Sharif Digital Repository

In this thesis, buckling of truncated conical shells made of composite laminates with general lamination sequence is investigated. The conical shell is considered under axial compression with simply supported or clamped boundary condition. First, Donnel type nonlinear equations and boundary conditions for doubly curved shells are obtained using Hamilton principle. Second, using adjacent equilibrium criterion, the nonlinear equations was linearized then with defining lame parameters and curvature radius, the linear equations of conical shell was extracted. The power series and Galerkin method was used to solve differential equations. The obtained results are in good agreement with available... 

In the present study, the buckling of generally laminated truncated conical shells having thickness variation expressed by a linear function, subjected to axial compression with simply or clamped supports has been considered. To begin with, the fundamental relations for a conical shell with variable thickness have been derived applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy; non-linear terms of Donnell equations by the help of adjacent-equilibrium criterion are linearized. Governing equations are solved using power series method and are applicable for all combinations of classical boundary conditions. The results are validated with Galerkin... 

During the past decade, element free methods have achieved great successes. One of these methods is the so called RKPM which has a suitable structure for use in fracture mechanics problems. Despite all characteristic abilities of element free methods; these methods due to their higher order continuous differentiable approximations fail to model discontinuous material properties of the subjected domains. In this study by improving the collocation method in RKPM treatment of such conditions have been achieved. Also in this study performance of a new meshfree method in fracture mechanics problems has been analyzed. GRKPM is one of these methods which its suitable accuracy and convergence has... 

Recently, there has been a strong interest in the development of a new class of meshfree methods. As an alternative to the finite element method (FEM), mainly due to elimination of high cost mesh generation processes. In addition, the size effect is currently a subject of increasing interest since it is an important parameter in predicting, correctly, the mechanical behavior of materials with microstructure. It was well established that classical linear elastic continua which neglects the higher order terms is not able to describe size effects. In contrast, enhanced continuum theories such as nonlocal or gradient-dependent models do involve an internal length scale. Thorough this length... 

Due to a rapid growth in the consumption of fossil fuels, the emission of greenhouse gases has multiplied in the atmosphere in the past few decades. This issue can directly affect on the rise of global temperature. Because of the intensification of the global warming, international organizations are looking for ways to reduce the greenhouse effect. One of these methods is injecting and trapping greenhouse gases, especially carbon dioxide, resulting from the operation of power plants and other large industries and preventing it from entering the atmosphere. The injection of carbon dioxide in underground salt water reservoirs can have various effects such as mechanical, hydraulic, thermal, and... 

Land subsidence is one of the consequences of groundwater withdrawal. This phenomenon can cause cracks in the surrounding structures, balance out the foundation of bridge piers, damage to roads, pipelines, etc. The main goal of this study is to provide a coupled flow-deformation model capable of simulation of land subsidence associated with groundwater extraction in unsaturated isotropic and true anisotropic aquifer systems, using the element-free Galerkin (EFG) method. Using this model and based on the geological features of an aquifer, we can easily forecast the hydraulic head change and land subsidence in different places and times during groundwater pumping. According to the current... 

In this study, a fully coupled three-dimensional numerical analysis of two-phase fluid flow and heat transfer through deformable porous media is presented in the context of extended element free Galerkin method. By coupling momentum balance equation for the whole mixture, continuity equations of wetting and non-wetting fluid phases and energy balance equation, the developed numerical algorithm is capable of simulating a wide range of engineering problems such as CO2 sequestration, nuclear waste disposal in deep underground strata, hydraulic fracturing in oil and gas reservoirs and so on.By taking the advantages of partition of unity property of MLS shape functions, weak and strong... 

Hydraulic fracturing is a process during which a viscous fluid under relatively high pressure and flow rate is injected into a wellbore to induce and propagate a system of cracks in the ground.Hydraulic fracturing of underground formations has been widely used in different fields of
engineering, such as petroleum engineering, geotechnical engineering, environmental engineering, mining engineering,and so on.Despite the technological advances in the techniques of in-situ hydraulic fracturing, the industry lacks a realistic and reliable numerical model to design cost - effective and efficient hydraulic fracturing treatment.This is due to the complex interaction and strong coupling between... 

Greenhouse gas emissions into the atmosphere have multiplied with the increase in fossil fuel consumption, which directly affects global warming. Global warming has other undesirable consequences such as rising sea water level and declining snow cover. To reduce greenhouse gases in the atmosphere, researchers have studied various ways, one of which is carbon dioxide injection into underground formations, which has a significant effect on reducing the amount of these gases in the atmosphere. Existence of high volume underground reservoirs with suitable conditions for gas injection to prevent gas escape has made it a widely used and effective method. Despite many advantages of this method, it... 

