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**Search for:**boundary-value-problems

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#### An existence-uniqueness theorem for a class of boundary value problems

, Article Fixed Point Theory ; Volume 13, Issue 2 , 2012 , Pages 589-592 ; 15835022 (ISSN) ; Pournaki, M. R ; Razani, A ; Sharif University of Technology
2012

Abstract

In this paper the solutions of a two-endpoint boundary value problem is studied and under suitable assumptions the existence and uniqueness of a solution is proved. As a consequence, a condition to guarantee the existence of at least one periodic solution for a class of Liénard equations is presented

#### Erratum to "On the existence of periodic solutions for a class of generalized forced Liénard equations" [Appl. Math. Lett. 20 (3) (2007) 248-254]

, Article Applied Mathematics Letters ; Volume 21, Issue 8 , August , 2008 , Page 880 ; 08939659 (ISSN) ; Razani, A ; Sharif University of Technology
2008

Abstract

In this work the second-order generalized forced Li ́enard equationx′′+(f(x)+k(x)x′)x′+g(x)=p(t)is considered and anew condition for guaranteeing the existence of at least one periodic solution for this equation is given

#### A numerical method for solving nth-order boundary-value problems

, Article Applied Mathematics and Computation ; Volume 196, Issue 2 , 2008 , Pages 889-897 ; 00963003 (ISSN) ; Jalilian, Y ; Sharif University of Technology
2008

Abstract

In this paper, we consider the solution of an nth order boundary-value problem. We solve this problem by changing the problem to a system of two integral-differential equations and using the variational iteration method. By giving three examples and comparing with the other methods, the efficiency of the method will be shown. © 2007 Elsevier Inc. All rights reserved

#### Application of neural network to find initial state of optimization parameters

, Article 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006, Chicago, IL, 5 November 2006 through 10 November 2006 ; 2006 ; 10716947 (ISSN); 0791837904 (ISBN); 9780791837900 (ISBN) ; Sayyaadi, H ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2006

Abstract

This paper derives an estimated function made by simple Neural Network to find initial state of optimization parameters. It changes a system of differential equations with boundary values to a system of equations with initial values. So a lot of time would be saved to solve it. As a result, the system with differential equations will reach the desired final state. Copyright © 2006 by ASME

#### Optimal approach to halo orbit control

, Article AIAA Guidance, Navigation, and Control Conference and Exhibit 2003, Austin, TX, 11 August 2003 through 14 August 2003 ; 2003 ; 9781563479786 (ISBN); 9781624100901 (ISBN) ; Jalali, M. A ; Pourtakdoust, S. H ; Sharif University of Technology
American Institute of Aeronautics and Astronautics Inc
2003

Abstract

Three-dimensional orbits in the vicinity of the collinear libration points of the Sun-Earth/Moon barycenter system are currently being considered for use with a number of missions planed for 2000 and beyond. Since such libration point trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. In this paper, circular restricted three body problem is reviewed and a numerical method to control spacecrafts on periodic halo orbits around L1 and L2 collinear points of the Sun-Earth/Moon barycenter system is investigated. The control approach is based on the optimal control theory and implements variation...

#### Large elastic-plastic deformation analysis of rectangular plates

, Article New and Emerging Computational Methods: Applications to Fracture, Damage and Reliability (2002 ASME Prssure Vessels and Piping Conference), Vancouver, BC, 5 August 2002 through 9 August 2002 ; Volume 438 , 2002 , Pages 153-159 ; 0277027X (ISSN) ; Shahi, M ; Sharif University of Technology
2002

Abstract

The purpose of this paper is to find a fast and simple solution for the large deformation of rectangular plates considering elastic-plastic behavior. This analysis contains material and geometric nonlinearities. For geometric nonlinearity the concept of load analogy is used. In this method the effect of nonlinear terms of lateral displacement is considered as suitable combination of additional fictitious lateral load, edge moment and in-plane forces acting on the plate. Variable Material Property (V.M.P.) method has been used for analysis of material nonlinearity. In this method, the basic relations maintain the form of stress-strain elastic formula, while material properties are modified to...

#### Boussinesq indentation of a transversely isotropic half-space reinforced by a buried inextensible membrane

, Article Applied Mathematical Modelling ; Vol. 38, issue. 7-8 , April , 2014 , p. 2163-2172 ; Ahmadi, S. F ; Eskandari, M ; Sharif University of Technology
Abstract

The normal indentation of a rigid circular disk into the surface of a transversely isotropic half-space reinforced by a buried inextensible thin film is addressed. By virtue of a displacement potential function and the Hankel transform, the governing equations of this axisymmetric mixed boundary value problem are represented as a dual integral equation, which is subsequently reduced to a Fredholm integral equation of the second kind. Two important results of the contact stress distribution beneath the disk region as well as the equivalent stiffness of the system are expressed in terms of the solution of the Fredholm integral equation. When the membrane is located on the surface or at the...

