1st Edition

Vijay Goyal and Vinay Goyal
eISBN-13: 9780578254876

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This book mainly focuses on the major area: Computational Mechanics. Computational mechanics is widely used in nanomechanics and micromechanics, continuum mechanics, and many other mechanical systems. The main focus throughout this book will be to address methods concerning the field of continuum mechanics. Continuum mechanics studies bodies at the macroscopic level by developing continuum models with a homogenized microstructure. The two traditional areas of application are solid and thermal-fluid mechanics.

Over the past century, energy and variational principles have become popular methods when obtaining approximate solutions to practical problems in applied mechanics. In addition, these methods enable engineers to carry out more effective simulations. In fact, most simulation and computation software are based upon concepts from energy and variational approaches.

This book combines the essential ideas and methods behind current energy applications and variational theory in theoretical, applied mechanics. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism.

Although there are some excellent books for engineering analysis using variational techniques to solve engineering problems, in this manuscript, we intend to guide the reader through the classical topics of energy and variational principles through the fundamental concepts to the extent of a first-year graduate student. What makes this book distinct from all others is that students usually grasp abstract and complex formulations through problem-solving, which is the major strength of this book.

This book is intended to provide a theoretical and practical foundation for approximations to differential equations, including the finite element method. The target audience is first-year graduate students who have had little exposure to energy and variational principles. Practicing engineers will also benefit from the approach of this manuscript as they will be able to learn the theoretical aspects of typical approximation methods such as the finite element methods, basically, by their own. Thus, we can assure that this book will fill up a void in the personal library of many engineers who are trying to, or planning, to these methods in their next analysis. The recommended background to successfully read this book is: solid mechanics, calculus, and basic programming knowledge is required.

When writing this textbook, we have kept the reader in mind at all times. After years of using this manuscript, engineering graduates (from the University of Puerto Rico at Mayaguez and University of California at Los Angeles) have found the manuscript very useful in their respective courses and jobs. In teaching and applying the subject for years, we have concluded that students and engineers too often take a black-box approach when using commercial computational software. Hence, the books primary goal is to provide a fundamental engineering treatment at a level that is reasonably accessible to those being exposed to the topic for the first time. The book also attempts to provide an intuitive as well as mathematical insight into the subject by using modern mathematical tools.

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ISBNs 9780578254876, 9780578254883
Publish Year 2022
Language English
Edition 1st