lecture 1 - introduction

ME466 ~ FINITE ELEMENT METHOD

An Introduction to Finite Element Analysis Using DR. MUHAMMAD ABID Faculty of Mechanical Engineering Ghulam Ishaq khan Institute of Engineering Sciences and Technology, Topi Pakistan January 2004

ME466 – FINITE ELEMENT METHODS

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Spring Semester 2004 Class Information: Lectures Lectures run on 02 days in Lecture Hall and 01day in Computer Lab in the Faculty of Mechanical Engineering. Occasionally, some excursions into the slot may be required to complete material. Tutorials Tutorials are based on the ‘doctors surgery’ format. One/two members of staff will be present in Computer Lab on following days to provide help/ support/advice on all aspects of running the software and helping with approaches to the coursework. Tutorials will start after Lecture 2. ANSYS 7 is installed in all computers of CM Lab. In addition, Pro-E is also installed on all computers if someone wants to use.

Timetable for Computer Lab - FME

10 - Pentium IV (Windows XP) Spring Semester 2004

Times Monday Tuesday Wednesday Thursday Friday

- Lecture

- Lab

Accessing the PC-Network It is essential that you have a PC username and Password. These can be obtained from administrator/ Lab Engineer Computer Lab FME. Thereafter, ANSYS can be found using the START bar button of WindowsNT. START→Programs→ANSYS 7→Interactive. Fill in the requred parameters and run. On-line Help Although a hard copy of ANSYS manuals is available in catalogue of Computer Lab, however these are all on-line and it is essential that you spend some time familiarising yourself with them. START→Programs→ANSYS 7→Help System will get you started. Navigate→Table Of Contents→Analysis Guides or Workbook Examples will be of good use.


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Internet Support All course material including past exercises and example input fileswill be made available during the Semester. Lecture notes will be available from ‘Central Services’. However, students can access this material via the internet using the following URL address, http://192.168.151.50 and by following the links shown. In addition, excellent web-based ANSYS tutorials from the University of Alberta have been made available. These can be viewed on-line or by downloading and uncompressing using the Winzip utility. Educational Version of ANSYS5.4 and ?? A ‘node and element’ limited version is available from market and can be arranged by yourself for your working at home. Finally… If you have any problems with the class, please e-mail me [email protected]. Don’t just drop in at my room. I will probably not see you as I have a very busy semester. The best way to cope with this class is to undertake all the exercises, which are given…take plenty of time over them in the early stages and then work on course works as they are given. Don’t wait till the dead lines are upon you!


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ME466 FINITE ELEMENT ANALYSIS

1.0 PRACTICAL STRESS ANALYSIS Introduction This class aims to present the essentials for performing modern computer aided engineering design specifically pertaining to stress analysis and strength design. In essence, the basic principles from previous mechanics courses will be adopted, identifying the following: * Stresses from simple components * Material behaviour & failure mechanisms * Fatigue & fracture * Simple component design However, the main emphasis of the course will develop advanced concepts of stress analysis as presently utilised within modern industry. The main technique for performing stress analysis and strength design is the finite element method. In addition to studying and mastering this technique, we will also examine important lessons from the past. Finite element analysis is the most popular means of simulating an engineering system. It is used daily by industry, indeed, hundreds of thousands of engineers world-wide have used the method for a variety of technical disciplines. For example, FEA has been used to simulate structural, mechanical, thermal, fluid flow, electrical and chemical systems. In fact, such is the uptake of the technique by engineers that over $5 billion is spent yearly on FEA in the US alone. In addition to the industrial uptake of the technique, thousands of engineers, scientists and mathematical are performing research into FEA. Over 10,000 articles in professional journals, more than 6,000 Ph.D. & Masters theses, more than 300 textbooks & monographs are available on the subject. It can be reasonably concluded that FEA is rapidly becoming an essential part of design improvement, optimisation, production process simulation and failure assessment.


