A First Course in Finite Elements

Abstract

This book is written to be an undergraduate and introductory graduate level textbook, depending on whether the more advanced topics appearing at the end of each chapter are covered. Without the advanced topics, the book is of a level readily comprehensible by junior and senior undergraduate students in science and engineering.Withthe advancedtopicsincluded,the book can serve asthetextbook forthe first coursein finite elements at the graduate level. The text material evolved from over 50 years of combined teaching experience by the authors of graduate and undergraduate finite element courses. The book focuses on the formulation and application of the finite element method. It differs from other elementary finite element textbooks in the following three aspects: 1. Itisintroductory and self-contained. Only amodest backgroundinmathematics and physicsis needed, all of whichis coveredin engineering and science curriculainthe firsttwo years. Furthermore, many of the specific topics in mathematics, such as matrix algebra, some topics in differential equations, and mechanics and physics, such as conservation laws and constitutive equations, are reviewed prior to their application. 2. It is generic. While most introductory finite element textbooks are application specific, e.g. focusing onlinear elasticity, the finite element method in this book is formulated as a general purpose numerical procedure for solving engineering problems governed by partial differential equations. The methodology for obtaining weak forms for the governing equations, a crucial step in the development and understanding of finite elements, is carefully developed. Consequently, students from various engineering and science disciplines will benefit equally from the exposition of the subject. 3. Itis a hands-on experience. The bookintegrates finite elementtheory, finite element code development and the application of commercial software package. Finite element code development is introduced through MATLAB exercises and a MATLAB program, whereas ABAQUS is used for demonstra