1st Edition

Computational Methods in Engineering Finite Difference, Finite Volume, Finite Element, and Dual Mesh Control Domain Methods

594 Pages 272 B/W Illustrations
by CRC Press

594 Pages 272 B/W Illustrations
by CRC Press

Also available as eBook on:

Computational Methods in Engineering: Finite Difference, Finite Volume, Finite Element, and Dual Mesh Control Domain Methods provides readers with the information necessary to choose appropriate numerical methods to solve a variety of engineering problems. Explaining common numerical methods in an accessible yet rigorous manner, the book details the finite element method (FEM), finite volume method (FVM) and importantly, a new numerical approach, dual mesh control domain method (DMCDM).

Numerical methods are crucial to everyday engineering. The book begins by introducing the various methods and their applications, with example problems from a range of engineering disciplines including heat transfer, solid and structural mechanics, and fluid mechanics. It highlights the strengths of FEM, with its systematic procedure and modular steps, and then goes on to explain the uses of FVM. It explains how DMCDM embodies useful parts of both FEM and FVM, particularly in its use of the control domain method and how it can provide a comprehensive computational approach. The final chapters look at ways to use different numerical methods, primarily FEM and DMCDM, to solve typical problems of bending of beams, axisymmetric circular plates, and other nonlinear problems.

This book is a useful guide to numerical methods for professionals and students in all areas of engineering and engineering mathematics.

1. Introduction and Preliminaries 2. The Finite Difference Method 3. The Finite Volume Method 4. The Finite Element Method 5. The Dual Mesh Control Domain Method 6. Nonlinear Problems with a Single Unknown 7. Bending of Straight Beams 8. Bending of Axisymmetric Circular Plates 9. Plane Elasticity and Viscous Incompressible Flows 10. Bending of Flat Plates

Biography

J. N. Reddy, the O’Donnell Foundation Chair IV Professor in J. Mike Walker ’66 Department of Mechanical Engineering at Texas A&M University, is a highly-cited researcher, author of 25 textbooks and over 800 journal papers, and a leader in the applied mechanics field for more than 50 years. He is well-known worldwide for his significant contributions to the field of applied and computational mechanics through the authorship of widely used textbooks on mechanics of materials, continuum mechanics, linear and nonlinear finite element analyses, variational methods, numerical methods, and composite materials and structures. His pioneering works on the development of shear deformation theories of beams, plates, and shells (that bear his name in the literature as the Reddy third-order plate theory and the Reddy layerwise theory), nonlocal and non-classical continuum mechanics have had a major impact, and have led to new research developments and applications. Some of his ideas on shear deformation theories and penalty finite element models of fluid flows have been implemented into commercial finite element software like Abaqus, NISA, and HyperXtrude (Altair).