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دسترسی آزاد مقاله
1 - یک ایده جدید برای اعمال شرایط مرزی اساسی در روش بدون المان گالرکین برای حل معادلات با مشتقات جزئی بیضوی
علی مس فروش کمیل ایزدپناهروش بدون المان گالرکین یک روش شناخته شده برای حل معادلات با مشتقات جزئی است. اعمال شرایط مرزی اساسی در این روش که بر اساس تقریب کمترین مربعات متحرک انجام می شود، با پیچیدگی هایی همراه است. از آنجا که توابع شکل تقریب کمترین مربعات متحرک در خاصیت دلتای کرونیکر صدق نمی کنن چکیده کاملروش بدون المان گالرکین یک روش شناخته شده برای حل معادلات با مشتقات جزئی است. اعمال شرایط مرزی اساسی در این روش که بر اساس تقریب کمترین مربعات متحرک انجام می شود، با پیچیدگی هایی همراه است. از آنجا که توابع شکل تقریب کمترین مربعات متحرک در خاصیت دلتای کرونیکر صدق نمی کنند، نمی توان همانند روش عناصر متناهی، شرایط مرزی اساسی را به صورت مستقیم در فرم ضعیف گالرکین معادله اعمال کرد و نیاز به روش های اصلاحی برای فرم ضعیف معادله داریم. در این مقاله یک ایده جدید برای اعمال شرایط مرزی اساسی در روش بدون المان گالرکین برای حل معادلات با مشتقات جزئی بیضوی معرفی می شود. این ایده بر اساس روش کمترین مربعات متحرک درونیاب است. در این روش ابتدا شرایط مرزی را در تقریب کمترین مربعات متحرک تابع اعمال می کنیم سپس تقریب حاصل را در روش بدون المان گالرکین به کار می بریم. بنابراین شرایط مرزی به صورت مستقیم اعمال می شود. در این مقاله ابتدا تقریب کمترین مربعات متحرک درونیاب معرفی می شود و سپس نحوه اعمال شرایط مرزی بیان خواهد شد. در انتها با ارائه چند مثال مختلف کارایی روش را نشان می دهیم. پرونده مقاله -
دسترسی آزاد مقاله
2 - The Ritz-Galerkin method for MHD Couette flow of non-Newtonian fluid
Z. Barikbin R. Ellahi S. AbbasbandyIn this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galer چکیده کاملIn this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution of algebraic equations. پرونده مقاله -
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3 - Implementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
J. Biazar T. HoulariThe determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equatio چکیده کاملThe determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $x=a'$, and determining $u(a',t)$ a stable solution will be achived. An illustrative example is provided to show the ability and the efficiency of this numerical ‎approach.‎ پرونده مقاله -
دسترسی آزاد مقاله
4 - Longitudinal and Lateral Vibration Analysis of Cables in a Cable Robot Using Finite Element Method
Hami Tourajizadeh Mahdi Yousefzadeh Moharram KorayemIn this paper, vibrational response of a variable-length cable in longitudinal, lateral and torsional directions is analysed in a cable robot using FE method. The flexibility of cables has remarkable effect on positioning of the end-effector in cable robots. Also consid چکیده کاملIn this paper, vibrational response of a variable-length cable in longitudinal, lateral and torsional directions is analysed in a cable robot using FE method. The flexibility of cables has remarkable effect on positioning of the end-effector in cable robots. Also considering the fact that the length of the cables are time dependent in a dynamic cable structure like robocrane, the numerical approaches are preferable compared to analytic solutions. To do so, the cable is divided into finite elements in which the virtual work equation and Galerkin method can be implemented for the equations. Considering the stiffness matrix, the characteristic equations and Eigen values of each element can be defined. A simulation study is done in the ANSIS on a planar robocrane with 2-DOF and also for a spatial case with 6-DOF that is controlled by the aid of six variable-length flexible cables in the space for two different types of solid and flexible end-effectors. Whole the cable robot flexibility is analyzed simultaneously instead of separation calculation of each cable. Not only all of the 3-D vibrating behaviour of the whole structure is studied in this paper but also the lengths of the cables are considered as variable. The vibrating response of mode shapes, amplitude and frequencies are extracted and analysed, and the results are compared for two case of solid and flexible end-effector which shows the effect of the flexibility in the position of the end-effector and the tension of the cables in different situations. پرونده مقاله -
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5 - Frequency Analysis of Ring-Stiffened Composite Cylindrical Shell using Experimental, Analytical and Finite Element Methods
