Search results for: Moment Equations

Authors: Seung-Won Lee, Jong Soo Lee, Won-Jik Yang, Hyung-Joon Kim

Abstract:

A capacity spectrum method (CSM), one of methodologies to evaluate seismic fragilities of building structures, has been long recognized as the most convenient method, even if it contains several limitations to predict the seismic response of structures of interest. This paper proposes the procedure to estimate seismic fragility curves using an incremental dynamic analysis (IDA) rather than the method adopting a CSM. To achieve the research purpose, this study compares the seismic fragility curves of a 5-story reinforced concrete (RC) moment frame obtained from both methods; an IDA method and aCSM. Both seismic fragility curves are similar in slight and moderate damage states whereas the fragility curve obtained from the IDA method presents less variation (or uncertainties) in extensive and complete damage states. This is due to the fact that the IDA method can properly capture the structural response beyond yielding rather than the CSM and can directly calculate higher mode effects. From these observations, the CSM could overestimate seismic vulnerabilities of the studied structure in extensive or complete damage states.

Keywords: Seismic fragility curve, Incremental dynamic analysis, Capacity spectrum method, Reinforced concrete moment frame.

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Authors: Jingbo Yang, Hong Li, Yang Liu, Siriguleng He

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In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.

Keywords: Pseudo-hyperbolic partial integro-differential equations, Nonconforming mixed element method, Semilinear, Error estimates.

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Authors: Minghui Wang

Abstract:

The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established.

Keywords: Matrix equation, Quaternionic matrix, Real representation, positive (semi)definite solutions.

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Authors: Thomas Kampke

Abstract:

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.

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Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

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

Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.

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Authors: M. Tehranizadeh, E. Shoushtari Rezvani

Abstract:

Seismic performance of steel moment-resisting frame structures is investigated considering nonlinear soil-structure interaction (SSI) effects. 10-, 15-, and 20-story planar building frames with aspect ratio of 3 are designed in accordance with current building codes. Inelastic seismic demands of the superstructure are considered using concentrated plasticity model. The raft foundation system is designed for different soil types. Beam-on-nonlinear Winkler foundation (BNWF) is used to represent dynamic impedance of the underlying soil. Two sets of pulse-like as well as no-pulse near-fault earthquakes are used as input ground motions. The results show that the reduction in drift demands due to nonlinear SSI is characterized by a more uniform distribution pattern along the height when compared to the fixed-base and linear SSI condition. It is also concluded that beneficial effects of nonlinear SSI on displacement demands is more significant in case of pulse-like ground motions and performance level of the steel moment-resisting frames can be enhanced.

Keywords: Soil-structure interaction, uplifting, soil plasticity, near-fault earthquake, tall building.

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Authors: Taher Lotfi , Parisa Bakhtiari , Katayoun Mahdiani , Mehdi Salimi

Abstract:

In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.

Keywords: Iinterval analysis, nonlinear equations, Ostrowski method.

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Authors: Xiguang Li

Abstract:

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

Keywords: Banach space, boundary value problem, differential equation, delay.

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Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Ze-Jun Hu, Ting-Zhu Huang, Ning-Bo Tan

Abstract:

To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package. 

Keywords: Navier-Stokes equations, Krylov subspace method, preconditioner, dimensional splitting, augmented Lagrangian preconditioner.

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Authors: A. Reyes-Salazar, M. D. Llanes-Tizoc, E. Bojorquez, F. Valenzuela-Beltran, J. Bojorquez, J. R. Gaxiola-Camacho, A. Haldar

Abstract:

Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated to lateral vibrations are commonly used to develop the matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the nonlinear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively, when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment resisting steel frames and the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: Moment-resisting steel frames, consistent and concentrated mass matrices, nonlinear seismic response, Rayleigh damping.

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Authors: Vigen Arakelian

Abstract:

The balancing of mechanisms is a well-known problem in the field of mechanical engineering because the variable dynamic loads cause vibrations, as well as noise, wear and fatigue of the machines. A mechanical system with unbalance shaking force and shaking moment transmits substantial vibration to the frame. Therefore, the objective of the balancing is to cancel or reduce the variable dynamic reactions transmitted to the frame. The resolution of this problem consists in the balancing of the shaking force and shaking moment. It can be fully or partially, by internal mass redistribution via adding counterweights or by modification of the mechanism's architecture via adding auxiliary structures. The balancing problems are of continue interest to researchers. Several laboratories around the world are very active in this area and new results are published regularly. However, despite its ancient history, mechanism balancing theory continues to be developed and new approaches and solutions are constantly being reported. Various surveys have been published that disclose particularities of balancing methods. The author believes that this is an appropriate moment to present a state of the art of the shaking force balancing studies completed by new research results. This paper presents an overview of methods devoted to the shaking force balancing of mechanisms, as well as the historical aspects of the origins and the evolution of the balancing theory of mechanisms.

