Search results for: nonlinear equation

Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculating the pressure losses in the real lungs is due to its complexity and diversity lengthy and inefficient process. For these calculations is necessary the lungs to slightly simplify (same cross-section over the length of individual generation) or use one of the models of lungs. The simplification could cause deviations from real values. The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli equation and continuity equation. Then, evaluate the desirability of using this formula to determine the pressure loss across the bronchial tree.

Keywords: pressure gradient, airways resistance, real geometry of bronchial tree, breathing

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Authors: M. R. Bekli, N. Mebarki, I. Chadou

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In this study, we focus on the structure functions and violation of scale invariance in the context of non-commutative standard model (NCSM). We find that this violation appears in the first order of perturbation theory and a non-commutative version of the DGLAP evolution equation is deduced. Numerical analysis and comparison with experimental data imposes a new bound on the non-commutative parameter.

Keywords: NCSM, structure function, DGLAP equation, standard model

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Authors: Haider M. Alsaeq

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The present research is an attempt to figure out the best configuration of composite cylindrical shells of the sandwich type, i.e. the lightest design of such shells required to sustain a certain load over a certain area. The optimization is based on elastic-plastic geometrically nonlinear incremental-iterative finite element analysis. The nine-node degenerated curved shell element is used in which five degrees of freedom are specified at each nodal point, with a layered model. The formulation of the geometrical nonlinearity problem is carried out using the well-known total Lagrangian principle. For the structural optimization problem, which is dealt with as a constrained nonlinear optimization, the so-called Modified Hooke and Jeeves method is employed by considering the weight of the shell as the objective function with stress and geometrical constraints. It was concluded that the optimum design of composite sandwich cylindrical shell that have a rigid polyurethane foam core and steel facing occurs when the area covered by the shell becomes almost square with a ratio of core thickness to facing thickness lies between 45 and 49, while the optimum height to length ration varies from 0.03 to 0.08 depending on the aspect ratio of the shell and its boundary conditions.

Keywords: composite structure, cylindrical shell, optimization, non-linear analysis, finite element

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Authors: F. Sabri, J. Jamali

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In this article, the wrinkling failure of orthotropic composite membranes due to in-plane shear deformation is investigated using nonlinear finite element analyses. A nonlinear post-buckling analysis is performed to show the evolution of shear-induced wrinkles. The method of investigation is based on the post-buckling finite element analysis adopted from commercial FEM code; ANSYS. The resulting wrinkling patterns, their amplitude and their wavelengths under the prescribed loads and boundary conditions were confirmed by experimental results. Our study reveals that wrinkles develop when both the magnitudes and coverage of the minimum principal stresses in the laminated composite laminates are sufficiently large to trigger wrinkling.

Keywords: composite, FEM, membrane, wrinkling

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

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Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle-based method, hyper-elasticity, analysis of stability

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Andrzej Mitura, Krzysztof Kecik, Michal Augustyniak

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This paper presents a numerical and experimental research of a nonlinear two degrees of freedom system. The tested system consists of a mechanical oscillator (the primary subsystem) with the attached pendulum (the secondary subsystem). The oscillator is suspended on a linear (or nonlinear) coil spring and a nonlinear magnetorheorogical damper and it is excited kinematically. Added pendulum can be used to reduce vibration of a primary subsystem or to energy harvesting. The numerical and experimental investigations showed that the pendulum can perform several types of motion, for example: chaotic motion, constant position in lower or upper (stable inverted pendulum), rotation, symmetrical or asymmetrical swinging vibrations. The main objective of this study is to determine an influence of system parameters for increasing the zone when the pendulum rotates. As a final effect a semi-active control method to change the pendulum solution on the rotation is proposed. To the implementation of this method the magnetorheorogical damper is applied. Continuous rotation of the pendulum is desirable for recovery of energy. The work is financed by Grant no. 0234/IP2/2011/71 from the Polish Ministry of Science and Higher Education in years 2012-2014.