Hadi Salimi Ali Davar Mohsen Heydari Beni Jafar Eskandari Jam Majid Eskandari ShahrakiIn this paper, free vibration of laminated composite cylindrical shells reinforced with circumferential rings, are investigated with experimental, analytical and finite element methods and natural frequencies are obtained. The analysis is carried out for clamp-free and چکیده کاملIn this paper, free vibration of laminated composite cylindrical shells reinforced with circumferential rings, are investigated with experimental, analytical and finite element methods and natural frequencies are obtained. The analysis is carried out for clamp-free and clamp-clamp boundary conditions and the results are compared with each other. To solve the problem, the equilibrium Equations of motions are written according to the classical shells theory and after simplification, the structural stiffness and mass matrices and the frequency Equation are derived using Galerkin method. The results obtained in this paper, are compared with the results available in the literatures, and the results of experimental and finite element methods and good agreement is observed. پرونده مقاله -
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6 - Dynamic Behavior Analysis of a Geometrically Nonlinear Plate Subjected to a Moving Load
A Mamandi R MohsenzadehIn this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by en چکیده کاملIn this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then the Galerkin’s method is used to transform the equations of motion into the three coupled nonlinear ordinary differential equations (ODEs) and then are solved in a semi-analytical way to get the dynamical responses of the plate under the traveling load. A parametric study is conducted by changing the size of moving mass/force and its velocity. Finally, the dynamic magnification factor and normalized time histories of the plate central point are calculated for various load velocity ratios and outcome nonlinear results are compared to the results from linear solution. پرونده مقاله -
دسترسی آزاد مقاله
7 - Higher-Order Stability Analysis of Imperfect Laminated Piezo-Composite Plates on Elastic Foundations Under Electro-Thermo-Mechanical Loads
B Mirzavand M BohloolyThis article provides a fully analytical approach for nonlinear equilibrium path of rectangular sandwich plates. The core of structure is made of symmetric cross-ply laminated composite and the outer surfaces are piezoelectric actuators which perfectly bonded to inner c چکیده کاملThis article provides a fully analytical approach for nonlinear equilibrium path of rectangular sandwich plates. The core of structure is made of symmetric cross-ply laminated composite and the outer surfaces are piezoelectric actuators which perfectly bonded to inner core. The structure is subjected to electro-thermo-mechanical loads simultaneously. One side of plate is rested on Pasternak type elastic foundation. The equilibrium equations of plate are derived based on the higher-order shear deformation theory of Reddy taking into account initial geometrical imperfection, nonlinear strain-displacement relations of von-Karman, temperature dependent properties, and different types of boundary conditions. Some numerical examples are presented to verify the accuracy of the proposed formulation. The effects of various parameters such as voltage on actuators, elastic foundation, imperfection, and pre-load condition on the buckling and postbuckling behaviors are studied. As an important finding of current research, there may be exists bifurcation point for imperfect plates by applying voltage on actuators. پرونده مقاله -
دسترسی آزاد مقاله
8 - Static Bending Analysis of Foam Filled Orthogonally Rib-Stiffened Sandwich Panels: A Mathematical Model
S Soleimanian A Davar J Eskandari Jam M Heydari BeniThe current study presents a mathematical modeling for sandwich panels with foam filled orthogonally rib-stiffened core using Heaviside distribution functions. The governing equations of the static problem have been derived based on classical lamination theory. The pres چکیده کاملThe current study presents a mathematical modeling for sandwich panels with foam filled orthogonally rib-stiffened core using Heaviside distribution functions. The governing equations of the static problem have been derived based on classical lamination theory. The present model contains three displacement variables considering all of the stiffness coefficients. A closed form solution using Galerkin’s method is presented for simply supported sandwich panels with foam filled orthogonally rib-stiffened core subjected to uniform lateral static pressure. Compared to previous researches, the present work is comprehensive enough to be used for symmetric, unsymmetric, laminated or filament wound panels with orthogrid stiffeners. The accuracy of the solution is checked both through comparisons with previous works, and the results of simulation with ABAQUS software. پرونده مقاله -
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9 - Investigation of Strain Gradient Theory for the Analysis of Free Linear Vibration of Nano Truncated Conical Shell
