The Finite Element Method

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# The Finite Element Method - PowerPoint PPT Presentation

The Finite Element Method. A self-study course designed for engineering students. Course Outline. Lesson 1: Introduction and overview Lesson 2: Brief history of the FEM Lesson 3: Basic concepts Lesson 4: Review of numerical methods Vectors Matrices Lesson 5: Method of Weighted Residuals

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### The Finite Element Method

A self-study course designed for engineering students

Course Outline
• Lesson 1: Introduction and overview
• Lesson 2: Brief history of the FEM
• Lesson 3: Basic concepts
• Lesson 4: Review of numerical methods
• Vectors
• Matrices
• Lesson 5: Method of Weighted Residuals
• Classical Solution Technique
• The Weak Statement
Course Outline con’t
• Lesson 6: 1-D Element
• Lesson 7: Shapes Functions – 1-D
• Lesson 8: Steady State Diffusion Equation
• Lesson 9: Natural Coordinate System
• Lesson 10: Time-Dependence
• Lesson 11: Matrix Formulation
• Lesson 12: Solution Methods
Course outline con’t
• Lesson 13: 2-D Triangular Element
• Lesson 14: The Mesh - triangles
• Lesson 15: Shape Functions
• Lesson 16: Area Coordinate System
• Lesson 17: Numerical Integration
• Lesson 18: Steady-State Diffusion Equation
• Lesson 19: Time Dependence
Course outline con’t
• Lesson 20: Bandwidth
• Lesson 21: Exercises
• Lesson 22: 2-D Quadrilateral Element
• Lesson 23: The Mesh - quadrilaterals
• Lesson 24: Shape Functions
• Lesson 25: Natural Coordinate System
• Lesson 26: Gaussian Quadrature Integration
Course outline con’t
• Lesson 27: Steady-State Diffusion Equation
• Lesson 28: Time Dependence (2)
• Lesson 29: Isoperimetric Element
• Lesson 30: Natural Coordinate System
• Lesson 31: Shape Functions
• Lesson 32: Element Matrices
• Lesson 33: FEM vs. FDM/FVM
Course outline con’t
• Lesson 34: The Chapeau Function
• Lesson 35: Accuracy
• Lesson 36: 3-D Elements
• Lesson 37: The Mesh (3)
• Lesson 38: Shape Functions
• Lesson 39: Applications – Elasticity
• Lesson 40: Applications – Heat Transfer
Course outline con’t
• Lesson 41: Applications – Fluid Flow
• Ideal
• Incompressible (penalty vs equal order)
• Compressible
• Lesson 42: Applications – Environmental
• Lesson 43: Mesh Adaptation (h vs p)
• Lesson 44: Boundary Elements
Course outline con’t
• Lesson 45: Exercises
• Lesson 46: Commercial Codes