June 17, 2021

## Interval Finite Element Method with MATLAB

Author : Sukanta Nayak,Snehashish Chakraverty
Release Date : 2018-02-05
Category : Technology & Engineering
Total pages :168

Interval Finite Element Method with MATLAB provides a thorough introduction to an effective way of investigating problems involving uncertainty using computational modeling. The well-known and versatile Finite Element Method (FEM) is combined with the concept of interval uncertainties to develop the Interval Finite Element Method (IFEM). An interval or stochastic environment in parameters and variables is used in place of crisp ones to make the governing equations interval, thereby allowing modeling of the problem. The concept of interval uncertainties is systematically explained. Several examples are explored with IFEM using MATLAB on topics like spring mass, bar, truss and frame. Provides a systematic approach to understanding the interval uncertainties caused by vague or imprecise data Describes the interval finite element method in detail Gives step-by-step instructions for how to use MATLAB code for IFEM Provides a range of examples of IFEM in use, with accompanying MATLAB codes

## Interval Finite Element Method with MATLAB

Author : Sukanta Nayak,Snehashish Chakraverty
Release Date : 2018-01-24
Category :
Total pages :168

Interval Finite Element Method with MATLAB provides a thorough introduction to an effective way of investigating problems involving uncertainty using computational modeling. The well-known and versatile Finite Element Method (FEM) is combined with the concept of interval uncertainties to develop the Interval Finite Element Method (IFEM). An interval or stochastic environment in parameters and variables is used in place of crisp ones to make the governing equations interval, thereby allowing modeling of the problem. The concept of interval uncertainties is systematically explained. Several examples are explored with IFEM using MATLAB on topics like spring mass, bar, truss and frame. Provides a systematic approach to understanding the interval uncertainties caused by vague or imprecise data Describes the interval finite element method in detail Gives step-by-step instructions for how to use MATLAB code for IFEM Provides a range of examples of IFEM in use, with accompanying MATLAB codes

## Pragmatic Introduction To The Finite Element Method For Thermal And Stress Analysis, A: With The Matlab Toolkit Sofea

Author : Petr Krysl
Publisher : World Scientific Publishing Company
Release Date : 2006-10-23
Category : Science
Total pages :292

This textbook provides an accessible and self-contained description of the Galerkin finite element method for the two important models of continuum mechanics, transient heat conduction and elastodynamics, from formulation of the governing equations to implementation in Matlab.The coverage follows an intuitive approach: the salient features of each initial boundary value problem are reviewed, including a thorough description of the boundary conditions; the method of weighted residuals is applied to derive the discrete equations; and clear examples are introduced to illustrate the method.

## Advanced Numerical and Semi-Analytical Methods for Differential Equations

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Release Date : 2019-03-20
Category : Mathematics
Total pages :256

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

## Fundamentals of Optimization Techniques with Algorithms

Author : Sukanta Nayak
Release Date : 2020-08-25
Category : Mathematics
Total pages :320

Optimization is a key concept in mathematics, computer science, and operations research, and is essential to the modeling of any system, playing an integral role in computer-aided design. Fundamentals of Optimization Techniques with Algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and MATLAB© code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced optimization techniques. It presents both theoretical and numerical perspectives in a clear and approachable way. In order to help the reader apply optimization techniques in practice, the book details program codes and computer-aided designs in relation to real-world problems. Ten chapters cover, an introduction to optimization; linear programming; single variable nonlinear optimization; multivariable unconstrained nonlinear optimization; multivariable constrained nonlinear optimization; geometric programming; dynamic programming; integer programming; multi-objective optimization; and nature-inspired optimization. This book provides accessible coverage of optimization techniques, and helps the reader to apply them in practice. Presents optimization techniques clearly, including worked-out examples, from traditional to advanced Maps out the relations between optimization and other mathematical topics and disciplines Provides systematic coverage of algorithms to facilitate computer coding Gives MATLAB© codes in relation to optimization techniques and their use in computer-aided design Presents nature-inspired optimization techniques including genetic algorithms and artificial neural networks

## The Finite Element Method Using MATLAB

Author : Young W. Kwon,Hyochoong Bang
Publisher : CRC Press
Release Date : 1997
Category : Science
Total pages :519

The finite element method (FEM) has become one of the most important and useful tools for scientists and engineers. This new book features the use of MATLAB to present introductory and advanced finite element theories and formulations. MATLAB is especially convenient to write and understand finite element analysis programs because a MATLAB program manipulates matrices and vectors with ease. The book is suitable for introductory and advanced courses in the Finite Element Method, as well as a reference for practicing engineers.

## Mathematical Reviews

Author : Anonim
Publisher : Unknown
Release Date : 2005
Category : Mathematics
Total pages :129

## Numerical Methods in Engineering with MATLAB ®

Author : Jaan Kiusalaas
Publisher : Cambridge University Press
Release Date : 2010
Category : Computers
Total pages :431

This textbook is for engineering students and practising engineers who wish to explore the power and efficiency of MATLAB.

## Numerical Methods in Engineering with Python

Author : Jaan Kiusalaas
Publisher : Cambridge University Press
Release Date : 2010-01-29
Category : Technology & Engineering
Total pages :422

This text is for engineering students and a reference for practising engineers, especially those who wish to explore Python. This new edition features 18 additional exercises and the addition of rational function interpolation. Brent's method of root finding was replaced by Ridder's method, and the Fletcher-Reeves method of optimization was dropped in favor of the downhill simplex method. Each numerical method is explained in detail, and its shortcomings are pointed out. The examples that follow individual topics fall into two categories: hand computations that illustrate the inner workings of the method and small programs that show how the computer code is utilized in solving a problem. This second edition also includes more robust computer code with each method, which is available on the book website. This code is made simple and easy to understand by avoiding complex bookkeeping schemes, while maintaining the essential features of the method.

## Proceedings of the 13th International Modal Analysis Conference

Author : Dominick J. DeMichele
Publisher : Unknown
Release Date : 1995
Category : Composite materials
Total pages :1881

## Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB

Author : Alexander Stanoyevitch
Publisher : Wiley-Interscience
Release Date : 2005
Category : Computers
Total pages :813

## Advanced Numerical Methods with Matlab 2

Author : Bouchaib Radi,Abdelkhalak El Hami
Publisher : John Wiley & Sons
Release Date : 2018-05-24
Category : Mathematics
Total pages :218

The purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or of engineering (mechanics of structures, mechanics of fluids, treatment signal, etc.). Each chapter of this book recalls the essence of the different methods resolution and presents several applications in the field of engineering as well as programs developed under Matlab software.

## The Numerical Solution of Ordinary and Partial Differential Equations

Author : Granville Sewell
Publisher : World Scientific
Release Date : 2014-12-16
Category : Mathematics
Total pages :348

## Mechanical Engineering, Materials and Energy

Author : Grace Chang
Publisher : Trans Tech Publications Ltd
Release Date : 2011-12-22
Category : Technology & Engineering
Total pages :1630

These are selected papers from the 2011 International Conference on Mechanical Engineering, Materials and Energy, ICMEME2011, held in Dalian. The papers reveal the latest developments, in the field of Mechanical Engineering, Materials and Energy ... from fundamentals to new technologies and applications. In particular, they cover the topics of Mechatronics and Automation, Mechanical Manufacturing Systems, Signal Processing, Manufacturing Technology and Processing and Materials Science and Technology.

## Fundamentals of Scientific Computing

Author : Bertil Gustafsson
Publisher : Springer Science & Business Media
Release Date : 2011-06-11
Category : Mathematics
Total pages :326

The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.