FEA Course Lecture III

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• FEA Course Lecture III Outline
• UCSD - 10/16/03
• Intro to 2-Dimensional FEs plates and shells.
• Fluid Mechanics Problem
• Heat Transfer (Thermal) Problem
• Plane Elasticity

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• 2-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.

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• C) For plane elasticity problem in 2-dimensional,
  we have
• Plane Problems are also known as Plane
  Elasticity Problems
• Plane a flat element with constant thickness
• There are two types of plane problems
• Plane Stress thickness of the third dimension
  of an
• elastic body is very small.
• Plane Strain - thickness of the third dimension
  of an
• elastic body is infinitely large.

Sigma_XZ Sigma_YZ Sigma_ZZ 0
tinfinity
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Governing Differential Equation Stress-Str
ain Relationships s E e Plane Stress
Plane Strain
C11 C22 (1-n)E/(1n)/(1-2n)
C11 C22 E/(1-n2)
C12 nE/(1-n2)
C12 nE/(1n)/(1-n)
C66 (1-2n)E/2/(1n)/(1-2n)
C66 (1-n)E/2(1-n2)
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• Types of Finite Elements used in Plane Elasticity
• a) CST Constant Strain Triangle

b) LST Linear Strain Triangle (Quadratic
Triangle)
c) Q4 Bilinear Quadrilateral
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d) Q8 Quadratic Quadrilateral
e) Q6 Improved Bilinear Quadrilateral f)
Elements with Drilling DOF (Degree of
Freedom) When using beams and shell elements (say
stiffeners) Folded Plates and Shells

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A) For heat transfer problem in 2-dimensional, we
have
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B) For fluid flow problem in 2-dimensional, we
have
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Review of Analysis Results. E.g., Plane
Elasticity. Exact Vs FE solution. Error
Estimation. SOFTWARE-Specific Session Build 2D
problem on ANSYS. Go through all steps. Thermal
problem on ANSYS Plane-stress problem on
ANSYS 2DFlow problem on ANSYS/FEMLAB. Homework 2
and Reading Assignments.