Finite Elements Methods in Mechanics

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.

Easy to follow the materials including the concepts, detail mathematics and programming Covers all basic areas of the mechanical engineering, such as fluid mechanics, heat conduction, beams and elasticity with detail derivations for the mass, stiffness and force matrices Gives physical feeling to the reader for finite element approximation by introduction of finite elements to the elevation of elastic membrane Detail treatment of computer methods with examples Conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution Variational and the Galerkin formulations of the heat conduction, beams and elasticity problems Includes supplementary material: sn.pub/extras

Contenu
Introduction and History.- Mathematical Foundations.- Finite Element of Elastic Membrane.- Elements and Local Coordinates.- Field Problems.- Conduction Heat Transfer in Solids.- Computer Methods.- Finite Elements of Beams.- Elasticity, Galerkin Formulations.- Elasticity, Variational Formulations.- Torsion of Prismatic Bars.- Thermoelasticity.- Incompressible Viscous Fluid Flow.- One-Dimensional Higher Order Elements.- Two-Dimensional Higher Order Elements.- Coupled Thermoelasticity.- Computer Programs.