Search results for: modified newmark method

Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring.

Keywords: buckling, stability, frame, modified newmark method

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The aim of this paper is to examine the behavior of elastic stability of reinforced and composite concrete struts with axial loads. The objective of this study is to verify the ability of the Modified Newmark Method to include geometric non-linearity in addition to non-linearity due to cracking, and also to show the advantage of the established method to reconsider an ignored minor parameter in mathematical modeling, such as the effect of the cracking by extra geometric bending moment Ny on cross-section properties. The purpose of this investigation is not to present some new results for the instability of reinforced or composite concrete columns. Therefore, no kinds of non-linearity involved in the problem are considered here. Only as mentioned, it is a part of the verification of the new established method to solve two kinds of non-linearity P- δ effect and cracking together simultaneously. However, the Modified Newmark Method can be used to solve non-linearity of materials and time-dependent behavior of concrete. However, since it is out of the scope of this article, it is not considered.

Keywords: stability, buckling, modified newmark method, reinforced

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The purpose of this article is to analyze the finite displacement of Columns by applying the Modified Newmark Method. This research will be performed on Columns subjected to compressive axial load, therefore the non-linearity of the geometry is also considered. If the considered strut is perfect, the governing differential equation contains a branching point in the solution path. Investigation into the Elastica is a part of generalizing the developed method. It presents the ability of the Modified Newmark Method in treating non-linear differential equations Derived from elastic strut stability problems. These include not only an approximate polynomial solution for the Elastica problems, but can also recognize the branching point and the stable solution. However, this investigation deals with the post-buckling response of elastic and pin ended columns subjected to central or equally eccentric axial loads.

Keywords: columns, structural modeling, structures & structural stability, loads

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.

Keywords: nonlinear, stability, buckling, modified newmark method

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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Differential equations are of fundamental importance in engineering and applied mathematics, since many physical laws and relations appear mathematically in the form of such equations. The equilibrium state of structures consisting of one-dimensional elements can be described by an ordinary differential equation. The response of these kinds of structures under the loading, namely relationship between the displacement field and loading field, can be predicted by the solution of these differential equations and on satisfying the given boundary conditions. When the effect of change of geometry under loading is taken into account in modeling of equilibrium state, then these differential equations are partially integrable in quartered. They also exhibit instability characteristics when the structures are loaded compressively. The purpose of this paper is to represent the ability of the Modified Newmark Method in analyzing flexural-torsional instability of struts for both bifurcation and non-bifurcation structural systems. The results are shown to be very accurate with only a small number of iterations. The method is easily programmed, and has the advantages of simplicity and speeds of convergence and easily is extended to treat material and geometric nonlinearity including no prismatic members and linear and nonlinear spring restraints that would be encountered in frames. In this paper, these abilities of the method will be extended to the system of linear differential equations that govern strut flexural torsional stability.

Keywords: instability, torsion, flexural, buckling, modified newmark method stability

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Authors: Saidi Abdelkrim, Hamouine Abdelmadjid, Abdellatif Megnounif

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The study of interaction between vehicles and bridge structures has become extremely important. Large deflections and vibration induced by heavy and high-speed vehicles affect significantly the safety and efficiency of bridge. The vibration of a bridge caused by passage of vehicles is one of the most imperative considerations in the design of a bridge as a common sort of transportation structure. A major goal of this study is to create a simplified model of a vehicle bridge system in MATLAB. The model will then be used to study the influence of parameters to vehicle-bridge vibrations.

Keywords: vehicle-bridge interaction, Newmark-β, MATLAB code

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: N. Guruprasad

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This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Ali H. Mahfouz, Gao Ming-Jun, Mohamad Sharif

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Slurry dredged soil at coastal area has a high water content, poor permeability, and low surface intensity. Hence, it is infeasible to use vacuum preloading method to treat this type of soil foundation. For the special case of super soft ground, a floating bridge is first constructed on muddy soil and used as a service road and platform for implementing the modified vacuum preloading method. The modified technique of vacuum preloading and its construction process for the super soft soil foundation improvement is then studied. Application of modified vacuum preloading method shows that the technology and its construction process are highly suitable for improving the super soft soil foundation in coastal areas.