A.R Sheykhi Sh Hosseini Hashemi A Maghsoudpour Sh Etemadi HaghighiIn this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into چکیده کاملIn this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with partial differentials along with the classical and non-classical boundary conditions. Galerkin’s method and the Generalized Differential Quadrature (GDQ) approach are applied to obtain the linear free vibrations of the carbon nano cone (CNC). The CNC is studied with simply supported boundary condition. The results of the new model are compared with those of the classical and couple stress theories, which point to the conclusion that the classical and couple stress models are special cases of modified strain gradient theory. Results also reveal that rigidity of the nano truncated conical shell in the strain gradient theory is greater than that in the modified couple stress and classical theories respectively, which leads to an increase in dimensionless natural frequency ratio. Moreover, the study investigates the effect of the size parameters on nano shell vibration for different lengths and vertex angles. پرونده مقاله -
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10 - An Analytical Solution on Size Dependent Longitudinal Dynamic Response of SWCNT Under Axial Moving Harmonic Load
F Khosravi M Simyari S. A Hosseini M GhadiriThe main purposes of the present work are devoted to the investigation of the free axial vibration, as well as the time-dependent and forced axial vibration of a SWCNT subjected to a moving load. The governing equation is derived through using Hamilton's principle. Erin چکیده کاملThe main purposes of the present work are devoted to the investigation of the free axial vibration, as well as the time-dependent and forced axial vibration of a SWCNT subjected to a moving load. The governing equation is derived through using Hamilton's principle. Eringen’s nonlocal elasticity theory has been utilized to analyze the nonlocal behaviors of SWCNT. A Galerkin method based on a closed-form solution is applied to solve the governing equation. The boundary conditions are considered as clamped-clamped (C-C) and clamped-free (C-F). Firstly, the nondimensional natural frequencies are calculated, as well as the influence of the nonlocal parameter on them are explained. The results of both boundary conditions are compared together, and both of them are compared to the results of another study to verify the accuracy and efficiency of the present results. The novelty of this work is related to the study of the dynamic forced axial vibration due to the axial moving harmonic force in the time domain. The previously forced vibration studies were devoted to the transverse vibrations. The effect of the geometrical parameters, velocity of the moving load, excitation frequency, as well as the small-scale effect, are explained and discussed in this context. According to the lack of accomplished studies in this field, the present work has the potential to be used as a benchmark for future works. پرونده مقاله -
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11 - A Comparative Study of Least-Squares and the Weak-Form Galerkin Finite Element Models for the Nonlinear Analysis of Timoshenko Beams
W Kim J.N ReddyIn this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on چکیده کاملIn this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In the linear analysis, numerical results of beam bending under different types of boundary conditions are presented along with exact solutions to investigate the degree of shear locking in the newly developed mixed finite element models. In the nonlinear analysis, convergences of nonlinear finite element solutions of newly developed mixed finite element models are presented along with those of existing traditional model to compare the performance. پرونده مقاله -
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12 - Thermal Stability of Thin Rectangular Plates with Variable Thickness Made of Functionally Graded Materials