Keywords: Inertia forces, shaking forces, balancing, dynamics.

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Authors: A. Elsayed Ahmed, A. Hafez, A. N. Ouda, H. Eldin Hussein Ahmed, H. Mohamed Abd-Elkader

Abstract:

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 nonlinear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: Equations of motion, linearization, modeling, nonlinear model, UAV.

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Authors: Kyung-Suk Choi, Hyung-Joon Kim

Abstract:

Modular structural systems are constructed using a method that they are assembled with prefabricated unit modular frames on-site. This provides a benefit that can significantly reduce building construction time. The structural design is usually carried out under the assumption that their load-carrying mechanism is similar to that of traditional steel moment-resisting systems. However, both systems are different in terms of beam-column connection details which may strongly influence the lateral structural behavior. Specially, the presence of access holes in a beam-column joint of a unit modular frame could cause undesirable failure during strong earthquakes. Therefore, this study carried out finite element analyses (FEMs) of unit modular frames to investigate the cyclic behavior of beam-column joints with the access holes. Analysis results show that the unit modular frames present stable cyclic response with large deformation capacities and their joints are classified into semi-rigid connections even if there are access holes.

Keywords: Unit modular frame, steel moment connection, nonlinear analytical model, moment-rotation relation, access holes.

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Authors: O. Miraliyari, M.M. Najafizadeh, A.R. Rahmani, A. Momeni Hezaveh

Abstract:

This paper presents the buckling analysis of short and long functionally graded cylindrical shells under thermal and mechanical loads. The shell properties are assumed to vary continuously from the inner surface to the outer surface of the shell. The equilibrium and stability equations are derived using the total potential energy equations, Euler equations and first order shear deformation theory assumptions. The resulting equations are solved for simply supported boundary conditions. The critical temperature and pressure loads are calculated for both short and long cylindrical shells. Comparison studies show the effects of functionally graded index, loading type and shell geometry on critical buckling loads of short and long functionally graded cylindrical shells.

Keywords: Buckling, Functionally graded materials, Short and long cylindrical shell, Thermal and mechanical loads.

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

Abstract:

In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: Fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability.

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Authors: K. Ganesan

Abstract:

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.

Keywords: Interval arithmetic, Interval matrix, linear equations.

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: Non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two- dimensional Schrodinger equation.

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Authors: N. M. Kamoh, D. G. Gyemang, M. C. Soomiyol

Abstract:

This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.

Keywords: Collocation shifted Legendre polynomials, Simpson’s rule and Volterra integro-differential equations.

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Authors: Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib

Abstract:

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating  that the flow equations possess an infinite set of solutions. 

Keywords: Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows

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Authors: Amit Goyal, Alka, Rama Gupta, C. Nagaraja Kumar

Abstract:

We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some cases, the BF equations could be solved for arbitrary timedependent coefficient of convection term.

Keywords: Solitary wave solution, Variable coefficient Burgers- Fisher equation, Auxiliary equation method.

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Authors: Elmira Tavasoli Yousef Abadi

Abstract:

All structural components influencing the inelastic analysis alter response modification factor too. Ductility of connections has been regarded among the factors which have a direct impact on steel frame response modification factor. The experience of recent earthquakes such as the 1994 Northridge earthquake showed that structural connections in steel frame incurred unexpected (brittle) fracture in beam-to-column connection area. One of the methods to improve performance of moment frames is to reduce the beam section near the connection to the column. Reduced Beam Section (RBS) refers to one of the proposed moment connections in FEMA350. Ductility is the most important advantage of this connection over the other moment connections; it is found as the major factor in suitable plastic behavior of structural system. In this paper, beam-to-column connection with RBS and wide-flange beams has been examined via software Abaqus 6.12. It is observed that use of RBS connections can improve the connection behavior at inelastic area to a large extent and avoid stress concentrations and large deformation in the column.

