HomeIntroduction To The Finite Element Methods
Introduction To The Finite Element Methods

Introduction To The Finite Element Methods

Editor: TORA DOW
 
  • Year: 2019
  • Binding: Hardback
  • Price: US $ 275.00

The Finite Element Method (FEM) is undoubtedly the most powerful method for solving boundary- and initial-value problems with partial differential equations numerically. As a result, it has had a huge impact on almost every field of engineering and applied research. The finite element approach showed great promise in the modelling of a variety of mechanical applications in aerospace and civil engineering at the outset. The finite element method is only now beginning to realise its full potential in terms of applications. Its application in coupled issues such as fluid-structure interaction, thermomechanical, thermochemical, thermo-chemo-mechanical problems, biomechanics, biomedical engineering, piezoelectric, ferroelectric, and electromagnetics is one of the most interesting prospects.



 This book aims to shed light on some of the unexplored aspects of finite element methods. It explains in detail the use and importance of this subject. The book contains method of weighted residuals, two-dimensional triangular element and isoparametric two-dimensional elements. This book picks up individual branches and explains their need and contribution in the growth of this field. It also deals with three-dimensional element, solid mechanics, boundary elements and meshless methods. The various subfields of engines along with technological progress that have future implications are glanced at in it. This book is a complete source of knowledge on the present status of this important field.




 


Preface


1. Introduction


1. Introduction


2. Short history


3. Orientation


4. The oop for the gfem


Conclusion


References


2. Method of Weighted Residuals and Galerkin Approximations


1. Introduction


2. Classical solutions


3. The “weak” statement


Conclusion


References


3. Finite Element Method in One Dimension


1. Introduction


2. Shape functions


3. Quadratic elements


4. Cubic elements


5. Steady conduction equation


6. Axisymmetric heat conduction


7. Natural coordinate system


8. Spatial discretization


Conclusion


References


4. Two-Dimensional Triangular Element


1. Introduction


2. The mesh


3. Linear shape functions


4. Area coordinates


5. Numerical intecration


6. Steady-state conduction with boundary convection


7. The quadratic triancular element


8. Bandwidth


Conclusion


References


5. Two-Dimensional Quadrilateral Element


1. Introduction


2. Bilinear rectangular element


3. Natural coordinate system


4. Numerical intecration usinc gaussian quadratures


5. The quadratic quadrilateral element


Conclusion


References


6. Isoparametric Two-Dimensional Elements


1. Introduction


2. Bilinear quadrilateral


3. Eight-noded quadratic quadrilateral


4. Linear triangle


5. Quadratic triangle


6. The element matrices


7. Inviscid flow example


Conclusion


References


7. Three-Dimensional Element


1. Introduction


2. Tetrahedron


3. Hexahedron


4. Numerical integration


5. Hexahedron


6. Time-dependent heat conduction with radiation and convection


7. Radiation


8. Shape factors


Conclusion


References


8. Finite Elements in Solid Mechanics


1. Introduction


2. Two-dimensional elasticity: stress/strain


3. Potential energy


4. Thermal stresses


5. Tetrahedron element


6. Element matrices


Conclusion


References


9. Introduction to Boundary Elements


1. Introduction


2. One-dimensional bem


3. Two-dimensional bem


4. Three-dimensional bem


5. Dual reciprocity method


Conclusion


References


10. Introduction to Meshless Methods


1. Introduction


2. History of mems


3. Radial basis functions


4. The kansa approach


5. 1-D formulation


6. 2-D formulation


7. Smooth particle hydrodynamics


Conclusion


References


Index

Tora Dow is a Research Professor at Technical College, Patagonia. She has obtained her Ph.D. in Engineering Mechanics from University of Science, Veracruz. Her research interests focus on areas of smart materials and structures, vibration analysis of continuous systems, composite materials and structures, finite element analysis and fracture mechanics. Dow has contributed several books, articles, and research papers on kinematics, fluid mechanics, energy and pneumatics. She has attended numerous scientific conferences and symposiums; and has presented 10 papers in the vast field of engineering.