Numerical Modeling In Science And Engineering

Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book cont

Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.

An unified approach to numerical modeling, integrating aspects of continuum mechanics, differential equations, and numerical analysis. Explains how to formulate a mathematical description of the phenomena under consideration, devise techniques for solving the governing equations, then refine the model and interpret the results. Emphasizes physical applications and relates the three major classes of partial differential equations -- elliptic, parabolic, and hyperbolic -- to steady-state systems, dissipative systems, and nondissipative systems, respectively. Also examines some higher-order equations, nonlinear equations, and coupled systems of equations.

Numerical modeling is the use of computational and mathematical methods to solve scientific problems. This book on numerical modeling in science and engineering deals with the basic elements that are dealt by this field such as algorithmic simulation, computer software development and computational intelligence. There has been rapid progress in this field and its applications are finding their way across multiple industries. This book studies, analyzes and upholds the pillars of numerical modeling and its utmost significance in modern times. While understanding the long-term perspective of the topics, the book makes an effort in highlighting their impact as a modern tool for the growth of the discipline. It will help the readers in keeping pace with the rapid changes in this field.

"This book includes over 800 problems including open ended, project type and design problems. Chapter topics include Introduction to Numerical Methods; Solution of Nonlinear Equations; Simultaneous Linear Algebraic Equations; Solution of Matrix Eigenvalue Problem; and more." (Midwest).

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

Numerical Modelling of Failure in Advanced Composite Materials comprehensively examines the most recent analysis techniques for advanced composite materials. Advanced composite materials are becoming increasingly important for lightweight design in aerospace, wind energy, and mechanical and civil engineering. Essential for exploiting their potential is the ability to reliably predict their mechanical behaviour, particularly the onset and propagation of failure. Part One investigates numerical modeling approaches to interlaminar failure in advanced composite materials. Part Two considers numerical modelling approaches to intralaminar failure. Part Three presents new and emerging advanced numerical algorithms for modeling and simulation of failure. Part Four closes by examining the various engineering and scientific applications of numerical modeling for analysis of failure in advanced composite materials, such as prediction of impact damage, failure in textile composites, and fracture behavior in through-thickness reinforced laminates. Examines the most recent analysis models for advanced composite materials in a coherent and comprehensive manner Investigates numerical modelling approaches to interlaminar failure and intralaminar failure in advanced composite materials Reviews advanced numerical algorithms for modeling and simulation of failure Examines various engineering and scientific applications of numerical modelling for analysis of failure in advanced composite materials