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#### A high-order nodal discontinuous galerkin method for solution of compressible non-cavitating and cavitating flows

, Article Computers and Fluids ; Volume 156 , 2017 , Pages 175-199 ; 00457930 (ISSN) ; Hajihassanpour, M ; Sharif University of Technology
Abstract

In this work, a high-order nodal discontinuous Galerkin method is applied and assessed for the simulation of compressible non-cavitating and cavitating flows. The one-fluid approach with the thermal effects is used to properly model the cavitation phenomenon. Here, the spatial and temporal derivatives in the system of governing equations are discretized using the nodal discontinuous Galerkin method and the third-order TVD Runge–Kutta method, respectively. Various numerical fluxes such as the Roe, Rusanov, HLL, HLLC and AUSM+-up and two discontinuity capturing methods, namely, the generalized MUSCL limiter and a generalized exponential filter are implemented in the solution algorithm. At...

#### A continuous vibration theory for rotors with an open edge crack

, Article Journal of Sound and Vibration ; Volume 333, Issue 15 , 21 July 2014 , Pages 3522–3535 ; Heydari, M ; Behzad, M ; Sharif University of Technology
Abstract

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free...

#### Some advantages of the elliptic weight function for the element free galerkin method

, Article 2005 ASME Pressure Vessels and Piping Conference, PVP2005, Denver, CO, 17 July 2005 through 21 July 2005 ; Volume 2 , 2005 , Pages 459-464 ; 0277027X (ISSN) ; Asghari, M ; Sharif University of Technology
2005

Abstract

In this paper, an anisotropic weight function in the elliptic form is introduced for the Element Free Galerkin Method (EFGM). In the circular (isotropic) weight function, each node has one characteristic parameter that determines its domain of influence. In the elliptic weight function, each node has three characteristic parameters that are major influence radius, minor influence radius and the direction of the major influence. Using the elliptic weight function each point of the domain may be affected by a less number of nodes in certain conditions. Thus, the computational cost of the method is decreased. In addition, the dependency of the solution on the method that is used for the...

#### Application of differential quadrature method to investigate dynamics of a curved beam structure acted upon by a moving concentrated load

, Article Indian Journal of Science and Technology ; Volume 5, Issue 8 , 2012 , Pages 3085-3089 ; 09746846 (ISSN) ; Kananipour, H ; Chavoshi, H ; Zarfam, R ; Sharif University of Technology
Abstract

Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM)...

#### Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential

, Article Positivity ; Volume 21, Issue 4 , 2017 , Pages 1545-1562 ; 13851292 (ISSN) ; Vaezpour, S. M ; Hesaaraki, M ; Sharif University of Technology
Abstract

This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type (Formula Presented.)▵2u-λM(‖∇u‖2)▵u-μ|x|4u=h(x)uγ+k(x)uα,under Navier boundary conditions, u= ▵u= 0. Here Ω⊂ RN, N≥ 1 is a bounded C4-domain, 0 ∈ Ω, h(x) and k(x) are positive continuous functions, γ∈ (0 , 1) , α∈ (0 , 1) and M: R+→ R+ is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for m0 and 0 < μ< μ∗. Here μ∗=(N(N-4)4)2 is the best constant in the Hardy inequality. Besides, if μ= 0 , λ> 0 and h, k are Lipschitz functions, we show that this problem has a positive smooth...

#### Nonlinear free vibrations of a Timoshenko beam using multiple scales method

, Article Proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis - 2004, Manchester, 19 July 2004 through 22 July 2004 ; Volume 2 , 2004 , Pages 101-106 ; 0791841731 (ISBN); 9780791841730 (ISBN) ; Ghorashi, M ; Sharif University of Technology
American Society of Mechanical Engineers
2004

Abstract

In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton's principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam

#### Elasto-plastic element-free Galerkin method

, Article Computational Mechanics ; Volume 33, Issue 3 , 2004 , Pages 206-214 ; 01787675 (ISSN) ; Toussi, H. E ; Fariborz, S. J ; Sharif University of Technology
Springer Verlag
2004

Abstract

In this paper the element free Galerkin method (EFGM) has been extended to be used in the elastoplastic stress analysis. The developed method has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. To do this, at the first step by using the incremental relations of plastic deformation a system of elastoplastic EFGM equations has been derived. Since the obtained relations are nonlinear, a nonlinear solution technique has been chosen. To examine the validity of this technique, stress fields in two different plates with and without a crack have been calculated and the results have been compared with other similar analytical works in the...

