Geotechnical Engineering Numerical Calculation

Author: Lei Xiaoyan
Editor-in-Chief: Jiang Xinxi
Publisher:
Publish Date: 2005-05-01
Features:
Introduction This book provides a detailed introduction to the numerical methods for solving problems such as plasticity, elastoplastic coupling, strain softening, viscoplasticity, and creep using the finite element method. It discusses the fundamental principles of numerical methods such as the boundary element method, discrete element method, joint elements, and infinite elements. It also examines special issues in geotechnical engineering, such as contact problems, anchor elements, inverse analysis of material parameters, coupled problems, and numerical calculations for dynamic problems. Finally, it introduces finite element error estimation and adaptive methods. This book can serve as a textbook for undergraduate and graduate students in geotechnical engineering programs in engineering colleges, as well as a reference for engineering technicians and teachers in civil, transportation, and hydraulic engineering fields.
Excerpt:
Chapter Nonlinear Finite Element Method
1.1 Overview of the Finite Element Method
The finite element method can be categorized into displacement methods, stress methods, and mixed methods based on the choice of unknown field variables. Displacement methods select node displacements as unknown field variables, stress methods select node stresses, and mixed methods select a combination of node displacements and stresses. This section provides a brief introduction to displacement finite element methods.
1.1.1 Element Types
Depending on the problems being addressed, they can be divided into plane problems and spatial problems, with corresponding elements referred to as plane elements and spatial elements. Common plane elements include triangular, quadrilateral, and arbitrary quadrilateral elements, while spatial elements include eight-node block elements and twenty-node curved surface elements. As shown in Figure 1.1.
1.1.2 Basic Equations
The displacement at any point within an element can be expressed using interpolation functions in terms of node displacements. For a plane problem, the displacement component is denoted as \( u \), and for a spatial problem, it is also denoted as \( u \).