conversion in a non-linear interferometer to create indistinguishable photon pairs, which leads to an effect called induced coherence without induced emission. Placing an object inside changes the interferometric pattern depending on the object’s properties. Digital phase-shifting holography records multiple images of the interference with determined phase shifts to reconstruct the complete interference shape, which can afterward be used to analyze the changes introduced by the object and conclude its properties. An extensive characterization of this method was done using a proof-of-principle setup. The measured spatial resolution, phase accuracy, and transmission accuracy are compared for different combinations of camera exposure times and the number of interference sampling steps. The current limits of this method are shown to allow further improvements. To summarize, this work presents an alternative holographic measurement method using non-linear interferometers in combination with quantum imaging to enable new ways of measuring and motivating continuing research.

Keywords: digital holography, quantum imaging, quantum holography, quantum metrology

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

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The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: super harmonic resonances, non-linear vibration, axially moving beam, Galerkin method

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Authors: Wen-Yuh Jywe, Bor-Jeng Lin, Jing-Chung Shen, Jeng-Dao Lee, Hsueh-Liang Huang, Tung-Hsien Hsieh

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In this study, a simple 2-D measurement system based on optical design was developed to measure the motion errors of the linear guideway. Compared with the transitional methods about the linear guideway for measuring the motion errors, our proposed 2-D optical measurement system can simultaneously measure horizontal and vertical running straightness errors for the linear guideway. The performance of the 2-D optical measurement system is verified by experimental results. The standard deviation of the 2-D optical measurement system is about 0.4 μm in the measurement range of 100 mm. The maximum measuring speed of the proposed automatic measurement instrument is 1 m/sec.

Keywords: 2-D measurement, linear guideway, motion errors, running straightness

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Authors: Mohammad Beyki, Justus Pawlak, Robert Patzke, Franz Renz

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In the context of planetary exploration, the MIMOS II (miniaturized Mössbauer spectrometer) serves as a proven and reliable measuring instrument. The transmission behaviour of the electronics in the Mössbauer spectroscopy is newly developed and optimized. For this purpose, the overall electronics is split into three parts. This elaboration deals exclusively with the first part of the signal chain for the evaluation of photons in experiments with gamma radiation. Parallel to the analysis of the electronics, a new method for the stability consideration of linear and non-linear systems is presented: The extended method of Lyapunov’s stability criteria. The design helps to weigh advantages and disadvantages against other simulated circuits in order to optimize the MIMOS II for the terestric and extraterestric measurment. Finally, after stability analysis, the controller design according to Ackermann is performed, achieving the best possible optimization of the output variable through a skillful pole assignment.

Keywords: Mössbauer spectroscopy, electronic signal amplifier, light processing technology, photocurrent, trans-impedance amplifier, extended Lyapunov method

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Authors: H. Y. Jung, Ju H. Park, S. M. Lee

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A sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The sector bounded nonlinear systems, which have a feedback connection with a linear dynamical system and nonlinearity satisfying certain sector type constraints. Also, the sampled-data control scheme is very useful since it is possible to handle digital controller and increasing research efforts have been devoted to sampled-data control systems with the development of modern high-speed computers. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: sampled-data control, fuel cell, linear matrix inequalities, nonlinear control

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Authors: Davide Forcellini, James Marshal Kelly

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Seismic isolation using multi-layer elastomeric isolators has been used in the United States for more than 20 years. Although isolation bearings normally have a large factor of safety against buckling due to low shear stiffness, this phenomenon has been widely studied. In particular, the linearly elastic theory adopted to study this phenomenon is relatively accurate and adequate for most design purposes. Unfortunately it cannot consider the large deformation response of a bearing when buckling occurs and the unresolved behaviour of the stability of the post-buckled state. The study conducted in this paper may be viewed as a development of the linear theory of multi-layered elastomeric bearing, simply replacing the differential equations by algebraic equations, showing how it is possible to evaluate the post-buckling behaviour and the interactions at large deformations.

Keywords: multi-layer elastomeric isolators, large deformation, compressive load, tensile load, post-buckling behaviour

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Authors: Jui-Pui Hung, Yong-Run Chen, Wei-Cheng Shih, Chun-Wei Lin

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This study was aimed to assess the variations of the modal characteristics of the feeding stage with different linear guide modulus. The dynamic characteristics of the feeding stage were characterized in terms of the modal stiffness, modal frequency and modal damping, which are assessed from the vibration tests. According to the experimental measurements, the actual preload of the linear guide modulus was found to deviate from the rated values as setting in factory. This may be due to the assemblage errors of guide modules. For the stage with linear guides, the dynamic stiffness was affected to change by the preload set on the rolling balls. The variation of the dynamic stiffness at first and second modes is 20.8 and 10.5%, respectively when the linear guide preload is adjusted from medium and high amount. But the modal damping ratio is reduced by 8.97 and 9.65%, respectively. For high-frequency mode, the modal stiffness increases by 171.2% and the damping ratio reduced by 34.4%. Current results demonstrate the importance in the determining the preloaded amount of linear guide modulus in practical application.

