FEA Course Lecture III – Outline UCSD - 10/16/03 Intro to 2-Dimensional FEs [plates and shells]. Fluid Mechanics Proble

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# FEA Course Lecture III – Outline UCSD - 10/16/03 Intro to 2-Dimensional FEs [plates and shells]. Fluid Mechanics Proble - PowerPoint PPT Presentation

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. 2-Dimensional Finite Elements

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## FEA Course Lecture III – Outline UCSD - 10/16/03 Intro to 2-Dimensional FEs [plates and shells]. Fluid Mechanics Proble

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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

Finite Elements Principles and Practices - Fall 03

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.

Finite Elements Principles and Practices - Fall 03

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

t=infinity

Finite Elements Principles and Practices - Fall 03

Governing Differential Equation:

• Stress-Strain Relationships
• s = E e Plane Stress Plane Strain

C11 = C22 = (1-n)E/(1+n)/(1-2n)

C11 = C22 = E/(1-n2)

C12 = nE/(1-n2)

C12 = nE/(1+n)/(1-n)

C66 = (1-2n)E/2/(1+n)/(1-2n)

C66 = (1-n)E/2(1-n2)

Finite Elements Principles and Practices - Fall 03

Types of Finite Elements used in Plane Elasticity

• a) CST – Constant Strain Triangle

b) LST – Linear Strain Triangle (Quadratic Triangle)

Finite Elements Principles and Practices - Fall 03

f) Elements with Drilling DOF (Degree of Freedom)

When using beams and shell elements (say stiffeners)

Folded Plates and Shells

Finite Elements Principles and Practices - Fall 03

A) For heat transfer problem in 2-dimensional, we have:

Finite Elements Principles and Practices - Fall 03

B) For fluid flow problem in 2-dimensional, we have:

Finite Elements Principles and Practices - Fall 03

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.

Finite Elements Principles and Practices - Fall 03