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extended-kantorovich-method
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Modeling squeezed film air damping in torsional micromirrors using extended Kantorovich method
, Article Meccanica ; Volume 48, Issue 4 , 2013 , Pages 791-805 ; 00256455 (ISSN) ; Ahmadian, M. T ; Farshidianfar, A ; Sharif University of Technology
2013
Abstract
The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for...
Analytical determination of shear correction factor for Timoshenko beam model
, Article Steel and Composite Structures ; Volume 29, Issue 4 , 2018 , Pages 483-491 ; 12299367 (ISSN) ; Faghidian, S. A ; Shodja, H. M ; Sharif University of Technology
Techno Press
2018
Abstract
Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the non-uniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution...
Modeling and Statical, Vibrational and Dynamical Analysis of Electrically actuated Microplates Using the Extended Kantorovich Method
, M.Sc. Thesis Sharif University of Technology ; Ahmadiyan, Mohammad Taghi (Supervisor)
Abstract
Nano/Microelectromechanical systems have generated a great impact on industry and technology. There are many applications for these systems in micropumps, airbag accelerometers and inkjet printer heads. In theses systems mechanical and electrical fields are involved with each other, and complexities due to this involvement has prevented the scientific society from an effective tool for analysis of this systems in computational point of view. So the objective of this project is to use the Extended Kantorovich method to solve the equations of microplate deformation due to electrostatic actuation. This method is based on variational principals and it uses an initial guess function which doesn’t...
Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method
, Article Archive of Applied Mechanics ; Volume 83, Issue 2 , February , 2013 , Pages 177-191 ; 09391533 (ISSN) ; Aghdam, M. M ; Kargarnovin, M. H ; Sharif University of Technology
2013
Abstract
Free vibration analysis of moderately thick rectangular FG plates on elastic foundation with various combinations of simply supported and clamped boundary conditions are studied. Winkler model is considered to describe the reaction of elastic foundation on the plate. Governing equations of motion are obtained based on the Mindlin plate theory. A semi-analytical solution is presented for the governing equations using the extended Kantorovich method together with infinite power series solution. Results are compared and validated with available results in the literature. Effects of elastic foundation, boundary conditions, material, and geometrical parameters on natural frequencies of the FG...
Application of the extended kantorovich method to the static deflection of microplates under capillary force
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE), 12 November 2010 through 18 November 2010 ; Volume 10 , November , 2010 , Pages 113-119 ; 9780791844472 (ISBN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Sharif University of Technology
2010
Abstract
The aim of this paper is to apply an Extended Kantorovich method (EKM) to simulate the static deflection of microplates under capillary force. The model accounts for the capillary force nonlinearity of the excitation. Starting from a one term Galerkin approximation and following the Extended Kantorovich procedure, the equations governing the microplate deflection are obtained. These equations are then solved iteratively with a rapid convergence procedure to yield the desired solution. The effects of capillary force on the pull-in phenomenon of microplates are delineated in some figures. It is shown that rapid convergence, high precision and independency of initial guess function makes the...
Bending analysis of thin skew plates using extended Kantorovich method
, Article ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, ESDA2010, 12 July 2010 through 14 July 2010, Istanbul ; Volume 2 , 2010 , Pages 39-44 ; 9780791849163 (ISBN) ; Joodaky, A ; Sharif University of Technology
2010
Abstract
An accurate approximate closed-form solution is presented for bending of thin skew plates with clamped edges subjected to uniform loading using the extended Kantorovich method (EKM). Successive application of EKM together with the idea of weighted residual technique (Galerkin method) converts the governing forth-order partial differential equation (PDE) to two separate ordinary differential equations (ODE) in terms of oblique coordinates system. The obtained ODE systems are then solved iteratively with very fast convergence. In every iteration step, exact closed-form solutions are obtained for two ODE systems. It is shown that some parameters such as angle of skew plate have an important...
Free vibration analysis of symmetrically laminated fully clamped skew plates using extended Kantorovich method
, Article Key Engineering Materials, 22 March 2011 through 24 March 2011, Kuala Lumpur ; Volume 471-472 , 2011 , Pages 739-744 ; 10139826 (ISSN) ; 9783037850596 (ISBN) ; Kargarnovin, M. H ; Aghdam, M. M ; Sharif University of Technology
2011
Abstract
In this paper, free vibration analysis of thin symmetrically laminated skew plates with fully clamped edges is investigated. The governing differential equation for skew plate which is a fourth order partial differential equation (PDE) is obtained by transforming the differential equation in Cartesian coordinates into skew coordinates. Based on the multi-term extended Kantorovich method (MTEKM) an efficient and accurate approximate closed-form solution is presented for the governing PDE. Application of the MTEKM reduces the governing PDE to a dual set of ordinary differential equations. These sets of equations are then solved with infinite power series solution, in an iterative manner until...
