Sharif Digital Repository

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... 

In this research, mathematical modeling, deriving equations of motion, solving equations and analyzing the response of motion vibrations of a moving mass with constant speed on a sandwich beam have been discussed. The sandwich beam consists of three layers, the middle layer of which is made of viscoelastic material, and the upper and lower layers are the Euler-Bernoulli beam model.At first, this sandwich beam is mathematically modeled, This mathematical modeling includes all the specifications of the system to obtain the equations that govern the behavior of the system. Then, the displacement field of the system has been extracted and the equations of motion of the system have been obtained... 

The present research aims to achieve two main objectives in the Rotordynamic. The first one is, study and calculate the linear dynamic coefficients of a tapered gas seal, and the second one is, analysis the dynamic behavior and stability of the Timoshenko rotor supported with tapered gas seal. Classical Reynolds equation is used to calculate the dynamic coefficients of tapered gas seal. At first, using the perturbation method, the perturbed equations for gas film thickness and pressure are obtained. The finite difference method (FDM) is utilized to transfer the obtained PDEs to the algebraic system of equations. The algebraic system of equations then solved, and the zeroth and first-order... 

In this project, vibration and stability condition of a pipe conveying flow has been studied for use in firefighting plane. The Plane is a multi-rotor that carries the pipe to a certain height and it does the washing work there, bassed on the fluid flow from the nozzle embedded in the end of the pipe. Due to the flexibility of the pipe in this application, structure modeling is based on cable without bending stiffness. The Galerkin method is used to solve equations by considering the assumed mode shape for structure. At first, by analyzing free vibrations, different boundary conditions were considered for the pipe and the natural frequencies and natural shape modes were extracted in... 

This study presents coupled bending and torsional vibration of rotating shaft. Jeffcott rotor and Euler Bernoulli beam model are used for simulating rotating shaft. The fractional damper is used for absorbing vibration of coupling lateral and torsional vibration. Based on Lagrange method and Hamilton principle, the formulation of Jeffcott rotor and Euler Bernoulli beam vibration are obtained. Then by transforming equations in Laplace domain, the characteristic equations are obtained. In Euler Bernoulli beam, the Galerkin method is implemented to solve the governing equations. The stability of structure is investigated in Laplace domain. The effect of various parameters including power of... 

The current study is dedicated to free vibration analysis of a thin cylindrical shell with an oblique end. To this end, governing equations of motion and the corresponding boundary conditions are derived using Hamiltonian formulations. The differential form of equations is obtained by applying by part integration to the integral form of equations of motion. Equations of motions have been solved by Galerkin method for two different kinds of boundary conditions. Convergence process for different kinds of conditions has been done and results compared with papers. The effect of different parameters such as, length of cylinder, oblique angle, thickness etc. on the fundamental frequencies has been... 

The current study is dedicated to free vibration and Aeroelastic Stability Analysis of Truncated Conical Panels in Supersonic Flows. Governing equations of motion and the corresponding boundary conditions are derived using Hamiltonian formulations. The aeroelastic stability problem is formulated based on first-order shear deformation theory as well as classical shell theory with the linearized first-order piston theory for aerodynamic loading and solved using Galerkin method. The flutter boundaries are obtained for truncated conical shells with different semi-vertex cone angles, different subtended angles, and different thickness  

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... 

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... 

Presence of fluid in closed ends beam can increase beam hardness against pressure and buckling loads. This behavior is due to incompressibility or very low compressibility of fluids. there is a lot of research in the literature focusing on fluid solid interaction in pipe flow, but there is not any reported research studying on fluid filled beam, where fluid doesn’t flow across the beam. In this research hollow beam is modeled with Euler -Bernoulli beam theorem. Potential energy and kinetic energy is derived with considering the incompressibility of fluid. Nonlinear system of equations is derived using Hamilton principle . this system is taken to time domain using Galerkin and assumed mode... 

With the recent trend to use thin shell structures in severe operational conditions, it is not sufficient to employ the classical linear theory to analyze their dynamic behavior, especially with large amplitudes. When the transverse deflection of a shell raise to the order of its thickness, the nonlinear effects grow significantly, leading to a variety of complex responses, such as the variable frequencies depending on the amplitude and the jump phenomenon. This dynamic behavior should be analyzed by the nonlinear theory of shells. In this research, the nonlinear vibration of composite shallow circular cylindrical shells is considered. The geometric nonlinear strains are of the von Karman... 

In the present work, the buckling behavior of a composite beam with circular, rectangular and pentagonal cross sections is investigated. The structural model is based on the first order shear deformation theory (FSDT) and incorporates other non-classical effects such as primary and secondary warpings and restrained warping. The linear buckling equations are derived from the non-linear governing equations of motion and their associated boundary conditions and solved using the Galerkin method for a composite beam with the clamped-free end condition and the special layup configuration of Circumferentially Asymmetric Stiffness (CAS) which induces elastic couplings between torsional and flexural... 

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... 

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 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... 

Thermal and compositional variations through porous media are the main causes of bringing changes in the density of the fluid in place and arising in density-driven flow. This phenomenon is usually called thermohaline or thermosolutal convection (TC). When the flow is driven by the concentration gradient of two different compositions the problem is called double-diffusive convection (DDC). This phenomenon can be observed in several applications as in geological carbon dioxide sequestration, geothermal systems, underground thermal energy storage, salt mining, salt domes, groundwater management, waste disposal, and seawater intrusion.Despite that TC processes are three-dimensional by nature... 

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... 

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... 

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...