M PouladvandIn this research, thermal buckling of thin rectangular plate made of Functionally Graded Materials (FGMs) with linear varying thickness is considered. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in چکیده کاملIn this research, thermal buckling of thin rectangular plate made of Functionally Graded Materials (FGMs) with linear varying thickness is considered. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The supporting condition of all edges of such a plate is simply supported. The equilibrium and stability equations of a FGM rectangular plate (FGRP) under thermal loads derived based on classical plate theory (CPT) via variational formulation, and are used to determine the pre-buckling forces and the governing differential equation of the plate. The buckling analysis of a functionally graded plate is conducted using; the uniform temperature rise, having temperature gradient through-the-thickness, and linear temperature variation in the thickness and closed-form solutions are obtained. The buckling load is defined in a weighted residual approach. In a special case the obtained results are compared by the results of functionally graded plates with uniform thickness. The influences of the plate thickness variation and the edge ratio on the critical loads are investigated. Finally, different plots indicating the variation of buckling load vs. different gradient exponent k, different geometries and loading conditions were obtained. پرونده مقاله -
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13 - Vibration Analysis of Orthotropic Triangular Nanoplates Using Nonlocal Elasticity Theory and Galerkin Method
A.R Shahidi S.H Shahidi A Anjomshoae E Raeisi EstabraghIn this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s a چکیده کاملIn this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the effect of the small scale on natural frequencies of nano scaled plates. Effect of nonlocal parameter, lengths of the nanoplate, aspect ratio, mode number, material properties, boundary condition and in-plane loads on the natural frequencies are investigated. It is shown that the natural frequencies depend highly on the non-locality of the nanoplate, especially at the very small dimensions, higher mode numbers and stiffer edge condition. پرونده مقاله -
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14 - Biaxial Buckling Analysis of Symmetric Functionally Graded Metal Cored Plates Resting on Elastic Foundation under Various Edge Conditions Using Galerkin Method
M Rezaei S Ziaee S ShojaIn this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minim چکیده کاملIn this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minimum potential energy. Afterwards, displacement field is solved using Galerkin method and the proposed process is examined through numerical examples. Effect of FGM power law index, plate aspect ratio, elastic foundation stiffness and metal core thickness on critical buckling load is investigated. The accuracy of this approach is verified by comparing its results to those obtained in another work, which is performed using Fourier series expansion. پرونده مقاله -
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15 - ارزیابی تاثیر ثوابت ناهمگنی مواد بر ضرایب شدت تنش در ورق پیزوالتریک مدرج تابعی با استفاده از روش بدون المان پتروف گالرکین محلی(MLPG)
محمد معدل شهرام شهروئیدر این مقاله از روش بدون المان پتروف گالرکین محلی برای به دست آوردن ضریب شدت تنش در ورق پیزو الکتریک مدرج تابعی تحت بارگذاری کششی یکنواخـت استفاده شده است. جهت مدل سازی میدان جابجایی و تنش، اطراف نوک ترک از روش مشاهده پذیری و اضافه نمودن گره ها و غنی سازی توابع پایه به چکیده کاملدر این مقاله از روش بدون المان پتروف گالرکین محلی برای به دست آوردن ضریب شدت تنش در ورق پیزو الکتریک مدرج تابعی تحت بارگذاری کششی یکنواخـت استفاده شده است. جهت مدل سازی میدان جابجایی و تنش، اطراف نوک ترک از روش مشاهده پذیری و اضافه نمودن گره ها و غنی سازی توابع پایه به دلیل وجود تکینگی اطراف نوک بهره گرفته شده است. همچنین از مدل تابع نمایی برای بیان تغییرات خواص جنس ماده پیزوالکتریک استفاده گردید. سپس میدان های جابجایی و پتانسیل الکتریکی تولید شده در اثر بارگذاری مکانیکی و تنش ها به ازای ثوابت ناهمگنی جنس متفاوت ماده پیزوالکتریک مدرج تابعی در راستاهای متفاوت ورق تنش از روش بدون المان محاسبه و با نتایج حاصل از نرم افزار اجزا محدود کامسول مقایسه گردید. در نهایت ضرایب شدت تنش از روش بدون المان با نتایج از حل تحلیلی مقایسه گردید که انطباق قابل قبولی را نشان داده است. پرونده مقاله -
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16 - Simulation and Analysis of Sandwich Panels Free Vibration with Corrugated Core Based on Galerkin Method
Gholamreza Banadcooki J. RezaeiPazhandThis paper aims to evaluate sandwich panels' free vibration with corrugated core by Element-free Galerkin methods and based on first order shear deformation theory (FSDT) investigated. The sandwich panels' free vibration with corrugated core consist of two sheets above چکیده کاملThis paper aims to evaluate sandwich panels' free vibration with corrugated core by Element-free Galerkin methods and based on first order shear deformation theory (FSDT) investigated. The sandwich panels' free vibration with corrugated core consist of two sheets above and below the panels, and a corrugated core in middle of these panels. The core equals to orthotropic sheet and the two panels equal to isotropic sheet. Dynamic equations of the members are obtained through first order shear deformation theory. The present research applies Galerkin numerical elementless method to solve equations of the problems. This method uses the functions of minimum moving squares. The model is simulated in cosmos software; the results are compared with the results of present papers, and show the accuracy of the method applied in the present paper. پرونده مقاله -
