1. Finite Elements Principles and Practices - Fall 03 FE Course Lecture II – Outline UCSD - 10/09/03 1.Review of Last Lecture (I) Formal Definition of FE: Basic FE Concepts Basic FE Illustration Some Examples of the Second Order Equations in 1- Dimension Some Examples of the Poisson Equation –. (k u) = f and Some Examples of Coupled Systems 2.Intro to 1-Dimensional FEs [Beams and Bars]. 1.Fluid Mechanics Problem 2.Heat Transfer (Thermal) Problem 3.Beam/Bar problem

2. Finite Elements Principles and Practices - Fall 03 1-Dimensional Finite Elements 1.Stiffness and Load Vector Formulations for mechanical, heat transfer and fluid flow problems. The system equation to be solved can be written in matrix form as: [K] { } = {q} Where [K] is traditional known as the stiffness or coefficient matrix (conductance matrix for heat transfer, flow-resistance matrix for fluid flow), { } is the displacement (or temperature, or velocity) vector and {q} is the force (or thermal load, or pressure gradient) vector.

3. Finite Elements Principles and Practices - Fall 03 A) For heat transfer problem in 1-dimensional, we have: fx = -Kdt/dx [Fourier Heat Conduction Equation] Q = -KAdt/dx (where Q=A fx) [KT}{T} = {Q} [applicable for steady-state heat transfer problems] 1 5 T base =100 o C T amb =20 o C 5

4. Finite Elements Principles and Practices - Fall 03 B) For fluid flow problem in 1-dimensional, we have: d 2 u/dy 2 – dp/dx = 0 [K F }{u} = {P} [applicable for steady-state flow problems]. P – pressure gradient

5. Finite Elements Principles and Practices - Fall 03 C) For stress problem in 1-dimensional, we have: d 2 u/dx 2 – q = 0 [K F }{u} = {F}. F – joint force. u=u o = 0 How about for a tube under pure torsion? How will the coefficients look like?

6. Finite Elements Principles and Practices - Fall 03 Review of Analysis Results. E.g., stress distribution. Exact Vs FE solution. Error Estimation. SOFTWARE-Specific Session: Intro to software-specific issues. h-elements, p-Elements, adoptive meshing. Build 1D problem on ANSYS. Go through all steps. Thermal problem on ANSYS Bar problem on ANSYS Flow problem on ANSYS/FEMLAB. Homework 1 and Reading Assignments.