Theory of Elasticity and Stress Concentration

Book Preface

The theory of elasticity is not applied mathematics. Solving differential equations and integral equations is not the objective of the theory of elasticity. Students and young researchers, who can use the modern commercial finite element method (FEM) software, are not attracted by the classical approach of applied mathematics. This situation is not good. Students, young researchers and young engineers skip directly from the elementary theory of the strength of materials to FEM without understanding the basic principles of the theory of elasticity. The author has seen many mistakes and judgement errors made by students, young researchers and young engineers in their applications of FEM to practical problems. These mistakes and judgement errors mostly come from a lack of basic knowledge of the theory of elasticity. Firstly, this book provides the basic but very important essence of the theory of elasticity. Second, many useful and interesting applications of the basic way of thinking are presented and explained. Readers do not need special mathematical knowledge to study this book. They will be able to understand the new approach of the theory of elasticity which is different from the classical mathematical theory of elasticity and will enjoy solving many interesting problems without using FEM.

The basic knowledge and engineering judgement acquired in Part I will encourage the readers to enter smoothly into Part II in which various important new ways of thinking and simple solution methods for stress concentration problems are presented. Approximate estimation methods for stress concentration will be very useful from the viewpoint of correct boundary conditions as well as the magnitude and relative importance of numerical variables. Thus, readers will be able to quickly find approximate solutions with practically sufficient accuracy and to avoid fatal mistakes produced by FEM calculations, performed without basic knowledge of the theory of elasticity and stress concentration.

The author believes with confidence that readers of this book will be able to develop themselves to a higher level of research and structural design.