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17 - Analysis of Free Vibration Sandwich Panels with trapezoidal Corrugated Core Based on Galerkin Method
Arman Gholamreza BanadCooki J.Rezaei PazhandThe purpose of this paper is to evaluate the free vibration of sandwich panels with corrugated core using the element-free Galerkin method and based on the first-order shear deformation theory (FSDT).The sandwich panels' free vibrations with corrugated core consist of t چکیده کاملThe purpose of this paper is to evaluate the free vibration of sandwich panels with corrugated core using the element-free Galerkin method and based on the first-order shear deformation theory (FSDT).The sandwich panels' free vibrations with corrugated core consist of two sheets above and below the panels, and a corrugated core in middle of these panels. The core equals to orthotropic sheet and the two panels equal to isotropic sheet. Dynamic equations of the members are obtained through FSDT. The present research applies Galerkin numerical element less method to solve equations of the problems. This method uses the functions of minimum moving squares. The model is simulated in cosmos software; the results are compared with the results of present papers, and show the accuracy of the method applied in the present paper. پرونده مقاله -
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18 - Free Vibration Analysis of Sandwich Beams with FG Face Sheets Based on the High Order Sandwich Beam Theory
Mohsen Rahmani Sajjad Dehghanpour Ali BarootihaIn this paper, the vibration behavior of the sandwich beams with functionally graded face-sheets is investigated based on the high order sandwich beam theory.The properties of the FGM are varied gradually across the thickness of the structures in accordant with the powe چکیده کاملIn this paper, the vibration behavior of the sandwich beams with functionally graded face-sheets is investigated based on the high order sandwich beam theory.The properties of the FGM are varied gradually across the thickness of the structures in accordant with the power-law rule. First-order shear deformation theory and polynomial patterns are used to model the displacements of the face-sheets and the core, respectively. The governing equations of the motion are obtained based on Hamilton’s energy principle and solved by a Galerkin method. An algebraic method is used to reduce the number of equations. Boundary conditions are considered as simply supported and clamped.The effect of the power-law index and geometrical variations are surveyed on the fundamental frequency parameter for different sandwich beams in some numerical examples. In order to verify the results of the present study, they are compared with special cases of the literature. پرونده مقاله -
دسترسی آزاد مقاله
19 - بررسی کارایی روش اصلاح شده‌ی بینیاز از المان گالرکین در حل مسائل استاتیکی و به‌سازی
رامین وفائی پور علی زارع علیرضا علیزاده مجدی فریبا بهروز سرندروش اجزای محدود (FEM) به طور گسترده‌ای در تحقیقات پیشین مورد استفاده قرار گرفته است. اگرچه روش اجزای محدود دقت کافی در تخمین مقادیر تغییرشکل و جابجایی‌ها دارد، اما محاسبه میدان تنش توسط این روش از دقت پایینی برخوردار است. در این مقاله روش بدون المان گالرکین (EFG) اصلاح چکیده کاملروش اجزای محدود (FEM) به طور گسترده‌ای در تحقیقات پیشین مورد استفاده قرار گرفته است. اگرچه روش اجزای محدود دقت کافی در تخمین مقادیر تغییرشکل و جابجایی‌ها دارد، اما محاسبه میدان تنش توسط این روش از دقت پایینی برخوردار است. در این مقاله روش بدون المان گالرکین (EFG) اصلاح شده برای حل مسائل الاستوستاتیک به صورت عددی پیشنهاد شده و مورد استفاده قرار گرفته است. برای توضیح ساده‌تر روابط پیشنهادی، ابتدا یک میله‌ی الاستیک یک بعدی در نظر گرفته شده است که تحت نیروی حجمی با تغییرات خطی در طول میله می‌باشد. مقایسه‌ای میان روش اصلی گالرکین بدون المان، روش گالرکین بدون المان اصلاح شده و راه حل دقیق برای بررسی دقت، کارایی و هزینه زمانی مورد نیاز انجام شده است. مطالعه‌ی ارائه شده نشان می‌دهد که روش‌های ذکر شده دارای دقت یکسانی هستند، اما روش اصلاح شده EFG در مقایسه با روش‌های دیگر نیاز به هزینه زمانی بیشتری برای حل مسائل با تعداد زیادی درجه آزادی دارد. پاسخ‌های روش گالرکین اصلاح شده و بدون المان اصلاح نشده با پاسخ های تحلیلی تیموشنکو برای خمش یک تیر الاستیک مقایسه شده است. این مقایسه نشان می‌دهد که روش‌های اصلاح شده و اصلی تطابق بسیار خوبی با روش‌های تحلیلی در محاسبه مقادیر جابجایی‌ها دارند. با وجود یکسانی دقت در تخمین جابجایی‌ها، محاسبه میدان تنش نشان می‌دهد که روش