Learning Guide for Solving Problems in Elasticity Theory

Author: Wang Junzhen
Editor-in-Chief: Xie Mingfang
Publisher:
Publishing Date: 2000-01-01
Features: This book is a supplementary reference for learning "Elasticity Theory," written according to the teaching requirements of elasticity theory in higher industrial schools. The book is divided into ten chapters: Introduction, Basic Theories of Plane Problems, Rectangular Coordinate Solutions of Plane Problems, Polar Coordinate Solutions of Plane Problems, Basic Theories of Spatial Problems, Solutions of Spatial Problems, Small Deflection Bending of Thin Plates, Finite Difference Method, Variational Methods in Elasticity Theory, and Finite Element Method for Plane Problems. Each chapter of the book is composed of four parts: Theoretical Summary, Typical Examples, Learning Methods and Problem-Solving Guidance, and Exercises and Reflections. Additionally, four mock exams are provided. Both exercises and exams include answers. The questions marked with numbers in the book are selected from the entrance exams of some key universities over the years. This book can serve as a supplementary text for undergraduate engineering students, correspondence students, self-learners, graduate students, teachers, and scientific and technological workers studying "Elasticity Theory."
Excerpt:
Methods and Solutions 1. Saint-Venant's Principle: This principle transforms surface forces on a small part of a body into statically equivalent but differently distributed surface forces, which only affect the stress distribution near the area and do not affect the stress distribution far away. This principle is also known as the principle of locality. In other words, if a balanced force system (i.e., zero resultant force and moment) acts on a small part of the boundary, this balanced force system only produces significant stress near the area, while its effect on the far area can be ignored. 2. Superposition Principle: Under linear elasticity and small deformation conditions, the superposition of solutions for two different sets of external forces acting on the same body is equal to the solution when both sets of external forces act on the body simultaneously. 3. Uniqueness Theorem: For an elastic body with known body forces, surface forces, or boundary displacements, the solution to an elasticity theory problem is unique. 4. Inverse Method and Semi-Inverse Method (1) The inverse method involves selecting a trial function (displacement, stress, or stress function) that satisfies the basic equations and then analyzing the boundary conditions to determine what problems can be solved. (2) The semi-inverse method is based on the boundary shape and loading characteristics of the elastic body. It first assumes some unknown quantities and then determines the other unknown quantities by satisfying all the basic equations and boundary conditions, or by modifying the assumed quantities until they are satisfied.