Keywords: RBS, seismic performance, beam-to-column connection, ductility, wide-flange beam.

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Authors: Serge B. Provost, Min Jiang

Abstract:

The density estimates considered in this paper comprise a base density and an adjustment component consisting of a linear combination of orthogonal polynomials. It is shown that, in the context of density approximation, the coefficients of the linear combination can be determined either from a moment-matching technique or a weighted least-squares approach. A kernel representation of the corresponding density estimates is obtained. Additionally, two refinements of the Kronmal-Tarter stopping criterion are proposed for determining the degree of the polynomial adjustment. By way of illustration, the density estimation methodology advocated herein is applied to two data sets.

Keywords: kernel density estimation, orthogonal polynomials, moment-based methodologies, density approximation.

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

Abstract:

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: Ameleh Aghajanloo, Moharam Dolatshahi Pirouz, Masoud Montazeri Namin

Abstract:

In this paper, a two-dimensional (2D) numerical model for the tidal currents simulation in Persian Gulf is presented. The model is based on the depth averaged equations of shallow water which consider hydrostatic pressure distribution. The continuity equation and two momentum equations including the effects of bed friction, the Coriolis effects and wind stress have been solved. To integrate the 2D equations, the Alternative Direction Implicit (ADI) technique has been used. The base of equations discritization was finite volume method applied on rectangular mesh. To evaluate the model validation, a dam break case study including analytical solution is selected and the comparison is done. After that, the capability of the model in simulation of tidal current in a real field is represented by modeling the current behavior in Persian Gulf. The tidal fluctuations in Hormuz Strait have caused the tidal currents in the area of study. Therefore, the water surface oscillations data at Hengam Island on Hormoz Strait are used as the model input data. The check point of the model is measured water surface elevations at Assaluye port. The comparison between the results and the acceptable agreement of them showed the model ability for modeling marine hydrodynamic.

Keywords: Persian Gulf, Tidal Currents, Shallow Water Equations, Finite Volumes

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Authors: J. Geiser, R. Röhle

Abstract:

In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.

Keywords: Chemical reactions, chemical vapor deposition, convection-diffusion-reaction equations, decomposition methods, multi-component transport.

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Authors: Chewa Thassana, Wicharn Techitdheera

Abstract:

The spin (ms) and orbital (mo) magnetic moment of the antiferromagnetic NiO and MnO have been studied in the local spin density approximation (LSDA+U) within full potential linear muffin-tin orbital (FP-LMTO method with in the coulomb interaction U varying from 0 to 10eV, exchange interaction J, from 0 to 1.0eV, and volume compression VC in range of 0 to 80%. Our calculated results shown that the spin magnetic moments and the orbital magnetic moments increase linearly with increasing U and J. While the interesting behaviour appears when volume compression is greater than 70% for NiO and 50% for MnO at which ms collapses. Further increase of volume compression to be at 80% leads to the disappearance of both magnetic moments.

Keywords: spin-orbital magnetic moment, Coulomb interaction U and exchange interaction J, volume compression VC, LSDA+U.

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Authors: Saemee Jun, Dong-Hyeon Shin, Tae-Sang Ahn, Hyung-Joon Kim

Abstract:

Building loss estimation methodologies which have been advanced considerably in recent decades are usually used to estimate socio and economic impacts resulting from seismic structural damage. In accordance with these methods, this paper presents the evaluation of an annual loss probability of a reinforced concrete moment resisting frame designed according to Korean Building Code. The annual loss probability is defined by (1) a fragility curve obtained from a capacity spectrum method which is similar to a method adopted from HAZUS, and (2) a seismic hazard curve derived from annual frequencies of exceedance per peak ground acceleration. Seismic fragilities are computed to calculate the annual loss probability of a certain structure using functions depending on structural capacity, seismic demand, structural response and the probability of exceeding damage state thresholds. This study carried out a nonlinear static analysis to obtain the capacity of a RC moment resisting frame selected as a prototype building. The analysis results show that the probability of being extensive structural damage in the prototype building is expected to 0.01% in a year.

Keywords: Expected annual loss, Loss estimation, RC structure, Fragility analysis.

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Authors: Vineet K. Srivastava, Mukesh K. Awasthi, Mohammad Tamsir

Abstract:

A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.

Keywords: Burgers’ equation, Implicit Finite-difference method, Newton’s method, Gauss elimination with partial pivoting.

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Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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