اصلاح شده دقت کمتری نسبت به روش اصلی دارد. نشان داده شده است که با افزایش تعداد درجات آزادی، دقت روش اصلاح شده برای تخمین میدان تنش بهبود می‌یابد. با این حال، روش اصلاح‌شده EFG نسبت به روش‌های دیگر زمان‌برتر است. بر اساس تمام نتایج فوق، روش گالرکین بدون المان اصلاح شده را می‌توان به عنوان یک روش قدرتمند بدون شبکه مبتنی بر حداقل مربعات متحرک که دارای توابع شکل با خواص درون یابی است معرفی کرد. برخورداری از توابع شکل درونیاب در این روش ترکیب آن را با سایر روش‌های عددی مقدور ساخته و اعمال شرایط مرزی را با هزینه محاسباتی کمتر مقدور می‌سازد. نتایج بدست آمده نشان می‌دهد که خطای محاسبات جابجایی در روش ارائه شده حداکثر به میزان 5% نسبت به روش حل تحلیلی بوده است. همچنین میزان حداکثر خطا در روش ارائه شده برای تخمین تنش‌ها برابر با 15% بوده است. پرونده مقاله -
دسترسی آزاد مقاله
20 - Shifted Chebyshev Approach for the Solution of Delay Fredholm and Volterra Integro-Differential Equations via Perturbed Galerkin Method
Kazeem Issa Jafar Biazar Babatunde YisaThe main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential differen چکیده کاملThe main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered, the new proposed approach performs better than many other methods. پرونده مقاله -
دسترسی آزاد مقاله
21 - Construction of Multi-Resolution Wavelet Based Mesh Free Method in Solving Poisson and Imaginary Helmholtz Problem
Mohammad Yousefi Amin Dehghani Ali Asghar AminiIn this paper, we propose a new multi-resolution wavelet based mesh free method for numerical analysis of electromagnetic field problems. In problems with variable object geometries or mechanical movements, the mesh free methods yield more accurate simulation results co چکیده کاملIn this paper, we propose a new multi-resolution wavelet based mesh free method for numerical analysis of electromagnetic field problems. In problems with variable object geometries or mechanical movements, the mesh free methods yield more accurate simulation results compared to the finite element approach in solving the inverse problem, because they are based on a set of nodes without using the connectivity of the elements. The wavelet based mesh free method requires effectively no local integration in the vicinity of nodes in numerical implementations. Moreover, wavelets give a more efficient approximation using multi-resolution analysis. On the other hand, boundary condition constraints are difficult to be applied on the wavelet based mesh free method. In order to apply boundary and interface conditions, we utilize a new form of jump functions in the set of basic functions. The boundary and interface conditions are applied effectively using the suggested slope jump functions. The simulation results of the proposed method using two different jump functions in solving some simple boundary problems are compared. The results are validated by analytical solutions. The results of this study can be used in future for inverse problem of Magnetic resonance electrical impedance tomography (MREIT) studies as an imaging technique for reconstructing the cross-sectional conductivity distribution of a human brain or body using EIT technique integrated with the MRI. پرونده مقاله -
دسترسی آزاد مقاله
22 - Galerkin Method for the Numerical Solution of the Advection-Diffusion Equation by Using Exponential B-splines
Melis Zorsahin Gorgulu Idris DagIn this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illus چکیده کاملIn this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies. پرونده مقاله -
دسترسی آزاد مقاله
23 - AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM
Hassan Jamali Ataollah Askari HemmatIn this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. T چکیده کاملIn this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is replaced by an adaptive approximation. Finally we prove that thisadaptive method has optimal computational complexity, that is itrecovers an approximate solution with desired accuracy at acomputational expense that stays proportional to the number of termsin a corresponding wavelet-best N-term approximation. پرونده مقاله -
دسترسی آزاد مقاله
24 - APPLICATION OF THE SINC APPROXIMATION TO THE SOLUTION OF BRATU'S PROBLEM
J. Rashidinia N. TaherIn this work, we study the performance of the sinc-Collocation method for solving Bratu's problem. For different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. The comparison of the obtained re چکیده کاملIn this work, we study the performance of the sinc-Collocation method for solving Bratu's problem. For different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. The comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with پرونده مقاله -
دسترسی آزاد مقاله
25 - USING PG ELEMENTS FOR SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