#### Global existence, blow-up and asymptotic behavior of solutions for a class of p(x)-Choquard diffusion equations in RN

, Article Journal of Mathematical Analysis and Applications ; Volume 506, Issue 2 , 2022 ; 0022247X (ISSN) ; Hamdani, M. K ; Bayrami Aminlouee, M ; Sharif University of Technology
Academic Press Inc
2022

Abstract

In this paper, we investigate the local and global existence, asymptotic behavior, and blow-up of solutions to the Cauchy problem for Choquard-type equations involving the p(x)-Laplacian operator. As a particular case, we study the following initial value problem [Formula presented] where p,q,V:RN→R and α:RN×RN→R are continuous functions that satisfy some conditions which will be stated later on, and u0:RN→R is the initial function. Under some appropriate conditions, we prove the local and global existence of solutions for the above Cauchy problem by employing the abstract Galerkin approximation. Moreover, the blow-up of solutions and large-time behavior are also investigated. © 2021...

####
Derivation of Dynamical Governing Equations of Convex Mirrors with

Network of Actuators

,
M.Sc. Thesis
Sharif University of Technology
;
Jalali, Mir Abbas
(Supervisor)
Abstract

The turbulence in the atmosphere will limit the performance of astronomical telescopes on the ground thus a technique for solving this problem is needed that is Adaptive optics technique. We know Adaptive optics in its simplest definition as a process to improve the quality of image by means of deformation of the wave fronts to compensate the beam path anomalies. The main components of this system are the wave front sensor and deformable mirror. Deformable mirror is used in the system of this technique also plays an important role in the correction of anomalies of eye. Type of actuators that can be used for deformable mirror, pattern of them, and also the way of connecting the actuators to...

#### Nonlinear Vibration Analysis of a Closed Ends ,Fluid-Filled Beam with Different Boundary Condition, Using Galerkin Method

, M.Sc. Thesis Sharif University of Technology ; Dehghani Firoozabadi, Rouhollah (Supervisor)
Abstract

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...

#### A comparative study of earthquake source models in high-order accurate tsunami simulations

, Article Ocean Modelling ; Volume 141 , 2019 ; 14635003 (ISSN) ; Bonev, B ; Hesthaven, J. S ; Sharif University of Technology
Elsevier Ltd
2019

Abstract

The discontinuous Galerkin method is used to solve the non-linear spherical shallow water equations with Coriolis force. The numerical method is well-balanced and takes wetting/drying into account. The two fold goal of this work is a comparative study of dynamic and static tsunami generation by seabed displacement and the careful validation of these source models. The numerical results show that the impact of the choice of seabed displacement model can be significant and that using a static approach may result in inaccurate results. For the validation of the studies, we consider measurements from satellites and buoy networks for the 2011 Tohoku event and the 2004 Sumatra–Andaman tsunami. The...

#### Dynamics of a laminated composite beam on pasternak-viscoelastic foundation subjected to a moving oscillator

, Article JVC/Journal of Vibration and Control ; Volume 14, Issue 6 , 2008 , Pages 807-830 ; 10775463 (ISSN) ; Jafari Talookolaei, R. A ; Esmailzadeh, E ; Sharif University of Technology
2008

Abstract

Dynamic behavior of a laminated composite beam (LCB) supported by a generalized Pasternak-type viscoelastic foundation, subjected to a moving two-degree-of-freedom (DOFs) oscillator with a constant axial velocity is studied. Analytical solution using the Galerkin method is sought and the couplings of the bending-tension, shear-tension, and bending-twist with the Poisson effect are considered. The possible separation of the moving oscillator from LCB during the course of motion is investigated by monitoring the contact force between the oscillator and LCB. The effects of the non-rigid foundation, oscillator parameters, and the load speed on the separation are also studied. It is found that...