Free Vibration Analysis of Moderately Thick Rectangular Plate Made of Functionally Graded Material on Arbitrary Supports Using Extended Kantorovich Method
, M.Sc. Thesis Sharif University of Technology ; Kargarnovin, Mohammad Hossein (Supervisor) ; Mohammadi Aghdam, Mohamamd (Supervisor)
Abstract
In this study, free vibration analysis of moderately thick rectangular FG plates with general boundary conditions is investigated. Governing equations of motion are obtained based on the Mindlin plate theory. A semi analytical solution is presented for the governing equations using extended Kantorovich method (EKM). Results are compared and validated with available results in the literature. Effects of different parameters such as boundary conditions, material and geometrical parameters on natural frequencies of the FG plates are investigated
Linear and Nonlinear Analysis of Functionally Graded Annular Sector Plate with Various Boundary Condition under Tranverse Mechanical Loading by Using Extended Kantorovich Method
, M.Sc. Thesis Sharif University of Technology ; Fallah Rajabzadeh, Famida (Supervisor)
Abstract
In this study, linear and nonlinear mechanical behavior of moderately thick annular sector plates made of functionally graded materials is investigated. In linear analysis, based on first order shear deformation theory, governing equation with two different approaches are derived. In first approach, by application of extended Kantorovich method (EKM), displacements field variables are expressed as separable function of and together, and two sets of ordinary differential equations (ODEs) by using the principle of minimum total potential energy are derived. In the second approach, within FSDT and using the principle of minimum total potential energy, the governing partial differential...
Free Vibration Analysis of FG Annular Sector Plates Using Extended Kantrovich Method
, M.Sc. Thesis Sharif University of Technology ; Fallah Rajabzadeh, Famida (Supervisor)
Abstract
In this study the free vibration of annular sector plates made of functional materials with using the extended Katrovich method is investigated for a variety of boundary conditions. For this purpose, based on the first order shear deformation theory and Hamilton's principle, equations of motion that they are five differential equations and coupled, are derived. Due to the difficulty of the equations obtained by applying extended kantrovich method on these equations, two ordinary differential equations obtained, the two categories combined fixed and simple boundary conditions will be solved by using generalized differential quadrature and in an iterative process system natural frequency is...
Nonlinear Vibration and Pull-in Analysis in Electrostatically Actuated Dual Axis Micromirrors
, M.Sc. Thesis Sharif University of Technology ; Ahmadian, Mohammad Taghi (Supervisor) ; Firoozbakhsh, Keykhosro (Supervisor)
Abstract
In recent decades, the important role of MEMS devices in optical systems has initiated the development of a new class of MEMS called Micro-Opto-Electro-Mechanical Systems (MOEMS), which torsional micromirror is one of these systems. Among variety kinds of micromirrors the dual axis micromirror has hopefully application such as high quality projection display, free-space fiber optical (FSO) communications and endoscopic optical coherence topography. Dual axis micromirror could play a key role in FSO applications such as satellite-to-satellite separated by hundreds of kilometers, as where. In medical applications, micromirror must could be able to rotates θ_x and θ_y.about two axis x and...
Nonlinear Analysis of FG Rectangular Plates under Mechanical and Thermo-Mechanical Loads using the Extended Kantorovich Method
, M.Sc. Thesis Sharif University of Technology ; Nasier, Asghar (Supervisor)
Abstract
The purpose of this research is to provide an analytical solution using first order shear deformation theory for nonlinear bending of rectangular FG plate under mechanical and thermal loads with different boundary conditions. To achieve this goal, extended Kantorovich method have been used. This method has a high convergence rate and is more accurate than other approximate methods, such as the Ritz and Galerkin methods, because the partially differential equations are converted to ordinary differential equations. In order to solving nonlinear odes the perturbation method is used. Material of the plate is a mixture of ceramic and metal and is modeled as an isotropic and non-homogeneous...
Interlaminar Stresses Analysis of Spherical Shell with Arbitrary Laminations and Boundary Conditions under Transverse Loads
, M.Sc. Thesis Sharif University of Technology ; Hosseini Kordkheili, Ali (Supervisor)
Abstract
Today, composites are widely used in various industries, thus the study and analysis of properties and their behaviors are very important. In addition, the use of multi-layered composites in the aerospace industry is important. The composite-elastomer structures, specially their spherical shape, are widely used as flexible joint in aerospace industries, such as the thrust vector control system in solid-propellant rockets and the helicopter industry. In this study, an analytical approach is proposed for calculating the interlaminar stresses of laminated plates and spherical shells with arbitrary laminations and boundary conditions based on a threedimensional multi-term extended Kantorovich...