Majid KaramiIn this paper, we use Petrov-Galerkin elements such as continuous and discontinuous Lagrange-type k-0 elements and Hermite-type 3-1 elements to find an approximate solution for linear Fredholm integro-differential equations on $[0,1]$. Also weshow the efficiency of this چکیده کاملIn this paper, we use Petrov-Galerkin elements such as continuous and discontinuous Lagrange-type k-0 elements and Hermite-type 3-1 elements to find an approximate solution for linear Fredholm integro-differential equations on $[0,1]$. Also weshow the efficiency of this method by some numerical examples پرونده مقاله -
دسترسی آزاد مقاله
26 - CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS
Hojatollah Adibi M. Shamooshaky Pouria AssarIn this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CA چکیده کاملIn this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for approximating logarithm-like singularintegrals and so reduces the solution of boundary integral equations to the solution of linear systems of algebraicequations. The properties of CAS wavelets are used to make the wavelet coe±cient matrices sparse, which eventuallyleads to the sparsity of the coe±cient matrix of the obtained system. Finally, the validity and e±ciency of the newtechnique are demonstrated through a numerical example. پرونده مقاله -
دسترسی آزاد مقاله
27 - Convergence of Legendre and Chebyshev multiwavelets in Petrov-Galerkin method for solving Fredholm integro-differential equations of high orders
Saeed AkhavanThis work was intended as an attempt to motivate readers for a comparison study of constructions of Legendre multiwavelet and Chebyshev multiwavelet. It is also shown how to use them in Petrov-Galerkin approach for solving Fredholm integro-differential equation of high چکیده کاملThis work was intended as an attempt to motivate readers for a comparison study of constructions of Legendre multiwavelet and Chebyshev multiwavelet. It is also shown how to use them in Petrov-Galerkin approach for solving Fredholm integro-differential equation of high orders of the second kind. In fact, a numerical technique for the discretization method of Fredholm integro-differential equations is presented that yields linear system. The important point to note here is the convergence of presented methods. For the first time, two conditions are proved for convergence of Legendre and Chebyshev multiwavelets in Petrov-Galerkin method. The proof of these conditions with using linear algebra and matrix theory ensures that Petrov-Galerkin methods has a unique approximation. Finally, some relevent numerical examples, for which the exact solution is known, will indicate accuracy and applicability of the proposed method. پرونده مقاله -
دسترسی آزاد مقاله
28 - Investigation of Dynamical Behavior (Transverse Vibration) and Instability Analysis of Carbon Nanotubes Conveying Nanofluid
سهیل اویسی حسن نحوی داود طغراییThis work focuses on the dynamical behavior of carbon nanotubes, including vibration, wave propagation and fluid-structure interaction. In the present research, transverse vibration of nano fluid conveying carbon nanotubes is investigated. To this end, based on the nonl چکیده کاملThis work focuses on the dynamical behavior of carbon nanotubes, including vibration, wave propagation and fluid-structure interaction. In the present research, transverse vibration of nano fluid conveying carbon nanotubes is investigated. To this end, based on the nonlocal and strain-inertia gradient continuum elasticity theories and by using rod and Euler-Bernoulli beam models, the system’s dynamical behavior is modeled and then, the governing equation of motion is solved and discretized by applying the weighted-residual Galerkin approximate method. Moreover, effect of considering nano-scale fluid flowing through the nanotube, the boundary conditions, the different elastic mediums and the van der Walls interaction between the layers of multi-walled carbon nanotubes on the natural frequencies, critical velocities and stability of the system are considered. The results show that the passing fluid flow and the axially moving of nanotube decrease the system’s natural frequencies especially for nanotubes with large internal radius and in high fluid flow and axially moving speeds of nanotube. In addition, it is observed that the natural frequencies and stability of the system strongly depend on the small-scale parameter (nano-scale), mainly in the longitudinal vibration پرونده مقاله -
دسترسی آزاد مقاله
29 - Free and Forced Vibration Analysis of Composite Laminated Conical Shells under Different Boundary Conditions Via Galerkin Method