Keywords: contact stiffness, feeding stage, linear guides, modal characteristics, pre-load

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

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This paper investigates stability problem for linear systems of neutral type with time-varying delay. By constructing various Lyapunov-Krasovskii functional, and utilizing some mathematical techniques, the sufficient stability conditions for the systems are established in terms of linear matrix inequalities (LMIs), which can be easily solved by various effective optimization algorithms. Finally, some illustrative examples are given to show the effectiveness of the proposed criterion.

Keywords: neutral systems, time-delay, stability, Lyapnov method, LMI

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Authors: Kelly F. Delgado-De Agrela, Sonia E. Ruiz, Marco A. Santos-Santiago

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An approach is proposed for the design of regular buildings equipped with non-linear viscous dissipating devices. The approach is based on a direct-displacement seismic design method which satisfies seismic performance objectives. The global system involved is formed by structural regular moment frames capable of supporting gravity and lateral loads with elastic response behavior plus a set of non-linear viscous dissipating devices which reduce the structural seismic response. The dampers are characterized by two design parameters: (1) a positive real exponent α which represents the non-linearity of the damper, and (2) the damping coefficient C of the device, whose constitutive force-velocity law is given by F=Cvᵃ, where v is the velocity between the ends of the damper. The procedure is carried out using a substitute structure. Two limits states are verified: serviceability and near collapse. The reduction of the spectral ordinates by the additional damping assumed in the design process and introduced to the structure by the viscous non-linear dampers is performed according to a damping reduction factor. For the design of the non-linear damper system, the real velocity is considered instead of the pseudo-velocity. The proposed design methodology is applied to an 8-story steel moment frame building equipped with non-linear viscous dampers, located in intermediate soil zone of Mexico City, with a dominant period Tₛ = 1s. In order to validate the approach, nonlinear static analyses and nonlinear time history analyses are performed.

Keywords: based design, direct-displacement based design, non-linear viscous dampers, performance design

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Authors: Azam Mohammadbagheri, Bahram Fathi

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DEA has become a very popular method of performance measure, but it still suffers from some shortcomings. One of these shortcomings is the issue of having multiple optimal solutions to weights for efficient DMUs. The cross efficiency evaluation as an extension of DEA is proposed to avoid this problem. Lam (2010) is also proposed a mixed-integer linear programming formulation based on linear discriminate analysis and super efficiency method (MILP model) to avoid having multiple optimal solutions to weights. In this study, we modified MILP model to determine more suitable weight sets and also evaluate the energy efficiency of MENA countries as an application of the proposed model.

Keywords: data envelopment analysis, discriminate analysis, cross efficiency, MILP model

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: Ismail Tas, Yusuf Ersoy Yildirim, Yavuz Fatih Fidantemiz, Aysegul Boyacioglu, Demet Uygan, Ozgur Ates, Erdinc Savasli, Oguz Onder, Murat Tugrul

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The biggest input of agricultural production is irrigation, water and energy. Although it varies according to the conditions in drip and sprinkler irrigation systems compared to surface irrigation systems, there is a significant amount of energy expenditure. However, this expense not only increases the user's control over the irrigation water but also provides an increase in water savings and water application efficiency. Thus, while irrigation water is used more effectively, it also contributes to reducing production costs. The Mobile Drip Irrigation System (MDIS) is a system in which new technologies are used, and it is one of the systems that are thought to play an important role in increasing the irrigation water utilization rate of plants and reducing water losses, as well as using irrigation water effectively. MDIS is currently considered the most effective method for irrigation, with the development of both linear and central motion systems. MDIS is potentially more advantageous than sprinkler irrigation systems in terms of reducing wind-induced water losses and reducing evaporation losses on the soil and plant surface. Another feature of MDIS is that the sprinkler heads on the systems (such as the liner and center pivot) can remain operational even when the drip irrigation system is installed. This allows the user to use both irrigation methods. In this study, the effect of MDIS and linear sprinkler irrigation method on sugar beet yield at different irrigation water levels will be revealed.

