FE Course Lecture II – Outline UCSD - 10/09/03 Review of Last Lecture (I) Formal Definition of FE: Basic FE Concepts Ba

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FE Course Lecture II – Outline UCSD - 10/09/03 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

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FE Course Lecture II – Outline

• UCSD - 10/09/03
• 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
• Intro to 1-Dimensional FEs [Beams and Bars].
• Fluid Mechanics Problem
• Heat Transfer (Thermal) Problem
• Beam/Bar problem

Finite Elements Principles and Practices - Fall 03

1-Dimensional Finite Elements

• 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] {D} = {q}
• Where
• [K] is traditional known as the ‘stiffness’ or ‘coefficient’ matrix (conductance matrix for heat transfer, flow-resistance matrix for fluid flow),
• {D}is the displacement (or temperature, or velocity) vector and
• {q} is the force (or thermal load, or pressure gradient) vector.

Finite Elements Principles and Practices - Fall 03

Tbase=100oC

Tamb=20oC

5

• 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

Finite Elements Principles and Practices - Fall 03

B) For fluid flow problem in 1-dimensional, we have:

• md2u/dy2 – dp/dx = 0
• [KF}{u} = {P} [applicable for steady-state flow problems]. P – pressure gradient

Finite Elements Principles and Practices - Fall 03

C) For stress problem in 1-dimensional, we have:

• -kd2u/dx2 – q = 0
• [KF}{u} = {F}. F – joint force.

u=uo = 0

How about for a tube under pure torsion? How will the coefficients look like?

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.

Finite Elements Principles and Practices - Fall 03