#### Modeling the interphase layer between CNT and matrix in nanocomposites using nonlinear large deformation hierarchical multiscale

, Article 4th International Conference on Multiscale Materials Modeling, MMM 2008, 27 October 2008 through 31 October 2008 ; 2008 , Pages 239-242 ; 9780615247816 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
Department of Scientific Computing, Florida State University
2008

Abstract

We have used a hierarchical multiscale modeling scheme for the analysis of carbon nanotube reinforced nanocomposites. This scheme consists of definition of two boundary value problems, one for macroscale (the scale in which the material exists homogeneously and we are interested in modeling the material behavior on that scale), and another for microscale (the scale in which the material becomes heterogeneous and microstructural constituents emerge). The coupling between these scales is done by using homogenization techniques. Using the presented scheme, we have studied carbon nanotube (CNT) reinforced composites behavior and the effects of an interphase layer between CNT and matrix material....

#### , M.Sc. Thesis Sharif University of Technology ; Hesaraki, Mahmoud (Supervisor)

Abstract

Our problem is to evaluation state and form of a tracer passing through the vessel. Using this method, we can identify the effect of during used in some defected parts of body. This evaluation leads to in solving a Laplace equation with mixed boundary condition. Separating that problem, we reach to a collection of algebraic and linear equations. Solving this system, we approximate coefficients of the solution with a series the existence and uniqueness of and analytic solution has been proved using the Eigen functions finally, using numerical algorithms, we have interpreted the analytical solutions.

#### Analysis of displacement and strain fields of a screw dislocation in a nanowire using gradient elasticity theory

, Article Scripta Materialia ; Volume 59, Issue 3 , August , 2008 , Pages 368-371 ; 13596462 (ISSN) ; Davoudi, K. M ; Gutkin, M. Y ; Sharif University of Technology
2008

Abstract

Displacement and strain fields of a screw dislocation in a nanowire are considered within the theory of gradient elasticity. The gradient solution of the corresponding boundary value problem is derived and discussed in detail. It is shown that the dislocation fields do not contain classical jumps and singularities at the dislocation line. The maximum values of the dislocation displacement and elastic strain strongly depend on both the dislocation position and nanowire radius, thus demonstrating a nonclassical size effect. © 2008 Acta Materialia Inc

#### Thermoelastic fields of a functionally graded coated lnhomogeneity with sliding/perfect interlaces

, Article Journal of Applied Mechanics, Transactions ASME ; Volume 74, Issue 3 , 2007 , Pages 389-398 ; 00218936 (ISSN) ; Shodja, H. M ; Sharif University of Technology
2007

Abstract

The determination of the thermo-mechanical stress field in and around a spherical/ cylindrical inhomogeneity surrounded by a functionally graded (FG) coating, which in turn is embedded in an infinite medium, is of interest. The present work, in the frame work of Boussinesq/Papkovich-Neuber displacement potentials method, discovers the potential functions by which not only the relevant boundary value problems (BVPs) in the literature, but also the more complex problem of the coated inhomogeneities with FG coating and sliding interfaces can be treated in a unified manner. The thermo-elastic fields pertinent to the inhomogeneities with multiple homogeneous coatings and various combinations of...

#### Mixed Boundary Value Problems in Transversely Isotropic Materials

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

By virtue of a robust and efficient method, the solution of triple and quadruple integral equations which are the keys of various mixed boundary value problems corresponding to half-space and full-space media is addressed. These multiple integral equations are reduced to a well-known Fredholm integral equation of the second kind. In order to write the governing integral equations of the problem, Green’s functions play an important role. Therefore, Green’s functions of homogeneous and non-homogeneous transversely isotropic media in the form of line integrals including Bessel functions are obtained. Three interesting mixed boundary value problems in transversely isotropic materials are...

#### Vertical Forced Vibration of a Rigid Disk in a Transversely Isotropic Full-Space

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor) ; Mohammadi Shodja, Hossein (Co-Advisor)
Abstract

This research is concerned with the investigation of forced time–harmonic vertical vibration of a rigid disk embedded in a transversely isotropic full space medium. By properties of integral transform methods, the generalized mixed boundary–value problem is formulated as a set of dual integral equations, which in turn, are reduced to a Fredholm equation of the second kind. The obtained Fredholm integral equation is solved by well-known numerical methods. Selected results for the load distribution on the disk and complex compliance are presented for various ranges of frequency.

