Finite Elements Methods in Mechanics

✍ Scribed by M. Reza Eslami (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 378
• Series: Solid Mechanics and Its Applications 216
• Edition: 1
• Category: Library

✦ Synopsis

This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams and elasticity with detailed derivations for the mass, stiffness and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems and the third one presents the three dimensional transient heat conduction problems. The programs are written in C++ environment.

✦ Table of Contents

Front Matter....Pages i-xvi
Introduction and History....Pages 1-5
Mathematical Foundations....Pages 7-34
Finite Element of Elastic Membrane....Pages 35-55
Elements and Local Coordinates....Pages 57-77
Field Problems....Pages 79-94
Conduction Heat Transfer in Solids....Pages 95-117
Computer Methods....Pages 119-156
Finite Element of Beams....Pages 157-186
Elasticity, Galerkin Formulations....Pages 187-207
Elasticity, Variational Formulations....Pages 209-228
Torsion of Prismatic Bars....Pages 229-236
Thermoelasticity....Pages 237-253
Incompressible Viscous Fluid Flow....Pages 255-284
One-Dimensional Higher Order Elements....Pages 285-312
Two-Dimensional Higher Order Elements....Pages 313-330
Coupled Thermoelasticity....Pages 331-361
Computer Programs....Pages 363-370

✦ Subjects

Theoretical and Applied Mechanics; Computational Science and Engineering; Theoretical, Mathematical and Computational Physics