آیدین نصیری راد رضا انصاری حسام روحیIn this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin m چکیده کاملIn this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary conditions upon the mechanical behavior of conical shells, the analysis is carried out for all possible boundary conditions. The response of forced vibration is calculated via the modal participation factor method. Numerical comparisons of free vibration with the results in the open literature are made to validate the present methodology. پرونده مقاله -
دسترسی آزاد مقاله
30 - Bending Analysis of Rectangular FGM Plates based on the Extended Kantorovich Method
محمد مهدی نجفی زاده مجید علوی فؤاد سلماسی شیما آذریBending analysis of FGM plates under uniform and sinusoidal loaded result in forth order partial differential equation. In this paper the analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure چکیده کاملBending analysis of FGM plates under uniform and sinusoidal loaded result in forth order partial differential equation. In this paper the analytical solution is based on the extended Kantorovich iterative procedure. The differential equations for the iterative procedure is derived using the Galerkin method. The solution was develope based on the classical plate’s theory (CLPT). The reliability of the present analytical method for FGM, under different boundary condition, was verified and approved when comparing Navier solution and finite element results with ANSYS solution. Since the FGM modeling is impossibility at ANSYS, a macro has used for modeling and analysis.The results show a high accuracy and the iterative process converges very rapidly. It was also found that the final form of the generated solutions is independent of the initial trial function. پرونده مقاله -
دسترسی آزاد مقاله
31 - Bending Analysis of Carbon Nanotubes with Small Initial Curvature Embedded on an Elastic Medium Based on Nonlocal Elasticity and Galerkin Method
اعظم عارفی محمود سلیمیCarbon nanotubes have an important role in reinforcing nanocomposits. Many experimental observations have shown that in the most nanostructures such as nanocomposites, carbon nanotubes (CNTs) are often characterized by a certain degree of waviness along their axial dire چکیده کاملCarbon nanotubes have an important role in reinforcing nanocomposits. Many experimental observations have shown that in the most nanostructures such as nanocomposites, carbon nanotubes (CNTs) are often characterized by a certain degree of waviness along their axial direction. In the present paper, the effects of initial curvature, influence of surrounding medium that is modeled as Winkler elastic foundation on behavior of slightly curved carbon nanotubes are investigated. To capture the small size effects, nonlocal elasticity theory is implemented. Bending governing equations are derived using the principle of minimum total potential energy and these nonlinear equations are solved by Newton Raphson method. It is shown that the larger the initial curvature, the higher deflection can occur. Furthermore, neglecting the effect of initial curvature of CNTs can lead to incorrect results. پرونده مقاله -
دسترسی آزاد مقاله
32 - Longitudinal Wave Propagation Analysis of Stationary and Axially Moving Carbon Nanotubes Conveying Fluid
سهیل اویسی حسن نحوی داود طغراییIn this study, the effect of small-scale of both nanostructure and nano-fluid flowing through it on the natural frequency and longitudinal wave propagation are investigated. Here, the stationary and axially moving single-walled carbon nanotube conveying fluid are studie چکیده کاملIn this study, the effect of small-scale of both nanostructure and nano-fluid flowing through it on the natural frequency and longitudinal wave propagation are investigated. Here, the stationary and axially moving single-walled carbon nanotube conveying fluid are studied. The boundary conditions for the stationary nanotube is considering clamped-clamped and pined-pined and for the axially moving SWCNT is simply supported end where the left-end has been restrained. To apply the nano-scale for fluid the Knudsen number and to apply the structure the nano-rod model and nonlocal theory are utilized. Next, using the approximate Galerkin method the governing equation of motion is discretized and solved. In addition, the ratio of the natural frequency and phase velocity to the wave number and also the influence of velocities of flowing fluid and axially moving structure on the natural frequency would be studied. It can be shown that the natural frequency and wave propagation velocity are depending to the nano-scale of the structure and fluid flowing through it. So that, by increasing the nonlocal parameter, the natural frequency is decreased and by increasing the Knudsen number the system frequency is increased hence, leading to a bigger wave پرونده مقاله
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