Material modelling, numerical methods, numerical formulations, FEM modelling

2010 ◽  
Keyword(s):  
Numerical Methods ◽  
Fem Modelling ◽  
Material Modelling ◽  
Methods Numerical

scholarly journals A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Zongqi Liang ◽  
Yubin Yan ◽  
Guorong Cai
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
The Stability ◽  
Predictor Corrector ◽  
Theoretical Results ◽  
Methods Numerical

A standard Crank-Nicolson finite-difference scheme and a Dufort-Frankel finite-difference scheme are introduced to solve two-dimensional damped and undamped sine-Gordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictor-corrector techniques are applied in the numerical methods. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

Analysis of Natural Frequencies of Voided Biaxial Concrete Slabs

2017 ◽  
Vol 738 ◽  
pp. 15-24
Author(s):  
Norbert Jendzelovsky ◽  
Kristina Zabakova Vrablova
Keyword(s):  
Numerical Calculation ◽  
Numerical Methods ◽  
3D Model ◽  
Natural Frequencies ◽  
Hollow Spheres ◽  
Concrete Slabs ◽  
Simply Supported ◽  
Floor Systems ◽  
Permanent Fillers ◽  
Methods Numerical

Voided slabs using voids formed by permanent fillers or removable forms have been used in reinforced concrete floor systems for more than 100 years. In this article we will focus on the natural frequency of voided biaxial slabs system Cobiax. Cobiax void former modules are synthetic hollow spheres or rotational ellipsoids mounted in the relevant spaces between the upper and lower reinforcement. We have analyzed the slabs of different thicknesses with adequate void former modules and spans following the manufacturer's recommendations. All models were considered as simply supported slabs. Natural frequencies calculated using simplified analytical methods have been compared with those obtained by numerical methods. Numerical calculation was done using the 2D elements with reduced properties and using the accurate 3D model of a structure.

scholarly journals Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ali Özyapıcı ◽  
Zehra B. Sensoy ◽  
Tolgay Karanfiller
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Rate Of Convergence ◽  
Nonlinear Equations ◽  
Science And Engineering ◽  
Root Finding ◽  
Wide Range ◽  
Newton Raphson ◽  
Methods Numerical

In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods

THE METHODS OF DEVELOPING COMPUTATIONAL THINKING OF STUDENTS WHILE STUDYING THE COURSE "NUMERICAL METHODS" BASED ON BLENDED LEARNING

2019 ◽  
pp. 34-41
Author(s):  
M. M. Klunnikova
Keyword(s):  
Numerical Methods ◽  
Blended Learning ◽  
Computational Thinking ◽  
Individual Characteristics ◽  
Diagnostic Model ◽  
Mathematics Students ◽  
Professional Activities ◽  
Cognitive Component ◽  
Professional Field ◽  
The Individual

The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

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