Keywords: autoparametric vibrations, chaos and rotation control, magnetorheological damper

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Authors: Marlon Gallo, Eduardo Miguel, Laura Oca, Eneko Gonzalez, Unai Iraola

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The heat generation of an energy storage system is an essential topic when designing a battery pack and its cooling system. Heat generation estimation is used together with thermal models to predict battery temperature in operation and adapt the design of the battery pack and the cooling system to these thermal needs guaranteeing its safety and correct operation. In the present work, a comparison between the use of a heat flux sensor (HFS) for indirect measurement of heat losses in a cell and the widely used and simplified version of Bernardi’s equation for estimation is presented. First, a Li-ion cell is thermally characterized with an HFS to measure the thermal parameters that are used in a first-order lumped thermal model. These parameters are the equivalent thermal capacity and the thermal equivalent resistance of a single Li-ion cell. Static (when no current is flowing through the cell) and dynamic (making current flow through the cell) tests are conducted in which HFS is used to measure heat between the cell and the ambient, so thermal capacity and resistances respectively can be calculated. An experimental platform records current, voltage, ambient temperature, surface temperature, and HFS output voltage. Second, an equivalent circuit model is built in a Matlab-Simulink environment. This allows the comparison between the generated heat predicted by Bernardi’s equation and the HFS measurements. Data post-processing is required to extrapolate the heat generation from the HFS measurements, as the sensor records the heat released to the ambient and not the one generated within the cell. Finally, the cell temperature evolution is estimated with the lumped thermal model (using both HFS and Bernardi’s equation total heat generation) and compared towards experimental temperature data (measured with a T-type thermocouple). At the end of this work, a critical review of the results obtained and the possible mismatch reasons are reported. The results show that indirectly measuring the heat generation with HFS gives a more precise estimation than Bernardi’s simplified equation. On the one hand, when using Bernardi’s simplified equation, estimated heat generation differs from cell temperature measurements during charges at high current rates. Additionally, for low capacity cells where a small change in capacity has a great influence on the terminal voltage, the estimated heat generation shows high dependency on the State of Charge (SoC) estimation, and therefore open circuit voltage calculation (as it is SoC dependent). On the other hand, with indirect measuring the heat generation with HFS, the resulting error is a maximum of 0.28ºC in the temperature prediction, in contrast with 1.38ºC with Bernardi’s simplified equation. This illustrates the limitations of Bernardi’s simplified equation for applications where precise heat monitoring is required. For higher current rates, Bernardi’s equation estimates more heat generation and consequently, a higher predicted temperature. Bernardi´s equation accounts for no losses after cutting the charging or discharging current. However, HFS measurement shows that after cutting the current the cell continues generating heat for some time, increasing the error of Bernardi´s equation.

Keywords: lithium-ion battery, heat flux sensor, heat generation, thermal characterization

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Authors: A. Mostafa

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This paper presents a numerical study on determination of ballistic limit velocity (V₅₀) of stainless steel 304 (SS 304) used in manufacturing security screens. The simulated ballistic impact tests were conducted on clamped sheets with different thicknesses using ABAQUS/Explicit nonlinear finite element (FE) package. The ballistic limit velocity was determined using three approaches, namely: numerical tests based on material properties, FE calculated residual velocities and FE calculated residual energies. Johnson-Cook plasticity and failure criterion were utilized to simulate the dynamic behaviour of the SS 304 under various strain rates, while the well-known Lambert-Jonas equation was used for the data regression for the residual velocity and energy model. Good agreement between the investigated numerical methods was achieved. Additionally, the dependence of the ballistic limit velocity on the sheet thickness was observed. The proposed approaches present viable and cost-effective assessment methods of the ballistic performance of SS 304, which will support the development of robust security screen systems.

Keywords: ballistic velocity, stainless steel, numerical approaches, security screen

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Authors: Jiya Mohammed, Tsadu Shuaib, Yusuf Abdulhakeem

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The research work focuses on the cases of MHD boundary layer flow past a stretching plate with heat transfer and viscous dissipation. The non-linear of momentum and energy equation are transform into ordinary differential equation by using similarity transformation, the resulting equation are solved using Adomian Decomposition Method (ADM). An attempt has been made to show the potentials and wide range application of the Adomian decomposition method in the comparison with the previous one in solving heat transfer problems. The Pade approximates value (η= 11[11, 11]) is use on the difficulty at infinity. The results are compared by numerical technique method. A vivid conclusion can be drawn from the results that ADM provides highly precise numerical solution for non-linear differential equations. The result where accurate especially for η ≤ 4, a general equating terms of Eckert number (Ec), Prandtl number (Pr) and magnetic parameter ( ) is derived which was used to investigate velocity and temperature profiles in boundary layer.

