Solution to Engineering Problems Using Finite Element Methods

This book focuses on finite element methods, a subset of computational mechanics. Over the past decades, finite element analysis (FEA) has become easier to use and implement, enabling engineering designers to carry out complex and more robust simulations. Furthermore, the steady growth of analysis software coincides with the availability and affordability of high-performance computing architectures, making FEA applications a possible reality for most engineers. Although there are some excellent books for engineering analysis using finite element techniques to solve engineering problems, the intent here is to guide the reader through the finite element method through the very basic concepts to the extent of a first-year graduate student.This book intends to provide the theoretical and practical foundation of the finite element method (FEM). The target audience is first-year graduate students who have had little to no exposure to the subject. However, practicing engineers will also benefit from the approach of this book as they will learn the theoretical aspects of finite element methods, basically, on their own. Thus, we can assure that this book will fill a void in the personal library of many engineers trying or planning to use finite element analysis in their next design. The recommended background to successfully read this book is solid mechanics, calculus, continuum mechanics, theory of elasticity, and basic programming knowledge.When writing this textbook, we have kept the reader in mind at all times. After years of using the earlier versions of the book, engineering graduates from various universities found the approach in this book instrumental in their respective 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 FEA software. As a result, they usually lack fundamental knowledge of finite element analysis software. Hence, the book’s primary goal is to provide a fundamental engineering treatment associated with FEM at a level that is reasonably accessible to those studying the topic for the first time. The book also provides intuitive and mathematical insight into finite element analysis using modern mathematical tools. After the reader has studied this book, he/she will be able to: explain what the finite element method is, use the theory of elasticity to provide a computational formulation of a structural problem, develop finite elements, and use computer codes to solve springs, axial bars, beams, and plate problems.