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Why Finite Element Analysis ? The reasons for needing the finite element method and its popularity can be appreciated if one imagines the problem of stresses and strains in components and structures in almost any branch of engineering. Most modern structures are complex in the extreme. Sometimes, however, a component may have a simple form, for example, a beam or a plate as in an automobile or aircraft structure. These forms can be solved straightforwardly by classical analysis using differential equations with one or two variables. However, ‘real’ structures involve three dimensions and therefore are much more complicated to analyse. Even if they are assemblages of beams, the local forces require to be resolved prior to analysing the beam in question. Therefore, the main aim is to develop a technique of analysing complex geometries in the first instance. Once the geometry can be adequately described, the laws of equilibrium, motion, strain compatibility and stress-strain relations can be invoked and the process of analysis can begin. The essence of the approach is to use a computer to describe the geometry of the complex structure using a ‘discretised approach’, where the geometric shape or internal stress-strain-displacement fields are described by a series of points or coordinates scattered over the surface or through the interior of the structure. The structure is hypothetically divided into finite elements which are small enough that the shape of the displacement field can be approximated without too much error, then the magnitude must be found. It is possible to assume allowable displacement shapes for these elements, for example, linear, quadratics, polynomials, trigonometric functions as so on. Thereafter, the individual elements must be assembled together in such a way as to ensure the displacements and stresses are continuous in some fashion across the element interfaces, the internal stresses are in equilibrium with each other and the applied loads and the prescribed boundary conditions are satisfied. Various engineers have been attributed to being the father of FEA, e.g., Courant (1943), however, the arrival of the digital computer especially in the aircraft industry led to a rapid interest in activity in the Boeing Corporation in the early 1950's. The Structural Dynamics Unit, led by M J Turner, formulated the method in 1954 and published it in 1956. The North American B-70 bomber was the first production airplane designed using FEA. The World Trade Center in New York and the John Hancock Centre in Chicago were the first buildings designed on the basis of FEA.


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Some Very Important Points. It is really important to remember that FEA technology is very recent. It is therefore a very lively and evolving area of technology. Any engineer who commits a career to this discipline commits to an area requiring continuing education in new concepts. It is therefore to be expected that engineers who are knowledgeable and experienced command high salaries and are at a premium. The computer is an essential part of FEA, for various activities * solid modelling, mesh generation, plotting * model checking, solution * results display and evaluation It is also a real nuisance unless the engineer learn with someone knows the computer well. It is recognised that the learning time associated with the computer is really frustrating.

YOU ARE WARNED!! Whilst the computer solves the mathematical equations and can be used to manipulate geometry on screen, the main role of the engineer is to interpret the results. This responsibility is both professional and (in some countries) legal. The importance of the engineer to structural safety is reflected in the US in the price of liability and malpractice insurance to the design firm: often 3-5% of gross income - this figure being higher the costs associated with a physician (doctor). To fulfil these responsibilities, engineers must exercise a healthy. The second responsibility is to ensure relevancy and accuracy. In essence, this is the main purpose of this course.


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2.0 THE BASIC PRINCIPLES

Basic Finite Element Concept In solving any structural problem, what ever the type of structure, whatever the type of loading, be it static or dynamic, and what ever the nature of the structural material, there are only three types of argument which can be deployed. These are quite separate and distinct and it is important to understand their simplicity especially when considering the intricacies of the finite element method. These arguments are

* Equilibrium These arguments relate stress to the applied forces, or often to other stresses whether there are applied forces or not. For example, in some dynamic problems, inertia forces can be inserted into the equations of equilibrium as if the problem was static. If the displacements are small, then the equations of equilibrium are linear.

* Compatibility

These arguments relate strains to displacements and are purely geometrical arguments which depend on the definition of strain and the type of deformation and geometry of the particular structure. If the displacements are small, then the compatibility equations are also linear.

* Stress-Strain Law

These ‘constitutive relations’ are empirical and depend on experimental evidence. They may included thermal effects, and for ferrous materials the relationship may be ‘elasto-plastic’ with irreversible plasticity. For many structural materials within their useful working range these laws may be taken as linear.

It is worth recalling that in stress analysis, the basic equations for displacement, stress and strain are known, but cannot be solved for complex geometries. However, the basic equations can be solved for simple shapes such as triangles or quadrilaterals, known as elements. The basic concept in the finite element method is that the real component is approximated by a finite element model made up of an assembly of these simpler shapes i.e. elements joined at common nodes. The actual problem is then solved by invoking the arguments of equilibrium, compatibility at the common nodes for each element, incorporating the appropriate stress-strain law, and applying the known restraints and forces.


