330:155g Finite Element Analysis - University of Northern …rao/155 FEA 1 Introduction.pdf · 330:155g Finite Element Analysis ... Elements Loads Supports ... approximate answer

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330:155g Finite Element Analysis

Nageswara Rao Posinasetti

2January 16, 2008 Rao, P.N.

1. IntroductionFinite element analysis is a computer-based numerical technique that is used to solve stress analysis, heat transfer, fluid flow and other types of engineering problems.Real power is in its ability to solve problems that do not fit any standard formula.


Before FEA

Tested till failure before the availability of FEM.

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Before FEAProblems are simplified using certain approximations before the availability of FEM.

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1. Introduction

It involves partitioning of a structure into a finite number of elements

Divide and ConquerElements are connected to one another at the corner points

These corner points are called nodes or nodal points

Each element is a simple geometric shapeTriangle, Quadrilateral, etc.


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1. Introduction

In order to completely define a finite element model

Nodal pointsElementsLoadsSupports Element related data


1. Introduction

FEA program formulates the equations for solutions

A nodal point can have upto 6 degrees of freedom3 translational (x, y, z) and 3 rotationalAn equilibrium equation for each degree of freedom

Equations are solved for displacement at each nodal pointDisplacements are then used to evaluate the stresses


1. Introduction

For the model to accurately represent the physical part, the number of elements should be large.Type of element should be correctly chosenBoundary conditions should be correctly applied.

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X1 2 3 4 5 6 7 8 9 10 11 12 13 14


1. Introduction

Process of data preparation is tedious and long.

It is called pre-processingResults obtained are also voluminous

It is called post-processing

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Steps in finite element analysis process

Pre-processingDefine the model

Discretize the part defining nodal points and elementsDefine element properties, material properties such as density, modulus elasticity, etc.Specify the boundary conditionsSpecify the loads


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Preprocessor

Modelling of the geometryGenerating the finite element mesh by making a suitable approximation to the geometryCalculates the nodes and elemental propertiesAllows for the specification of the support condition and loading conditions for the individual element positions.Allows the material properties to be specified.



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Analysis

Formulates the equations that describe each elements’ stiffness and assembles all of the equations so that they form a set of simultaneous equationsSolves the system of equations for the displacement at each nodal pointUses the nodal point displacements to solve for stress within each element


Results

Results generated from the analysis are voluminous depending upon the number of elements considered.For proper understanding one has to go through all the data tables.


Postprocessor

Post processing involves the ability to go through a large amount of data generated during the solving process and convert it into an easily understood form for the design purpose.

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1.2 Library of Element Types

Depending upon the part geometry and the type of analysis required a number of different types of elements are available in FEA


2-node linear 3-node quadratic

3-node linear 6-node quadratic 4-node linear 8-node quadratic

4-node linear 10-node quadratic

a) one dimensional

b) Two dimensional

c) Three dimensional

Triangular Quadrilateral

Tetrahedral


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1.3 Advantages of using FEA

Irregular shaped partsParts made from different materialsIrregularly placed loadsLarge number of supportsProvides results throughout the part (all points)Easy to change the model


Why Use FEA?Provides a non-destructive means of testing products.Faster prototyping for “what if” scenarios.Design optimization.Speed up time to market by shortening the design cycle.

Courtesy Algor Inc, Pittsburgh


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Best Practices

FEA requires engineering judgment. In the best case, you should know the approximate answer before you begin.

Proper selection of elements, materials, loads, constraints and analysis parameters comes from experience.



Best Practices

Understand that the computer model never matches reality (it’s only an approximation).The surest route to failure in FEA is to underestimate the complexity of the technology.



Aerospace IndustryOrbital Technologies Corporation

The above illustration shows how engineers analyzed a Biomass Production System to conduct biotechnology plant research.

FEA in Different Industries


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Automotive IndustryDanly Engineering Services, Division of EnprotechMechanical Services, Inc.

