Louis Komzsik – författare

Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that allone needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation.

This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book.

This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that allone needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation.

This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book.

This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

This book is a concise, self-contained treatment of the finite element method and all the computational techniques needed for its efficient use and practical implementation. This book describes the process of transforming the physical problem into a mathematical model, the reduction of the mathematical model to a numerically solvable computational form, and many practical engineering analysis solution techniques applied in various industries.

The first edition of this book was published in 2004, two decades ago. Since then, finite element analysis (FEA) has become a fundamental component of product development software tools (CAD, CAE, CAM) used in many industrial fields of engineering, particularly in mechanical and aerospace engineering. It has also become a popular text in computational science in engineering (CSE) and applied mathematics courses in academia, one of the reasons for the new edition.

This new edition presents finite element solutions to advanced industrial applications in response to readers of the earlier editions. These are heat transfer, wave propagation, topology optimization, and fluid dynamics. These topics were requested both by engineering and applied mathematics students as well as practicing mechanical and aerospace engineers. It also contains the numerical solution of a structural example to aid the teaching of finite element analysis using this textbook.

This book is a concise, self-contained treatment of the finite element method and all the computational techniques needed for its efficient use and practical implementation. This book describes the process of transforming the physical problem into a mathematical model, the reduction of the mathematical model to a numerically solvable computational form, and many practical engineering analysis solution techniques applied in various industries.

The first edition of this book was published in 2004, two decades ago. Since then, finite element analysis (FEA) has become a fundamental component of product development software tools (CAD, CAE, CAM) used in many industrial fields of engineering, particularly in mechanical and aerospace engineering. It has also become a popular text in computational science in engineering (CSE) and applied mathematics courses in academia, one of the reasons for the new edition.

This new edition presents finite element solutions to advanced industrial applications in response to readers of the earlier editions. These are heat transfer, wave propagation, topology optimization, and fluid dynamics. These topics were requested both by engineering and applied mathematics students as well as practicing mechanical and aerospace engineers. It also contains the numerical solution of a structural example to aid the teaching of finite element analysis using this textbook.

Rotor dynamics is both a classical and a modern branch of engineering science. The rotation of rigid bodies, mainly those with regular shapes such as cylinders and shafts, has been well understood for more than a century. However, analyzing the rotational behavior of flexible bodies, especially those with irregular shapes like propellers and blades, requires more modern tools such as finite elements, hence the title and focus of this book.

In the dozen years since the original publication, this book was used in teaching engineering students at universities and in consulting in the industry. During those activities, several topics were deemed to require further explanations. Students requested a deeper finite element technology foundation in certain places to make the book self‑contained in that regard also. Some desired more details about the computational and numerical solutions. These requests are answered in new sections of this edition. Practicing engineers asked for a detailed industrial application case study and such was added in a new chapter dealing with wind turbines.

This book is composed of two parts, the first focusing on the theoretical foundation of rotor dynamics and the second focusing on the engineering analysis of industrial structures. The theoretical foundation is built on physics, calculus, and finite element technology chapters. Computational and numerical techniques provide free vibration and response analyses solutions. The industrial engineering analysis part contains chapters analyzing jet‑engine turbine wheels, aircraft propellers, and wind turbine blades. This book concludes with a new industrial case study based on a recent modern wind turbine development project.

Rotor dynamics is both a classical and a modern branch of engineering science. The rotation of rigid bodies, mainly those with regular shapes such as cylinders and shafts, has been well understood for more than a century. However, analyzing the rotational behavior of flexible bodies, especially those with irregular shapes like propellers and blades, requires more modern tools such as finite elements, hence the title and focus of this book.

In the dozen years since the original publication, this book was used in teaching engineering students at universities and in consulting in the industry. During those activities, several topics were deemed to require further explanations. Students requested a deeper finite element technology foundation in certain places to make the book self‑contained in that regard also. Some desired more details about the computational and numerical solutions. These requests are answered in new sections of this edition. Practicing engineers asked for a detailed industrial application case study and such was added in a new chapter dealing with wind turbines.

This book is composed of two parts, the first focusing on the theoretical foundation of rotor dynamics and the second focusing on the engineering analysis of industrial structures. The theoretical foundation is built on physics, calculus, and finite element technology chapters. Computational and numerical techniques provide free vibration and response analyses solutions. The industrial engineering analysis part contains chapters analyzing jet‑engine turbine wheels, aircraft propellers, and wind turbine blades. This book concludes with a new industrial case study based on a recent modern wind turbine development project.