Keywords: MHD, Adomian decomposition, boundary layer, viscous dissipation

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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: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability

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Authors: Amar Khoukhi, Mohamed Shahab

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This paper presents the optimal control problem of mobile robot motion as a nonlinear programming problem (NLP) and solved using a direct method of numerical optimal control. The NLP is initialized with a B-Spline for which node locations are optimized using a genetic search. The system acceleration inputs and sampling periods are considered as optimization variables. Different scenarios with different objectives weights are implemented and investigated. Interesting results are found in terms of complying with the expected behavior of a mobile robot system and time-energy minimization.

Keywords: multi-objective control, non-holonomic systems, mobile robots, nonlinear programming, motion planning, B-spline, genetic algorithm

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Authors: Ali Albadri

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The logistics equation has never been used or studied in scientific fields outside the field of ecology. It has never been used to understand the behavior of a dynamic system of mechanical machines, like an escalator. We have studied the compatibility of the logistic map against real measurements from an escalator. This study has proven that there is good compatibility between the logistics equation and the experimental measurements. It has discovered the potential of a relationship between the fractal dimension and the non-linearity parameter, R, in the logistics equation. The fractal dimension increases as the R parameter (non-linear parameter) increases. It implies that the fractal dimension increases as the phase of the life span of the machine move from the steady/stable phase to the periodic double phase to a chaotic phase. The fractal dimension and the parameter R can be used as a tool to verify and check the health of machines. We have come up with a theory that there are three areas of behaviors, which they can be classified during the life span of a machine, a steady/stable stage, a periodic double stage, and a chaotic stage. The level of attention to the machine differs depending on the stage that the machine is in. The rate of faults in a machine increases as the machine moves through these three stages. During the double period and the chaotic stages, the number of faults starts to increase and become less predictable. The rate of predictability improves as our monitoring of the changes in the fractal dimension and the parameter R improves. The principles and foundations of our theory in this work have and will have a profound impact on the design of systems, on the way of operation of systems, and on the maintenance schedules of the systems. The systems can be mechanical, electrical, or electronic. The discussed methodology in this paper will give businesses the chance to be more careful at the design stage and planning for maintenance to control costs. The findings in this paper can be implied and used to correlate the three stages of a mechanical system to more in-depth mechanical parameters like wear and fatigue life.

Keywords: logistcs map, bifurcation map, fractal dimension, logistics equation

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Authors: Zhaojun Wang, Zongdi Sun, Qinqin Cui, Xingwan Ren

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Based on multivariate statistical analysis theory, this paper uses the principal component analysis method, Mahalanobis distance analysis method and fitting method to establish the photovoltaic health model to evaluate the health of photovoltaic panels. First of all, according to weather conditions, the photovoltaic panel variable data are classified into five categories: sunny, cloudy, rainy, foggy, overcast. The health of photovoltaic panels in these five types of weather is studied. Secondly, a scatterplot of the relationship between the amount of electricity produced by each kind of weather and other variables was plotted. It was found that the amount of electricity generated by photovoltaic panels has a significant nonlinear relationship with time. The fitting method was used to fit the relationship between the amount of weather generated and the time, and the nonlinear equation was obtained. Then, using the principal component analysis method to analyze the independent variables under five kinds of weather conditions, according to the Kaiser-Meyer-Olkin test, it was found that three types of weather such as overcast, foggy, and sunny meet the conditions for factor analysis, while cloudy and rainy weather do not satisfy the conditions for factor analysis. Therefore, through the principal component analysis method, the main components of overcast weather are temperature, AQI, and pm2.5. The main component of foggy weather is temperature, and the main components of sunny weather are temperature, AQI, and pm2.5. Cloudy and rainy weather require analysis of all of their variables, namely temperature, AQI, pm2.5, solar radiation intensity and time. Finally, taking the variable values in sunny weather as observed values, taking the main components of cloudy, foggy, overcast and rainy weather as sample data, the Mahalanobis distances between observed value and these sample values are obtained. A comparative analysis was carried out to compare the degree of deviation of the Mahalanobis distance to determine the health of the photovoltaic panels under different weather conditions. It was found that the weather conditions in which the Mahalanobis distance fluctuations ranged from small to large were: foggy, cloudy, overcast and rainy.