Keywords: super soft foundation, dredger fill, vacuum preloading, foundation treatment, construction technology

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Authors: Kobamelo Mashaba

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The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: single-degree-of-freedom system (SDOF), linear acceleration method, nonlinear excited system, equivalent displacement method, equivalent energy method

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Authors: A. A. Soliman

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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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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: Kritsada Pipitthapan

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WO3/SiO2 catalysts were modified by an ion exchange method with sodium hydroxide or potassium hydroxide solution. The performance of the modified catalysts was tested in the metathesis of ethylene and trans-2-butene to propylene. During ion exchange, sodium and potassium ions played different roles. Sodium modified catalysts revealed constant trans-2-butene conversion and propylene selectivity when the concentrations of sodium in the solution were varied. In contrast, potassium modified catalysts showed reduction of the conversion and increase of the selectivity. From these results, potassium hydroxide may affect the transformation of tungsten oxide active species, resulting in the decrease in conversion whereas sodium hydroxide did not. Moreover, the modification of catalysts by this method improved the catalyst stability by lowering the amount of coke deposited on the catalyst surface.

Keywords: acid sites, alkali metal, isomerization, metathesis

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Authors: Dalal N. Hammod, Ekhlas K. Gbashi

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Today, cryptography is used in many applications to achieve high security in data transmission and in real-time communications. AES has long gained global acceptance and is used for securing sensitive data in various industries but has suffered from slow processing and take a large time to transfer data. This paper suggests a method to enhance Advance Encryption Standard (AES) Algorithm based on time and permutation. The suggested method (MAES) is based on modifying the SubByte and ShiftRrows in the encryption part and modification the InvSubByte and InvShiftRows in the decryption part. After the implementation of the proposal and testing the results, the Modified AES achieved good results in accomplishing the communication with high performance criteria in terms of randomness, encryption time, storage space, and avalanche effects. The proposed method has good randomness to ciphertext because this method passed NIST statistical tests against attacks; also, (MAES) reduced the encryption time by (10 %) than the time of the original AES; therefore, the modified AES is faster than the original AES. Also, the proposed method showed good results in memory utilization where the value is (54.36) for the MAES, but the value for the original AES is (66.23). Also, the avalanche effects used for calculating diffusion property are (52.08%) for the modified AES and (51.82%) percentage for the original AES.

Keywords: modified AES, randomness test, encryption time, avalanche effects

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Authors: Keshab Shrestha, Hung-Suck Park

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Emergy accounting of the systems networks is guided by a definite rule called ‘emergy algebra’. The systems networks consist of two types of branching. These are the co-product branching and split branching. The emergy accounting procedure for both the branching types is different. According to the emergy algebra, each branch in the co-product branching has different transformity values whereas the split branching has the same transformity value. After the transformity value of each branch is determined, the emergy is calculated by multiplying this with the energy. The aim of this research is to solve the problems in determining the transformity values in the co-product branching through the introduction of a new methodology, the modified physical quantity method. Initially, the existing methodologies for emergy accounting in the co-product branching is discussed and later, the modified physical quantity method is introduced with a case study of the Eucalyptus pulp production. The existing emergy accounting methodologies in the co-product branching has wrong interpretations with incorrect emergy calculations. The modified physical quantity method solves those problems of emergy accounting in the co-product branching systems. The transformity value calculated for each branch is different and also applicable in the emergy calculations. The methodology also strictly follows the emergy algebra rules. This new modified physical quantity methodology is a valid approach in emergy accounting particularly in the multi-production systems networks.

Keywords: co-product branching, emergy accounting, emergy algebra, modified physical quantity method, transformity value

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Authors: Gülşah Çelik Gül, Figen Kurtuluş

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Magnesium containing boron compounds with hexagonal structure have been drawn much attention due to their superconductive nature. The main target of this work is new modified microwave oven by on our own has an ability about passing through a gas in the oven medium for attainment of oxygen-free compounds such as c-BN.  Mg containing boride was synthesized by modified-microwave method under nitrogen atmosphere using amorphous boron and magnesium source in appropriate molar ratio. Microwave oven with oxygen free environment has been modified to aimed to obtain magnesium boride without oxygen. Characterizations were done by powder X-ray diffraction (XRD), and Fourier transform infrared (FTIR) spectroscopy. Mg containing boride, generally named magnesium boride, with amorphous character without oxygen is obtained via designed microwave oven system.

