Finite Element Method: Basics

Computers have dramatically changed the engineering work in design and analysis. Previously tedious and time consuming computations have been replaced by use of routine computer programs. Computations have become cheaper and more accurate. Although the most important thing is that through the development of computational techniques it has become possible to study complicated physical problems and processes. In particular the Finite Element Method (FEM), has emerged during the past 25 years. The development of FEM is so profound that the method has become a kind of universal tool for solving various types of engineering problems. A number of advanced, user-friendly computer programs, for various fields of application are currently available for practical problems. The method is used on a daily basis in civil, mechanical, aircraft, geotechnical, and environmental engineering, as well as in many other fields. This book introduces the basics and foundation of the FEM, and provides the reader with a thorough understanding of the method including background, development, application and potential or prospects of the method. The authors have tried to put the derivations in an elementary form so that it appeals especially to readers who are not familiar with the method. Every practical analysis using the FEM requires access to computers. Therefore an effort has been made to describe the development and the use of computer programs. The use and possibilities of FEM in the design and analysis process are also described. Here, automated error analysis and mesh refinement and coupling to CAD are important features. The book presumes a modest knowledge in matrix algebra, differential and integral calculus, beyond the level of senior high school. The book is intended to be used as an introductory text book at technical faculties as well as in training programs for engineers.

Table of Contents:
Introduction; Approximate Solution of Linear Stationary Boundary Value Problems; Heat Conducting in One Dimension; Stationary Heat Conduction in Two Dimensions; One-Dimensional Elasticity Problems; Two-Dimensional Elasticity Problems; Three-Dimensional Elasticity Problems; Bars Beams and Frames; Elastic Plates in Bending; Establishment and Solution of Systems of Equations; Accuracy and Efficiency of Calculations; Adaptive Technique; Transient Heat Flow; Groundwater Flow and Consolidation; Fluid Mechanics; Structural Dynamics; Mathematical Tools; Survey Over Approximation Methods for Boundary Value Problems; Computer Aided Engineering -- Programs and Trends; Index.