Keywords: fitting, principal component analysis, Mahalanobis distance, SPSS, MATLAB

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Authors: Murat Gunduz, Mustafa Ozdemir

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In this research, a framework is to be proposed to model the safety performance in construction sites. Determinants of safety performance are to be defined through extensive literature review and a multidimensional safety performance model is to be developed. In this context, a questionnaire is to be administered to construction companies with sites. The collected data through questionnaires including linguistic terms are then to be defuzzified to get concrete numbers by using fuzzy set theory which provides strong and significant instruments for the measurement of ambiguities and provides the opportunity to meaningfully represent concepts expressed in the natural language. The validity of the proposed safety performance model, relationships between determinants of safety performance are to be analyzed using the structural equation modeling (SEM) which is a highly strong multi variable analysis technique that makes possible the evaluation of latent structures. After validation of the model, a safety performance index assessment tool is to be proposed by the help of software. The proposed safety performance assessment tool will be based on the empirically validated theoretical model.

Keywords: Fuzzy set theory, safety performance assessment, safety index, structural equation modeling (SEM), construction sites

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Authors: Ga Ye Kim, Hee Sun Kim, Yeong Soo Shin

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Many studies have been done on the repair and strengthening method of concrete structure, so far. The traditional retrofit method was to attach fiber sheet such as CFRP (Carbon Fiber Reinforced Polymer), GFRP (Glass Fiber Reinforced Polymer) and AFRP (Aramid Fiber Reinforced Polymer) on the concrete structure. However, this method had many downsides in that there are a risk of debonding and an increase in displacement by a shortage of structure section. Therefore, it is effective way to enlarge the structural member with polymer mortar or Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) as a means of strengthening concrete structure. This paper intends to investigate structural performance of reinforced concrete (RC) beams enlarged with polymer mortar and compare the experimental results with analytical results. Nonlinear finite element analyses were conducted to compare the experimental results and predict structural behavior of retrofitted RC beams accurately without cost consuming experimental process. In addition, this study aims at comparing differences of retrofit material between commonly used material (polymer mortar) and recently used material (UHPFRC) by conducting nonlinear finite element analyses. In the first part of this paper, the RC beams having different cover type were fabricated for the experiment and the size of RC beams was 250 millimeters in depth, 150 millimeters in width and 2800 millimeters in length. To verify the experiment, nonlinear finite element models were generated using commercial software ABAQUS 6.10-3. From this study, both experimental and analytical results demonstrated good strengthening effect on RC beam and showed similar tendency. For the future, the proposed analytical method can be used to predict the effect of strengthened RC beam. In the second part of the study, the main parameters were type of retrofit materials. The same nonlinear finite element models were generated to compare the polymer mortar with UHPFRCC. Two types of retrofit material were evaluated and retrofit effect was verified by analytical results.

Keywords: retrofit material, polymer mortar, UHPFRC, nonlinear finite element analysis

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Authors: Armenuhi Ghazaryan, Qnarik Poghosyan, Tadevos Markosyan

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We have considered the high-order harmonic generation in-plane graphene quantum dots of hexagonal shape by the independent quasiparticle approximation-tight binding model. We have investigated how such a nonlinear effect is affected by a strong optical wave field, quantum dot typical band gap and lateral size, and dephasing processes. The equation of motion for the density matrix is solved by performing the time integration with the eight-order Runge-Kutta algorithm. If the optical wave frequency is much less than the quantum dot intrinsic band gap, the main aspects of multiphoton high harmonic emission in quantum dots are revealed. In such a case, the dependence of the cutoff photon energy on the strength of the optical pump wave is almost linear. But when the wave frequency is comparable to the bandgap of the quantum dot, the cutoff photon energy shows saturation behavior with an increase in the wave field strength.

Keywords: strong wave field, multiphoton, bandgap, wave field strength, nanostructure

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Authors: Ehsan Sadie

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The use of steel braces in concrete structures has been considered by researchers in recent decades due to its easy implementation, economics and the ability to create skylights in braced openings compared to shear wall openings as well as strengthening weak concrete structures to earthquakes. The purpose of this article is to improve and strengthen concrete structures with steel bracing. In addition, cases such as different numbers of steel braces in different openings of concrete structures and interaction between concrete frames and metal braces have been studied. In this paper, by performing static nonlinear analysis and examining ductility, the relative displacement of floors, examining the performance of samples, and determining the coefficient of behavior of composite frames (concrete frames with metal bracing), the behavior of reinforced concrete frames is compared with frame without bracing. The results of analyzes and studies show that the addition of metal bracing increases the strength and stiffness of the frame and reduces the ductility and lateral displacement of the structure. In general, the behavior of the structure against earthquakes will be improved.

