scholarly journals Numerical Solution of the Modified Equal Width Wave Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Turabi Geyikli
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Wave Equation ◽  
Numerical Solution ◽  
Wave Motion ◽  
B Spline ◽  
Spline Finite Element ◽  
Method Accuracy ◽  
Good Agreement

Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws and error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.

scholarly journals UMERICAL SOLUTION OF THE PROBLEM OF BEAM ANALYSIS WITH THE USE OF B-SPLINE FINITE ELEMENT METHOD

2020 ◽  
Vol 16 (3) ◽  
pp. 12-22
Author(s):  
Pavel Akimov ◽  
Marina Mozgaleva ◽  
Taymuraz Kaytukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Basis Functions ◽  
Numerical Implementation ◽  
Bernoulli Beam ◽  
B Spline ◽  
Bending Analysis ◽  
Beam Analysis ◽  
Spline Finite Element

Numerical solution of the problem of beam analysis (bending analysis of the Bernoulli beam) with the use of B-spline finiteelement method is under consideration in the distinctive paper. The original continual and finiteelement formulations of the problem are given, some actual aspects of construction of normalized basis functions of a B-spline are considered, the corresponding local constructions for an arbitrary finiteelement are described, some information about the numerical implementation and an example of analysis are presented.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

scholarly journals Evaluation of Pile’s Buckling Under Axial Load by B-Spline Method and Comparison With Finite Element Method and Exact Solution

2018 ◽  
Vol 8 (2) ◽  
pp. 29-34
Author(s):  
A. Moghaddam ◽  
A. Nayeri ◽  
S.M. Mirhosseini
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Numerical Methods ◽  
High Volume ◽  
Spline Method ◽  
B Spline ◽  
Volume Calculations ◽  
Reaction Coefficient ◽  
Element Method

Abstract Although various analytical and numerical methods have been proposed by researchers to solve equations, but use of numerical tools with low volume calculations and high accuracy instead of other numerical methods with high volume calculations is inevitable in the analysis of engineering equations. In this paper, B-Spline spectral method was used to study buckling equations of the piles. Results were compared with the calculated amounts of the exact solution and finite element method. Uniform horizontal reaction coefficient has been used in most of proposed methods for analyzing buckling of the pile on elastic base. In reality, soil horizontal reaction coefficient is nonlinear along the pile. So, in this research by using B-Spline method, buckling equation of the pile with nonlinear horizontal reaction coefficient of the soil was investigated. It is worth mentioning that B-Spline method had not been used for buckling of the pile.

Numerical algorithm for predicting wheel flange wear in trams – Validation in a curved track

2019 ◽  
Vol 234 (10) ◽  
pp. 1156-1169
Author(s):  
Bartosz Łuczak ◽  
Bartosz Firlik ◽  
Tomasz Staśkiewicz ◽  
Wojciech Sumelka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Effort ◽  
Wheel Wear ◽  
Curved Track ◽  
Method Accuracy ◽  
Elliptic Contact ◽  
Method Analysis ◽  
Good Agreement ◽  
Element Method

In tram operations, flange wear is predominant due to the low-radius curves and inappropriate technical conditions of the infrastructure; hence, investigations should be focused on the interaction between the wheel flange and the rail gauge corner. Moreover, the calculation methods based on the Hertzian model (elliptic contact patch) provide less accurate results due to the contact occurrence in the wheel flange region. This paper presents a methodology of a finite element method to predict the tram wheel wear in complex motions. The new procedure is based on the Abaqus software and several other sub-procedures written in Python and Fortran. Multibody simulations were used to determine the wheel–rail alignment. In this method, accuracy was chosen at the expense of the computational effort. The main steps are: preparation of models and ride scenarios, multibody simulation for calculating the wheel–rail alignment for different track scenarios and multiple runs of finite element method analysis to determine the wear magnitude. The proposed methodology presents a good agreement with the measurements and can be considered as guidelines for a proper configuration of the flange-designing experimental setup where the influence of the technical conditions of the infrastructure should be introduced adequately.

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