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Finite Elements Principles and Practices - Fall 03 FEA Course Lecture III – Outline UCSD - 10/16/03 1.Intro to 2-Dimensional FEs [plates and shells]. 1.Fluid Mechanics Problem 2.Heat Transfer (Thermal) Problem 3.Plane Elasticity

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Finite Elements Principles and Practices - Fall 03 2-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.

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Finite Elements Principles and Practices - Fall 03 C) For plane elasticity problem in 2-dimensional, we have: 1.Plane Problems – are also known as Plane Elasticity Problems 2.Plane – a flat element with constant thickness 3.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. t=infinity Sigma_XZ = Sigma_YZ = Sigma_ZZ = 0

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Finite Elements Principles and Practices - Fall 03 Governing Differential Equation: Stress-Strain Relationships = E Plane Stress Plane Strain C11 = C22 = E/(1- 2 ) C12 = E/(1- 2 ) C66 = (1- E/2(1- 2 ) C11 = C22 = (1- E/(1+ )/(1-2 ) C12 = E/(1+ )/(1- ) C66 = (1-2 E/2/(1+ )/(1-2 )

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Finite Elements Principles and Practices - Fall 03 1.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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Finite Elements Principles and Practices - Fall 03 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 d) Q8 – Quadratic Quadrilateral

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Finite Elements Principles and Practices - Fall 03 A) For heat transfer problem in 2-dimensional, we have:

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Finite Elements Principles and Practices - Fall 03 B) For fluid flow problem in 2-dimensional, we have:

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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.

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