Finite element week 1
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The document outlines a 16-week course on the finite element method (FEM). It introduces FEM and its applications in heat transfer, fluid mechanics, and solid mechanics. Over the course, students will learn how to formulate the finite element equation, create elements to model problems, and solve problems using FEM software. Assessment includes homework, programming tests, a midterm, and a final exam.
Finite element week 1
- 1. FINITE ELEMENT METHOD Week # 1
- 2. Course Descriptions formulation and calculation of the finite element ma Procedures and modeling in finite element method / / stiffness matrices for spring and basic structural e trices method of weighted res lements idua / ls / Galerkin finite element method / general element interpolation functions applications in heat transfer, fluid and s formula olid mec tio ha n / nics Week # 1
- 3. Objectives :- to how does the FEM work :- to the finite element equation :- to the elements in problem modeling :- to problem by using FE introduce formulate create solve a M :- to the computer programs in sopply lving various problems Week # 1
- 4. Interesting Topics (1/2) Introduction to Finite Element Method Mathematical Preliminaries Spring and Bar Element Stiffness Matrices Analysis of Truss Structures Beam Theory and Flexural Beam Element W W W W W Week # 1
- 5. Interesting Topics (2/2) Weighted Residuals Method and Galerkin Finite Element Method Interpolation (Shape) Functions Applications in Heat Transfer Applications in Fluid Mechanics Applications in Solid Mechanic W W W W W s Week # 1
- 6. Grade Compositions Homeworks 10 % Program Testing 40 % Mid-Term Examination 20 % Final-Term Examination 30 % Total 100 % W W W W Week # 1
- 7. Course Outlines (1/16) Course Descriptions Objectives Interesting Topics Course Outlines Y Y Y Y Overviews (Week # 1) Week # 1
- 8. Course Outlines (2/16) Brief History and Recent Developments Basic Idea & Basic Concepts Applications of FEM Advantages of FEM Existing Computer Programs for FEM Examples of Finite Element Analysis Y Y Y Y Y Y Introduction to WeekFEM ( # 2) Week # 1
- 9. Course Outlines (3/16) Vector Analysis Matrix Operations Linear Algebra Calculus (Differentiation & Integration) Numerical Integration (Gauss Quadrature) Y Y Y Y Y Mathematical Prelim Wi ena ekries ( # 3) Week # 1
- 10. Course Outlines (4/16) Elastic Spring System Linear Spring Element Elastic Bar and Truss Elements Y Y Y Spring and Bar Element Stiffness Matrice Weeks ( # 4) Week # 1
- 11. Course Outlines (5/16) Minimum (Stationary) Potential Energy Introduction of Truss Structures Nodal Equilibrium Equations Y Y Y Analysis of Truss Structures (Week # 5) Week # 1
- 12. Course Outlines (6/16) Transformation of Element Direct Assembly of Global Stiffness Matrix Applying Boundary Conditions and Constraint Forces Strain and Stress in Truss Element Y Y Y Y Analysis of Truss Structures (Week # 6) Week # 1
- 13. Course Outlines (7/16) Introduction to Elementary Beam Theory Flexure Element Stiffness Matrix for Flexure Element Element Load Vector Work Equivalence for Distributed Loads Flexural Element with Axial Loading Y Y Y Y Y Y Beam Theory and Flexural Beam Element Week( # 7) Week # 1
- 14. Course Outlines (8/16) *** Mid-Term Examination *** Week # 1
- 15. Course Outlines (9/16) Method of Weighted Residuals Galerkin Finite Element Formulation Y Y Weighted Residuals Method and Galerkin Finite Element M Weeeth kod ( # 9) Week # 1
- 16. Course Outlines (9/16) Application of Galerkin FEM to Bar and Beam Elements Application to 1-D Heat Conduction Y Y Weighted Residuals Method and Galerkin Finite Element M Weeketho #d ( 10) Week # 1
- 17. Course Outlines (10/16) Compatibility and Completeness Polynomial Forms : 1-D Elements Polynomial Forms : 2-D and 3-D Elements 2-D Elements : 3-Node Triangular Elements 2-D Elements : 6-Node Triangular Elements 2-D El Y Y Y Y Y Y ements : 4-Node Rectangular Elements 2-D Elements : 8-Node Rectangular ElementsY Interpolation (Shape) Functions (Week # 11) Week # 1
- 18. Course Outlines (11/16) 1-D Conduction : Quadratic Element 1-D Conduction with Convection Heat Transfer in 2-D Y Y Y Applications in Heat WT era eknsfe #r ( 12) Week # 1
- 19. Course Outlines (12/16) Week # 1 Heat Transfer with Mass Transport Axisymmetric Heat Transfer Time Dependent Heat Transfer Y Y Y Applications in Heat WT era eknsfe #r ( 13)
- 20. Course Outlines (13/16) Week # 1 Introduction Incompressible Flow Stream Function in 2-D Flow Velocity Potential Function in 2-D Flow Incompressible Viscous Flow Y Y Y Y Y Applications in Fluid Mechanics (Week # 14)
- 21. Course Outlines (15/16) Week # 1 Introduction Plane Stress and Plane Strain Problems Y Y Applications in Solid Mechanics (Week # 15)
- 22. Course Outlines (15/16) Week # 1 Isoparametric Formulation of Plane Element 3-D Stress Elements Strain and Stress Computation Y Y Y Applications in Solid Mechanics (Week # 16)
- 23. Textbooks / Additional Reading Hutton, D.V., (2004), Fundamentals of Finite Element Analysis, International Ed., Mc-Graw Hill, Singapore rd Reddy, J.N., (2006), An Introduction to the Finite Element Method, 3 Ed.,International Ed., Mc-Graw Hill, Singapore nd Chandrupatla, T.R. and Belegundu, A.D., (1997), Introduction to Finite Elements in Engineering, 2 Ed., International Ed., Prentice-Hall, New Jersey Week # 1