Keywords: behavior coefficient, bracing, concrete structure, convergent bracing, earthquake, linear static analysis, nonlinear analysis, pushover curve

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Authors: Hafiza Rizwana Kausar

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In this paper, we formulate the wave equation in modified theories, particularly in f(R) theory, scalar-tensor theory, and metric palatine f(X) theory. We solve the wave equation in each case and try to find maximum possible solutions in the form polarization modes. It is found that modified theories present at most six modes however the mentioned metric theories allow four polarization modes, two of which are tensor in nature and other two are scalars.

Keywords: gravitational waves, modified theories, polariozation modes, scalar tensor theories

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Authors: Yasemin Kaya, Ahmet N. Eraslan

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In this study, the thermoelastic behavior of a long tube is studied by taking into account the temperature dependency of all mechanical and thermal properties. As the tube is heated slowly, an uncoupled solution procedure is adopted under free and radially constrained boundary conditions. The nonlinear heat conduction equation is solved by a finite element collocation procedure and the corresponding distributions of stress and strain are computed by shooting iterations. The computational model is verified in comparison to the analytical solution by shutting down the temperature dependency of physical properties. In the analysis, experimental data available in the literature is used to describe the coefficient of thermal expansion $\alpha$, the thermal conductivity $k$, the modulus of rigidity $G$, the yield strength $\sigma_{0}$, and the Poisson's ratio $\nu$ of Nickel. Results of the analysis are presented in comparison to those having constant physical properties. As a result of the calculations, the temperature dependency of the material properties should be taken into account at higher temperature ranges.

Keywords: thermoelasticity, long tube, temperature-dependent properties, internal heating

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Authors: Kahil Amar, Nekmouche Aghiles, Titouche Billal, Hamizi Mohand, Hannachi Naceur Eddine

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The ductility is an important parameter in the nonlinear behavior of portal structures reinforced concrete. It may be explained by the ability of the structure to deform in the plastic range, or the geometric characteristics in the map may influence the overall ductility. Our study is based on the influence of geometric slenderness (Lx / Ly) on the overall ductility of these structures, a study is made on a structure has 05 floors with varying the column section of 900 cm², 1600 cm² and 1225 cm². A slight variation in global ductility is noticed as (Lx/Ly) varies; however, column sections can control satisfactorily the plastic behavior of buildings.

Keywords: ductility, nonlinear behavior, pushover analysis, geometric slenderness, structural behavior

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Authors: Rahisham Abd Rahman

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In this paper, a nonlinear pollution model has been proposed to compute electric field distribution over the polymeric insulator surface under wet contaminated conditions. A 2D axial-symmetric insulator geometry, energized with 11kV was developed and analysed using Finite Element Method (FEM). A field-dependent conductivity with simplified assumptions was established to characterize the electrical properties of the pollution layer. Comparative field studies showed that simulation of dynamic pollution model results in a more realistic field profile, offering better understanding on how the electric field behaves under wet polluted conditions.

Keywords: electric field distributions, pollution layer, dynamic model, polymeric outdoor insulators, finite element method (FEM)

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Authors: Swarn Singh, Suruchi Singh

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In this paper, we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme. In this paper we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme.

Keywords: convergence, finite difference scheme, Pennes bio-heat equation, stability

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Authors: T. Yilmaz, N. Kirac

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Beam-column elements are defined as structural members subjected to a combination of axial and bending forces. Lateral torsional buckling is one of the major failure modes in which beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting. This study presents a compact closed-form equation that it can be used for calculating critical lateral torsional-buckling load of beam-columns with monosymmetric sections in the presence of a known axial load. Lateral-torsional buckling behavior of beam-columns subjected to constant axial force and various transverse load cases are investigated by using Ritz method in order to establish proposed equation. Lateral-torsional buckling loads calculated by presented formula are compared to finite element model results. ABAQUS software is utilized to generate finite element models of beam-columns. It is found out that lateral-torsional buckling load of beam-columns with monosymmetric sections can be determined by proposed equation and can be safely used in design.