Keywords: MDIS, linear sprinkler, sugar beet, irrigation efficiency

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Authors: Min-Su Song, Haeng-Bok Kil, Eui-Rim Jeong

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This paper proposes a new method to reduce the overhead by pilots for single carrier frequency domain equalization (SC-FDE) transmission. In the conventional SC-FDE transmission structure, the overhead by transmitting pilot is heavy because the pilot are transmitted at every SC-FDE block. The proposed SC-FDE structure has fewer pilots and many SC-FCE blocks are transmitted between pilots. The channel estimation and equalization is performed at the pilot period and the channels between pilots are estimated through linear interpolation. This reduces the pilot overhead by reducing the pilot transmission compared with the conventional structure, and enables reliable channel estimation and equalization.

Keywords: channel estimation, linear interpolation, pilot overhead, SC-FDE

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Authors: Jude K. Safo

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Knowledge Graphs KG) and their relation to Graph Embeddings (GE) represent a unique data structure in the landscape of machine learning (relative to image, text and acoustic data). Unlike the latter, GEs are the only data structure sufficient for representing hierarchically dense, semantic information needed for use-cases like supply chain data and protein folding where the search space exceeds the limits traditional search methods (e.g. page-rank, Dijkstra, etc.). While GEs are effective for compressing low rank tensor data, at scale, they begin to introduce a new problem of ’data retreival’ which we observe in Large Language Models. Notable attempts by transE, TransR and other prominent industry standards have shown a peak performance just north of 57% on WN18 and FB15K benchmarks, insufficient practical industry applications. They’re also limited, in scope, to next node/link predictions. Traditional linear methods like Tucker, CP, PARAFAC and CANDECOMP quickly hit memory limits on tensors exceeding 6.4 million nodes. This paper outlines a topological framework for linear mapping between concepts in KG space and GE space that preserve cardinality. Most importantly we introduce a traceable framework for composing dense linguistic strcutures. We demonstrate performance on WN18 benchmark this model hits. This model does not rely on Large Langauge Models (LLM) though the applications are certainy relevant here as well.

Keywords: representation theory, large language models, graph embeddings, applied algebraic topology, applied knot theory, combinatorics

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Authors: D. Erdenechimeg, T. Bujinlkham, N. Erdenepurev

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The anti-corrosion performance of fatty acid coated mild steel samples is studied. Samples of structural steel coated with collector reagents deposited from surfactant in ethanol solution and overcoated with an epoxy barrier paint. A quantitative corrosion rate was determined by linear polarization resistance method using biopotentiostat/galvanostat 400. Coating morphology was determined by scanning electronic microscopy. A test for hydrophobic surface of steel by surfactant was done. From the samples, the main component or high content iron was determined by chemical method and other metal contents were determined by Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) method. Prior to measuring the corrosion rate, mechanical and chemical treatments were performed to prepare the test specimens. Overcoating the metal samples with epoxy barrier paint after exposing them with surfactant the corrosion rate can be inhibited by 34-35 µm/year.

Keywords: corrosion, linear polarization resistance, coating, surfactant

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Authors: J. Jena, Monica Saxena

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In this paper, the propagation of weak nonlinear waves in non-equilibrium flow has been studied in detail using the perturbation method. The expansive action of receding piston undergoing infinite acceleration has been discussed. Central expansion fan, compression waves and shock fronts have been discussed and the solutions up to the first order in the characteristic plane and physical plane have been obtained.

Keywords: Characteristic wave front, weak non-linear waves, central expansion fan, compression waves

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Authors: Ayhan Ince

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In this paper, an analytical simplified method for calculating elasto-plastic stresses strains of notched bodies subject to non-proportional loading paths is discussed. The method was based on the Neuber notch correction, which relates the incremental elastic and elastic-plastic strain energy densities at the notch root and the material constitutive relationship. The validity of the method was presented by comparing computed results of the proposed model against finite element numerical data of notched shaft. The comparison showed that the model estimated notch-root elasto-plastic stresses strains with good accuracy using linear-elastic stresses. The prosed model provides more efficient and simple analysis method preferable to expensive experimental component tests and more complex and time consuming incremental non-linear FE analysis. The model is particularly suitable to perform fatigue life and fatigue damage estimates of notched components subjected to non-proportional loading paths.

Keywords: elasto-plastic, stress-strain, notch analysis, nonprortional loadings, cyclic plasticity, fatigue

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Authors: Martin Cermak, Stanislav Sysala

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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MATLAB.

Keywords: isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution

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Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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