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Basic Finite Element Analysis Procedure The basic finite element analysis procedure can be broken down into three simple steps. In fact, these steps also represent the major processors within typical finite element programs, e.g. ANSYS. They comprise:

* PREPROCESSING Enter the appropriate preprocessor (e.g. /PREP7) Define the analysis job title Define the element type(s) Define the element real constants Define the element properties (e.g. material properties) Define the geometry (solid) model Define the mesh type and element size Generate the finite element model Save the database Exit the preprocessor

* SOLUTION Enter the solution processor (e.g. /SOLUTION) Define the analysis type (e.g. static stress analysis) and options Apply the known boundary conditions Apply the known loads Execute the solver Exit the solution processor

* POSTPROCESSING Enter the postprocessor (e.g. /POST1) Read in the results from appropriate load step (SET,LAST) Plot, print, graph, sort, combine results Exit postprocessor


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ANSYS Analysis Procedures It is worth having a look at a simple two dimensional stress analysis problem prior to understanding the mathematics involved with the finite element method. For this we will consider a simple bracket with a hole, fully restrained at one end and subject to a point load at the lowest point of the hole. In this example, the following points need to be examined:

* Techniques of geometry modelling - Keypoints, lines and areas - Geometric construction (arcs, intersections, fillets)

* Simple Mesh Generation

- Choice of elements (STIF2 or STIF42) - Element (material properties) - Element shape (tri/quad) - Mesh density (element size) - Automatic generation of FE model - Model optimisation

* Boundary Conditions

- Selecting - Symmetry - Pressure surfaces

* Solution & Postprocessing

- Model database, results files - Plotting, printing etc.. results

* Analysis Checking

- Is it correct ? This is the common route for carrying out an FE analysis of a component, however, it is not the procedure for formulating the `Engineering Problem'.


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Practical Stress Analysis using FEA The best approach to performing useful, practical stress analysis using FEA is to know the code which you are working with and it capabilities really well, and then to keep away from the computer until the problem has been fully formulated on paper. This is the key to successful FE analysis. It is essential that the problem is clearly defined. Practical stress analysis is best carried out using the following approach. 1) Define the Engineering Problem Objectives:

What is the problem to be solved? Why is the analysis being carried out? Is this the most appropriate method? What do I expect to get out of the analysis? What results are required and to what accuracy?

Geometry:

How realistic is the geometry model suggested? Do I need to consider all the small holes and fillet radii? Do I need a submodel? What about symmetry? Are there any other simplifications I can make? Are there drawing available? Is there a CAD model? Can I Use IGES translation? Does the component conform to the drawing? What are the manufacturing tolerances?

Loading:

What is the location and magnitude of the load. Is it applied over time or ramped on in one step? Static or dynamic? Is there any interaction between the various load steps?

Constraints:

Are the supports rigid or flexible? What type are required e.g. rigid, roller, spring, gap, frictional contact..? How does the constraint effect the stresses? Where does the effect of the constraint die away?

2) Derive the Mechanical Model Model the Geometry:

Symmetric, axi-symmetric, cyclic symmetric, tolerances ?


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Model the Material: How accurate is the data? Linear or non-linear relationships? Limitations: yield strength, ultimate strength, fatigue life.

Model the Loads:

Is it a point load or distributed? Does this make any difference? Model the Restraints:

Are boundary conditions rotational and/or translational? What is the worst case? 3) Generate the Finite Element Model and Analyse Create the geometry or solid model

Select the element type and shape Control the mesh density Generate the mesh Apply the loads and restraints Execute a solution

4) Checking and Debugging - Refining the Model Interpretation of the Results: Selecting the correct load step, and plotting, listing, printing the results. Stress

contour plots, reactions, displaced shapes, etc. Use the most appropriate graphics features which are available. Check nodal versus element solution.

Assessment of the Results: Are the results what I expect? Do either the load representation or boundary

conditions dominate the results? What is the error in the model? Is this good enough? Can it be improved? Do I have enough element in the region of highest stress? Do I have too many?

Procedure for Remodelling: Should I carry out one or two more runs? What about submodelling?


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These procedures may, at first appear simple and have an obvious common-sense approach. However, it is very clear that the majority of poor or incorrect analyses can be overcome by adopting the above procedures. It is also worth mentioning the existence of NAFEMS*, formerly the National Agency for Finite Element Methods and Standards (now a private DTI funded company) which publishes various documents and now issues conformance certificates to companies who have approved documented procedures for carrying out and checking finite element analyses to BS 5750 and ISO9000/1. * For further reading, see `A Finite Element Primer' produced by NAFEMS (1987), Birniehill, East Kilbride, Glasgow

lecture 1 - introduction

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