Keywords: lateral-torsional buckling, stability, beam-column, monosymmetric section

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Authors: N. Q. Bau, N. V. Nghia

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The acoustomagnetoelectric (AME) field in a rectangular quantum wire with an infinite potential (RQWIP) is calculated in the presence of an external magnetic field (EMF) by using the quantum kinetic equation for the distribution function of electrons system interacting with external phonons and electrons scattering with internal acoustic phonon in a RQWIP. We obtained ananalytic expression for the AME field in the RQWIP in the presence of the EMF. The dependence of AME field on the frequency of external acoustic wave, the temperature T of system, the cyclotron frequency of the EMF and the intensity of the EMF is obtained. Theoretical results for the AME field are numerically evaluated, plotted and discussed for a specific RQWIP GaAs/GaAsAl. This result has shown that the dependence of the AME field on intensity of the EMF is nonlinearly and it is many distinct maxima in the quantized magnetic region. We also compared received fields with those for normal bulk semiconductors, quantum well and quantum wire to show the difference. The influence of an EMF on AME field in a RQWIP is newly developed.

Keywords: rectangular quantum wire, acoustomagnetoelectric field, electron-phonon interaction, kinetic equation method

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Ayaz Ahmad

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TOPIC: A study of the formation ,existness and stability of localised pulses in pde Ayaz Ahmad ,NITP, Abstract:In this paper we try to govern the evolution deterministic variable over space and time .We analysis the behaviour of the model which allows us to predict and understand the possible behaviour of the physical system .Bifurcation theory provides a basis to systematically investigate the models for invariant sets .Exploring the behaviour of PDE using bifurcation theory which provides many challenges both numerically and analytically. We use the derivation of a non linear partial differential equation which may be written in this form ∂u/∂t+c ∂u/∂x+∈(∂^3 u)/(∂x^3 )+¥u ∂u/∂x=0 We show that the temperature increased convection cells forms. Through our work we look for localised solution which are characterised by sudden burst of aeroidic spatio-temporal evolution. Key word: Gaussian pulses, Aeriodic ,spatio-temporal evolution ,convection cells, nonlinearoptics, Dr Ayaz ahmad Assistant Professor Department of Mathematics National institute of technology Patna ,Bihar,,India 800005 [email protected] +91994907553

Keywords: Gaussian pulses, aeriodic, spatio-temporal evolution, convection cells, nonlinear optics

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Authors: Raj Nandkeolyar, Precious Sibanda

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The flow of a viscous, incompressible, and electrically conducting fluid under the influence of aligned magnetic field acting along the direction of fluid flow over an exponentially stretching sheet is investigated numerically. The nonlinear partial differential equations governing the flow model is transformed to a set of nonlinear ordinary differential equations using suitable similarity transformation and the solution is obtained using a local linearization method followed by the Chebyshev spectral collocation method. The effects of various parameters affecting the flow and heat transfer as well as the induced magnetic field are discussed using suitable graphs and tables.

Keywords: aligned magnetic field, exponentially stretching sheet, induced magnetic field, magnetohydrodynamic flow

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Authors: Jelena R. Pejović, Nina N. Serdar

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This paper presents an analysis of the “Performance-Based” seismic design method, in order to overcome the perceived disadvantages and limitations of the existing seismic design approach based on force, in engineering practice. Bearing in mind, the specificity of the earthquake as a load and the fact that the seismic resistance of the structures solely depends on its behaviour in the nonlinear field, traditional seismic design approach based on force and linear analysis is not adequate. “Performance-Based” seismic design method is based on nonlinear analysis and can be used in everyday engineering practice. This paper presents the application of this method to eight-story high reinforced concrete building with combined structural system (reinforced concrete frame structural system in one direction and reinforced concrete ductile wall system in other direction). The nonlinear time-history analysis is performed on the spatial model of the structure using program Perform 3D, where the structure is exposed to forty real earthquake records. For considered building, large number of results were obtained. It was concluded that using this method we could, with a high degree of reliability, evaluate structural behavior under earthquake. It is obtained significant differences in the response of structures to various earthquake records. Also analysis showed that frame structural system had not performed well at the effect of earthquake records on soil like sand and gravel, while a ductile wall system had a satisfactory behavior on different types of soils.

Keywords: ductile wall, frame system, nonlinear time-history analysis, performance-based methodology, RC building

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