Keywords: magnesium containing boron compounds, modified microwave synthesis, powder X-ray diffraction, FTIR

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Authors: Hao-Su Liu, Jun-Qing Lei

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This study introduces the theory of modified particle swarm optimizer and its application in time-domain expressions for bridge self-excited aerodynamic forces. Based on the indicial function expression and the rational function expression in time-domain expression for bridge self-excited aerodynamic forces, the characteristics of the two methods, i.e. the modified particle swarm optimizer and conventional search method, are compared in flutter derivatives’ fitting process. Theoretical analysis and numerical results indicate that adopting whether the indicial function expression or the rational function expression, the fitting flutter derivatives obtained by modified particle swarm optimizer have better goodness of fit with ones obtained from experiment. As to the flutter derivatives which have higher nonlinearity, the self-excited aerodynamic forces, using the flutter derivatives obtained through modified particle swarm optimizer fitting process, are much closer to the ones simulated by the experimental. The modified particle swarm optimizer was used to recognize the parameters of time-domain expressions for flutter derivatives of an actual long-span highway-railway truss bridge with double decks at the wind attack angle of 0°, -3° and +3°. It was found that this method could solve the bounded problems of attenuation coefficient effectively in conventional search method, and had the ability of searching in unboundedly area. Accordingly, this study provides a method for engineering industry to frequently and efficiently obtain the time-domain expressions for bridge self-excited aerodynamic forces.

Keywords: time-domain expressions, bridge self-excited aerodynamic forces, modified particle swarm optimizer, long-span highway-railway truss bridge

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: I. Algul, G. Akgun, H. Kurtaran

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Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.

Keywords: differential quadrature method, doubly curved panels, laminated composite materials, small displacement

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Maryam Samani. Ahmad Golchin. Hosseinali Alikkani. Ahmad Baybordi

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Natural diatomite was modified by grinding and acid treatment to increase surface area and to decrease the impurities. Surface area and pore volume of the modified diatomite were 67.45 m² g-1 and 0.105 cm³ g-¹ respectively, and used to immobilize Pb, Zn and Cu in an urban soil. The modified diatomite was added to soil samples at the rates of 2.5, 5, 7.5 and 10% and the samples incubated for 60 days. The addition of modified diatomite increased SSA of the soil. The SSAs of soils with 2.5, 5.0, 7.5 and 10% modified diatomite were 20.82, 22.02, 23.21 and 24.41 m² g-¹ respectively. Increasing the SSAs of the soils by the application of modified diatomite reduced the DTPA extractable concentrations of heavy metals compared with un-amendment control. The concentration of Pb, Zn and Cu were reduced by 91.1%, 82% and 91.1% respectively. Modified diatomite reduced the concentration of Exchangeable and Carbonate bounded species of Pb, Zn and Cu, compared with the control. Also significantly increased the concentration of Fe Mn- OX (Fe-Mn Oxides) and OM (Organic Matter) bound and Res (Residual) fraction. Modified diatomite increased the urease, dehydrogenase and alkaline phosphatase activity by 52%, 57% and 56.6% respectively.

Keywords: modified diatomite, chemical specifications, specific surface area, enzyme activity, immobilization, heavy metal, soil remediation

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Authors: Haibo Zhao, Thomas Andre, Katherine Avery, Alper Kiziltas, Deborah Mielewski

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Silica aerogels were fabricated through a modified rapid supercritical extraction (RSCE) process. The silica aerogels were made using a tetramethyl orthosilicate precursor and then placed in a hot press and brought to the supercritical point of the solvent, ethanol. In order to control the pressure release without a pressure controller, a needle valve was used. The resulting aerogels were then characterized for their physical and chemical properties and compared to silica aerogels created using similar methods. The aerogels fabricated using this modified RSCE method were found to have similar properties to those in other papers using the unmodified RSCE method. Silica aerogel infused glass blanket composite, graphene reinforced silica aerogel composite were also successfully fabricated by this new method. The modified RSCE process and system is a prototype for better gas outflow control with a lower cost of equipment setup. Potentially, this process could be evolved to a continuous low-cost high-volume production process to meet automotive requirements.

Keywords: aerogel, automotive, rapid supercritical extraction process, low cost production

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Authors: Rakhshan Hakimelahi

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In recent years, zinc oxid nano tubes have attracted much attention. The direct use of zinc oxid nano tubes modified by SiO2 as recoverable catalysts for organic reactions is very rare. The catalysts were characterized by XRD. The average particle size of ZnO catalysts is 57 nm and there are high density defects on nano tubes surfaces. A simple and efficient method for the quinazolin derivatives synthesis from the condensation isatoic anhydride and an aromatic aldehyde with ammonium acetate in the presence of a catalytic amount zinc oxid nano tubes modified by SiO2 is described. The reason proposed for higher catalytic activity of zinc oxid nano tubes modified by SiO2 is a combination effect of the small particle size and high-density surface defects. The practical and simple method led to excellent yields of the 2,3-Di hydro quinazolin-4(1H)-one derivatives under mild conditions and within short times.

Keywords: 2, 3-Dihydroquinazolin-4(1H)-one derivatives, reusable catalyst, SiO2, zinc oxid nanotubes

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