Nonlinear Vibration and Pull-in Analysis in Electrostatically Actuated Nano/Micromirrors
, Ph.D. Dissertation Sharif University of Technology ; Ahmadian, Mohammad Taghi (Supervisor)
Abstract
The important role of MEMS devices in optical systems has initiated the development of a new class of MEMS called Micro-Opto-Electro-Mechanical Systems (MOEMS), which mainly includes nano/micromirrors and torsional nano/microactuators. These devices have found variety of applications in optical switches, displays, micro scanning mirrors, optical cross-connects, interferometery, spectroscopy, aberration correction and biomedical imaging. In this project, the static and dynamic behavior of electrostatic nano/micromirrors under the effect of intermolecular surface forces and squeezed film damping are studied. The prior art published in the literature have mainly used pure torsion models. In a...
Bending Analysis of Rectangular FG Micro Plates using Modified Couple Stress Theory and first Order Shear Deformation Theory
, M.Sc. Thesis Sharif University of Technology ; Fallah Rajabzadeh, Famida (Supervisor) ; Farrahi, Gholamhossein (Supervisor)
Abstract
Based on the modified couple stress and Mindlin plate theories, a Levy type solution is presented for bending and vibration analysis of rectangular isotropic micro plates with simple supports at opposite edges and different boundary conditions at the other two ones. Modified couple stress theory is taken into account to capture the size effect and the governing equations are derived using Hamilton's principle, and solved by Levy solution and space-state method. The results are verified with the existing ones in the literature. As a benchmark, additional tables for vertical deflections and free vibrations of plate with various boundary conditions are presented
Geometric Interpretation to Generative Models and Optimal Transportation
, M.Sc. Thesis Sharif University of Technology ; Bahraini, Alireza (Supervisor)
Abstract
As the core of this thesis, we express the relation between optimal transportation and convex geometry especially the variational approach to solve Alexandrov problem, which leads to a geometric interpretation to adversarial models and propose a novel framework for these models. Along the way, we peruse generative adversarial networks from optimal transportation view and show that generator calculates the transportation map and the discriminator computes Wasserestein distance, which is equivalent to Kantorovich potential. By using optimal mass transportation theory and choosing an especial cost function c, we see that the generator and discriminator are equivalent. Therefore, once the...
Nonlinear Analysis of Pull-in, Contact Time and Dynamic Behavior of Microswitches Under Static and Dynamic Electric Force With Movable Base
, M.Sc. Thesis Sharif University of Technology ; Ahmadian, Mohammad Taghi (Supervisor)
Abstract
Micro electromechanical systems (MEMS) such as sensors and actuators are gaining more popularity in recent years. These systems have different application in automation, medicine and other industries. Mechanical structures are governed by electrical systems in MEMS devices and this is one of the challenges of MEMS studies. Usually these systems made by one deformable beam or plate over a fixed substrate. Due to applied voltage between substrate and deformable plate or beam, the deformable plate deflects toward the fixed substrate. The voltage at which the system becomes unstableis called pull-in voltage. Pull-in voltage is the most important characteristics of MEMS beyond which pull-in takes...
Nonlinear analysis of pull-in voltage for a fully clamped microplate with movable base
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) ; Volume 10 , 2012 , Pages 71-75 ; 9780791845264 (ISBN) ; Moeenfard, H ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
Micro-electro-mechanical systems (MEMS) such as sensors and actuators are rapidly gaining popularity in a variety of industrial applications. Usually these systems are constructed by a cantilever beam or plate along with a fixed substrate. The movable beam or plate deflects due to applied voltage between the plates. Pull-in voltage and contact time are the most important characteristic of these systems. Allowing the substrate to be movable in vertical direction pull-in voltage in comparison with the fixed substrate is expected to be much smaller. In this paper the pull-in voltage and the point at which pull-in takes place for a fully clamped microplate is evaluated. The nonlinear...
Analytical modeling of squeeze film damping in micromirrors
, Article Proceedings of the ASME Design Engineering Technical Conference, 28 August 2011 through 31 August 2011, Washington, DC ; Volume 7 , 2011 , Pages 79-85 ; 9780791854846 (ISBN) ; Ahmadian, M. T ; Farshidianfar, A ; Sharif University of Technology
2011
Abstract
In the current paper, Extended Kantorovich Method (EKM) has been utilized to analytically solve the problem of squeezed film damping in micromirrors. A one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that since EKM is highly convergent, practically one iterate is...
Application of the extended kantorovich method to the static deflection of electrically actuated microplates
, Article 2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008, Boston, MA, 31 October 2008 through 6 November 2008 ; Volume 13, Issue PART A , 2009 , Pages 325-331 ; 9780791848746 (ISBN) ; Moeenfard, H ; Pirbodaghi, T ; Sharif University of Technology
2009
Abstract
The aim of this paper is to present an Extended Kantorovich approach to simulate the static deflection of microplates under electrostatic voltage. The model accounts for the electric force nonlinearity of the excitation. Starting from a one term Galerkin approximation and following the Extended Kantorovich procedure, the equations governing the microplate deflection are obtained. These equations are then solved iteratively with a rapid convergence procedure to yield the desired solution. The results are validated, comparing them with other theoretical results and experimental findings, reported in the literature. It is shown that rapid convergence, high precision and independency of initial...