#### Flexural-torsional behavior of thin-walled composite beams with closed cross-section

, Article Thin-Walled Structures ; Volume 45, Issue 7-8 , 2007 , Pages 699-705 ; 02638231 (ISSN) ; Haddadpour, H ; Kouchakzadeh, M. A ; Sharif University of Technology
2007

Abstract

This paper investigates the static and dynamic characteristics of composite thin-walled beams that are constructed from a single-cell box. The structural model considered herein incorporates a number of nonclassical effects, such as material anisotropy, transverse shear, warping inhibition, nonuniform torsional model and rotary inertia. The governing equations were derived using extended Hamilton's principle and solved using extended Galerkin's method. The effects of fiber orientation on static deflection and natural frequencies are considered and a number of important conclusions are outlined. © 2007 Elsevier Ltd. All rights reserved

#### Effects of rotary inertia and shear deformation on nonlinear vibration of micro/nano-beam resonators

, Article 2005 ASME International Mecahnical Engineering Congress and Exposition, IMECE 2005, Orlando, FL, 5 November 2005 through 11 November 2005 ; Volume 7 MEMS , 2005 , Pages 439-445 ; 1096665X (ISSN); 079184224X (ISBN); 9780791842249 (ISBN) ; Alasty, A ; ASME Micro Electro Mecahnical Systems Division ; Sharif University of Technology
2005

Abstract

In this paper, the large amplitude tree vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton's principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the...

#### A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

, Article Engineering Analysis with Boundary Elements ; Vol. 39, issue. 1 , 2014 , pp. 53-63 ; ISSN: 09557997 ; Pak, A ; Sharif University of Technology
Abstract

In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the...

#### Non-isothermal simulation of the behavior of unsaturated soils using a novel EFG-based three dimensional model

, Article Computers and Geotechnics ; Volume 99 , 2018 , Pages 93-103 ; 0266352X (ISSN) ; Pak, A ; Samimi, S ; Sharif University of Technology
Elsevier Ltd
2018

Abstract

In this paper, a three-dimensional simulation of fully coupled multiphase fluid flow and heat transfer through deforming porous media is presented in the context of EFG mesh-less method. Spatial discretization of the system of governing equations is performed using EFG and a fully implicit finite difference scheme is employed for temporal discretization. Penalty method is used for imposition of essential boundary conditions. The developed numerical tool is employed to simulate two problems of nuclear waste disposal and CO2 sequestration in deep underground strata. The obtained results demonstrate the capability and robustness of the developed EFG code. © 2018 Elsevier Ltd

#### A high-order nodal discontinuous Galerkin method to solve preconditioned multiphase Euler/Navier-Stokes equations for inviscid/viscous cavitating flows

, Article International Journal for Numerical Methods in Fluids ; Volume 92, Issue 5 , 2020 , Pages 478-508 ; Hejranfar, K ; Sharif University of Technology
John Wiley and Sons Ltd
2020

Abstract

In this study, a high-order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier-Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual-time stepping...

#### An implicit dual-time stepping high-order nodal discontinuous Galerkin method for solving incompressible flows on triangle elements

, Article Mathematics and Computers in Simulation ; Volume 168 , 2020 , Pages 173-214 ; Hejranfar, K ; Sharif University of Technology
Elsevier B.V
2020

Abstract

In this work, a high-order nodal discontinuous Galerkin method (NDGM) is developed and assessed for the simulation of 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several...

#### A high-order nodal discontinuous Galerkin method for simulation of three-dimensional non-cavitating/cavitating flows

, Article Finite Elements in Analysis and Design ; Volume 200 , 2022 ; 0168874X (ISSN) ; Hejranfar, K ; Sharif University of Technology
Elsevier B.V
2022

Abstract

In this study, the nodal discontinuous Galerkin method is formulated in three-dimensions and applied to simulate three-dimensional non-cavitating/cavitating flows. For this aim, the three-dimensional preconditioned Navier-Stokes equations based on the artificial compressibility approach considering appropriate source terms to model cavitating phenomena are used. The spatial derivative terms in the resulting equations are discretized by utilizing the nodal discontinuous Galerkin method on tetrahedral elements and the derivative of the solution vector with respect to the artificial time is discretized by applying an explicit time integration method. An artificial viscosity method is formulated...

#### A continuous vibration theory for beams with a vertical edge crack

, Article Scientia Iranica ; Volume 17, Issue 3 B , 2010 , Pages 194-204 ; 10263098 (ISSN) ; Ebrahimi, A ; Meghdari, A ; Sharif University of Technology
2010

Abstract

In this paper, a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement field is a superposition of the classical Euler-Bernoulli beam's displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of J-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modified...