#### Elastic Responses of a Half-Space Reinforced by a Buried Extensible Membrane under Internal Loading

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract

In order to improve mechanical properties and increase the load capacity of soil so many different methods are innovated and utilized. Through This variety we can mention cement and asphalt concrete pavements which are the most common methods, cement sprinkling for consolidation of inclined surfaces and utilizing geotextiles and geomembranes which are recent methods. As far as a method becomes more common in industry, analytical study on effect of these methods on soil properties drew more attention in researches.In this research a homogenous elastic half-space is reinforced by an extensible thin plate and studied under various loads. The plate is considered as a buried infinite plane with...

#### Developing consistent inlet thermal boundary condition in micro/nano scale channels with heat transfer

, Article 1st ASME Micro/Nanoscale Heat Transfer International Conference, MNHT08, Tainan, 6 January 2008 through 9 January 2008 ; Volume Parts A and B , 2008 , Pages 691-700 ; 0791842924 (ISBN); 9780791842928 (ISBN) ; Vakilipour, S ; Sharif University of Technology
2008

Abstract

In this work, we present a more realistic inlet boundary condition to simulate compressible and incompressible flows through micro and nano channels considering consistent momentum and heat transfer specifications there. At solid walls, a constant wall temperature with suitable jump is applied as the wall thermal boundary condition; however, two types of thermal inlet boundary conditions are investigated at the inlet. We firstly examine the classical inlet boundary condition, which specifies a uniform temperature distribution right at the real inlet. Alternatively, we apply the same boundary condition but at a fictitious place far upstream of the real channel inlet. To validate our results,...

#### Numerical study of flow and heat in long micro and nano channels

, Article 1st ASME Micro/Nanoscale Heat Transfer International Conference, MNHT08, Tainan, 6 January 2008 through 9 January 2008 ; Volume Parts A and B , 2008 , Pages 1299-1307 ; 0791842924 (ISBN); 9780791842928 (ISBN) ; Vakilipour, S ; Sharif University of Technology
2008

Abstract

In this work, we extend a numerical tool capable of solving compressible and incompressible gas flows to study the momentum and heat transfer rates in micro/nano channels with high aspect ratio (L/H = 8000), where the compressibility effect is dominant. The constant heat flux thermal boundary condition is firstly applied at the wall. Next, the flow regime is extended to the early transition regime employing a high order slip velocity boundary condition based on the kinetic theory assumptions. The accuracy of the present results in the slip flow regimes is evaluated against other available theoretical and experimental results. The thermal and compressibility effects on the pressure and...

#### Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers

, Article Microsystem Technologies ; Volume 14, Issue 2 , 2008 , Pages 145-157 ; 09467076 (ISSN) ; Alasty, A ; Akbari, J ; Sharif University of Technology
2008

Abstract

In this paper, the two-point boundary value problem (BVP) of the nano-cantilever deflection subjected to Casimir and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the nano-beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the beam are computed under the combined effects of electrostatic and Casimir forces. Electrostatic microactuators...

#### On the existence of positive solution for second-order multi-points boundary value problems

, Article Journal of Computational and Applied Mathematics ; Volume 193, Issue 1 , 2006 , Pages 269-276 ; 03770427 (ISSN) ; Mehri, B ; Sharif University of Technology
2006

Abstract

Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically. © 2005 Elsevier B.V. All rights reserved

#### Closed form solutions for the motion of electrically excited micro-cantilever beams

, Article 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006, Chicago, IL, 5 November 2006 through 10 November 2006 ; 2006 ; 1096665X (ISSN); 0791837904 (ISBN); 9780791837900 (ISBN) ; Ahmadian, M. T ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2006

Abstract

The differential equation governing the motion of an electrically excited capacitive microcantilever beam is a nonlinear PDE [1]. Accurate analysis about its motion is of great importance in MEMS' dynamical response. In this paper first the nonlinear 4th order 2 point boundary value problem (ODE) governing the static deflection of the system is solved using three methods. 1. The nonlinear part is linearized and its exact solution is obtained. 2. For low applied DC voltages (not near pull-in) the solutin is found using the direct straight forward perturbation analysis. 3. Numerical computer solutions which are used for the previous solution's verifications. The next parts are devoted to the...

#### Axisymmetric circular indentation of a half-space reinforced by a buried elastic thin film

, Article Mathematics and Mechanics of Solids ; Vol. 19, issue. 6 , 2014 , p. 703-712 ; Eskandari, M ; Sharif University of Technology
Abstract

The analytical treatment of an axisymmetric rigid punch indentation of an isotropic half-space reinforced by a buried extensible thin film is addressed. With the aid of appropriate displacement potential functions, Hankel transforms, and some mathematical techniques, the mixed boundary value problem under consideration is reduced to a Fredholm integral equation of the second kind. The most interesting results of the problem, including the equivalent normal stiffness of the system and the contact stress distribution beneath the rigid punch, are expressed in terms of the solution of the obtained Fredholm integral equation. Some limiting cases corresponding to inextensible and extremely...