In this thesis, we consider an implicit approximation scheme for the stochastic heat equation with additive and multiplicative space-time white noise. we use the spectral Galerkin method in space combined with the linear implicit Euler method in time to simulate weak approximation error  

High power, broadband amplifiers at microwave and millimeter wave frequencies are needed for military and civilian applications. High power, broadband, high linearity, low noise, high efficiency and graceful degradation on failure are among the most important features in amplifier design. Solid state and vacuum tube devices have many disadvantages. A promising solution has been spatial power combining technique. Spatial power combining is a method of coherently combining the power of many amplifying devices using free space as the power dividing/combining medium within a guided wave structure in contrast to traditional circuit based amplifiers. This thesis presents the design and fabrication... 

In this thesis we study Galerkin methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. The strong error of convergence for spatially semidiscrete approximations as well as a spatio-temporal discretization which is based on a linear implicit Euler–Maruyama method, are also investigated. We see that the obtained error estimates in both cases as well as the regularity results for the mild solution of the SPDE are optimal. The results hold for different Galerkin methods such as the standard finite element method or spectral Galerkin. At the end, these theoretical findings are accompanied by several numerical... 

Existing closed form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be applied for coastal aquifers where seawater intrusion induces a variable velocity field. The Fourier series method is adapted to obtain a semi-analytical solution for contaminant transport in confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. The developed method can be applied for different scenarios of contamination. Two scenarios dealing with, respectively, contaminant leakage from a source at the aquifer top surface and aquifer contamination from the landward boundary are... 

In this thesis, a reduced model of a distributed one-dimensional Solid Oxide Fuel Cell (SOFC) system is presented. Consequently the reduced model is used to estimate the states of the exact model. The reduced model is derived using the exact solution of the distributed model and implementing the Karhunen-Loève-Galerkin procedure. To achieve an exact solution of the distributed model, method of lines is used. In the method of lines, accuracy of the solution depends on the number of grid points. To increase the accuracy, the number of grid points should be increased which will lead to a high order dynamic model. Such a model is not suitable for state estimation, optimization or control... 

In this thesis we study sharp spatial and temporal mean-square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infinite dimensional fractional Brownian motion with the Hurst parameter greater than one-half. In addition, the mean-square numerical approximations of such problems are investigated, performed by the spectral Galerkin method in space and the linear implicit Euler method in time. We see that by using the obtained sharp regularity properties of the problems one can identify optimal mean-square convergence rates of the full discrete scheme. At the end, these theoretical findings are accompanied by several numerical... 

Because the structural stability is directly related with structural damage, it is considered one of the most important issues in the industry. One of the applied cases in the stability issue discuss about the stability of the beam under follower loads. Follower loads obtained from aerodynamic pressure, rocket’s thrust, dry friction of the rotating disk, drilling and etc. Because the follower loads are always perpendicular to the beam cross section, thus with changing the angle of their location, their directions are changed. Spatial dependence makes a non-conservative and dynamic problem. So these loads causes dynamic instability that say flutter. In this study, the stability of a... 

In this dissertation, hybrid meshless method for electromagnetic wave scattering has been presented. The idea of the dissertation is the use of two robust meshless shape functions i.e. MLS and RPIM simultaneously to solve differential and integral equations from 3D scattering equations respectively. Finite element method (FEM) and method of moments (MoM) are used extremely for computing scattering problems. These methods are powerful and their results are accurate enough. One of their disadvantages is the need of mesh generation. Mesh generation in FEM is a time consuming process. Furthermore, in electromagnetic problems that involve geometrical, the use of an underlying mesh creates... 

In this study, the linear dynamic response of an inclined FGM Timoshenko beam on linear viscoelastic foundation subjected to a traveling mass with constant and variable velocity is investigated. Timoshenko beam theory and von-karman strain-displacement relations are utilized to model the problem. the FGM beam is made of metal and ceramic and it is assumed that material properties of the beam vary continuously in the thickness direction according to the exponential law and the power-law form. The kelvin-voigt damping model is applied to model the internal damping of the FGM beam. The partial differential equations of motion for the bending rotation of cross-section, longitudinal and... 

Microelectromechanical have wide application in mechanic, aerospace, medical, transport and information technology.
Due to large scale application and production, low costs and low energy consumption, these systems have been used in wide range of fields of engineering. Electrostatically actuated microbeams are extensively used as microelectromechanical systems (MEMS) such as microswitch and microresonator. The main component of electrically driven is microbeam. Microbeam acts as top surface of a capacitor with fixed bottom. The capacitance of capacitor changes due to the deflection of the microbeam. In this study static deflection of electrostatically actuated microbeam has been...