The above illustration shows how engineers analyzed a power press with additional cutouts. Courtesy Algor Inc,

Pittsburgh



Biomedical IndustryOphthalmic Consultants of Boston and the Tufts University School of Medicine

The above illustration shows stresses on an eye as it underwent a 30° saccadic eye movement. This was modeled to help understand why retinal detachments occur.




Power/Utility IndustryCronulla Sewage Treatment Plant

The above illustration shows how engineers modeled a piping system to verify that the number of bellows could safely be reduced by using lightweight, spiral-wound stainless steel. This allowed them to keep a $90 million sewage treatment plant upgrade on budget.


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1.4 Historical Development

Concept first appeared in 1956Name “Finite Element” is used in 1960 by Clough1970’s large programs running in mainframe computers1980’s moved to personal computers and widespread use


CAD to FEA

There are many approaches for integrating CAD systems to FEA


CAD System

Geometricmodeller

Pre-Processor

CADGeometry

FE Mesh

FullFEM model

FEAnalysis

FE Pre-Processor

FE PostProcessor

Inventor to Algor

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Geometricmodeller

FEAnalysis

FE Pre-Processor

FE PostProcessor

Integrated FEA System, e.g. Algor


Design problemSelect a round bar to be constructed from an AISI 1020 cold-drawn steel to support the 300-pound ball. Assume a safety factor of 2, and determine the deflection for the size selectedYield stress = 61,000 psi


Design problemCantilever beamMax bending moment = 300 x 36

= 10,800 in-lbStress in the beam, S = M/ZS = 10,800 x 32 / (Π d3)Allowable stress = 61,000 / 2 = 30,500 psiEquating the above two, and solvingd = 1.533 in = 1.625 in (preferred size)Deflection = -FL3 / (3EI) = 0.455 in

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Problem using FEA

Start with 2 in dia; Max stress = 13,751 lower than the allowable 30,500 psi


Problem using FEA (contd..)

Next try 1.5 in dia; Max stress = 32,599 higher than the allowable 30,500 psi



Next try 1.625 in dia; Max stress = 25,635 lower than the allowable 30,500 psi - Acceptable

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For 1.625 in dia; Max displacement = 0.47 in Compare this to analytical solution of 0.455 in, a 3% error


Analytical Problem Solving Process

Establish clearly defined goalCompile and qualify the inputsSolve the problem with the most appropriate meansVerify and document the results


What is the goal of the Analysis?

The decisions to be madeHow important is the exact solution to the problem?

This will help in identifying the precision of the inputs to the problem.

What information from the analysis will help in taking the engineering decision

When can you stop analyzing?Which shortcuts are allowed?

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Common MisconceptionsMeshing is everything

Current preprocessor are efficient and generally give good meshes. But that is not the end since it is only an input.Boundary conditions and forces are added by the user. The accuracy of the results depend to a great extent on them.

FEA replaces testingDepends on the confidence in the analytical methods used.There is no guarantee that the results are accurate.


Common Misconceptions

Finite element analysis is easyDon’t underestimate the complexity of the problem.Don’t jump to conclusions too quickly.Some little experiments may be required to gauge the forces and reactions in the part.Interpreting the results is also an important task.


Common Misconceptions

Finite element analysis is hardIt is estimated that 20% creativity and 80% hard work and patience.Learned through more practice

Learning the interface equals learning FEA

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Questions or Comments?


ExercisesDefine the terms: nodal point, element and degree of freedomWhat does the term discretization mean in the finite element method?List three different material properties that must be defined for each of the element.Explain why the computer is necessary in the use of the finite element method.Explain why computer graphic techniques are used during the postprocessing phase of a finite element analysis. What is the alternative to using these graphical displays?What advantage would a company derive by performing a finite element analysis of an existing part, which can be strain gauged and tested in a lab?

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330:155g Finite Element Analysis - University of Northern …rao/155 FEA 1 Introduction.pdf · 330:155g Finite Element Analysis ... Elements Loads Supports ... approximate answer