Engineering Elasticity and Finite Element Method

Author: Lu Mingwan
Publisher:
Publish Date: 2005-10-01
Features: The main features of this book are: concise and systematic presentation of the basic concepts, methods, and general principles of three-dimensional elastodynamics. It emphasizes the importance of tensor concepts and lays a solid theoretical foundation for correctly conducting finite element stress analysis. The teaching method involves elaborating on physical concepts and basic ideas, simplifying mathematical proofs and derivations, and highlighting the flexible application of theory. Classic examples of weakly coupled mechanics with significant engineering application value are explained in detail. Elastic mechanics knowledge related to establishing reasonable simplified models and correct boundary conditions is added. Matrix methods are introduced for general theoretical derivations. The basic ideas of the finite element method are briefly introduced, and finite element programs and examples are used as auxiliary teaching tools. This book is designed as a textbook for "Engineering Elastodynamics" or "Elastodynamics and Finite Elements." The purpose is to concisely and systematically explain the basic concepts, principles, and methods of elastodynamics, laying a solid theoretical foundation for engineering finite element stress analysis. The presentation emphasizes the explanation of physical concepts and basic ideas, highlights the flexible application of fundamental theory, and focuses on the explanation of engineering application examples. Exercises are provided at the end of each chapter for readers to practice. Additional mathematical knowledge is supplemented in the appendix. The first part of the book covers basic theory, emphasizing the correct understanding of fundamental concepts such as stress and strain tensors, equilibrium and compatibility, and boundary conditions, as well as the general principles of elastodynamics. The second part discusses specialized problems, selecting topics such as plane problems, axisymmetric problems, torsion of cylindrical rods, and plate and shell problems. The third part introduces the concepts of strain energy and complementary energy, energy principles and direct methods, and briefly explains the basic ideas of the finite element method. This book can be used as a textbook for undergraduate or graduate students in engineering disciplines, as well as a reference for engineers and researchers engaged in stress analysis and strength design.