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Beginners' Guide:Getting Started with FEA

LISA Finite Element AnalysisSoftware Version 8.0.0

2013

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Contents

Chapter 1Welcome to FEA 4

1.1 Simple overview of the Finite Element Method, 4

1.2 Basic operations in the graphics area, 6 1.2.1 Basic graphics tutorial, 6

1.2.2 Solution tutorial, 10

Chapter 2Modeling 12

2.1 The finite element model, 12

2.2 Manual meshing, 13 2.2.1 T-shaped beam tutorial, 13

2.3 Creating, 19 2.3.1 Quick element, 19 2.3.2 New node and new element, 19 2.3.3 Insert node between, 19 2.3.4 Templates, 20 2.3.5 Curve generator, 20 2.3.6 Polyline, 21 2.3.7 Automesh 2D, 22 2.3.8 Plates, 23

2.4 Editing, 24 2.4.1 Move, 24 2.4.2 Rotate, 24 2.4.3 Mirror, 24 2.4.4 Scale, 24 2.4.5 Hollow, 25 2.4.6 Fit to sphere/cylinder/cone, 25 2.4.7 Merge nearby nodes, 25 2.4.8 Delete unused nodes, 25 2.4.9 Invert, 26

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2.5 Converting a two dimensional mesh into a three dimensional mesh, 26 2.5.1 Extrude, 26 2.5.2 Revolve, 26 2.5.3 Loft, 26

2.6 Refinement, 27 2.6.1 Refine x2, 27 2.6.2 Refine Custom, 27 2.6.3 Quad local refinement x2, 28 2.6.4 Quad local refinement x3, 28 2.6.5 Change element shape, 28

Chapter 3Analysis Types 30

3.1 Static analysis of a pressurized cylinder, 32

3.2 Thermal analysis of a plate being cooled, 37

3.3 Modal vibration of a cantilever beam, 42

3.4 Dynamic response of a crane frame, 46

3.5 Magnetostatic analysis of a current carrying wire, 50

3.6 DC circuit analysis, 53

3.7 Electrostatic analysis of a capacitor, 56

3.8 Acoustic analysis of an organ pipe, 60

3.9 Buckling of a column, 76

3.10 Fluid flow around a cylinder, 79

Chapter 4Modeling Tutorials 83

4.1 Tapers, rectangle and V shaped cut-outs, 83

4.2 Rib, counter-bore and rounds, 91

4.3 Intersecting holes and polygon shapes, 112

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Chapter 11 Welcome to FEA

This guide assumes that you are new to LISA and indeed may be new to finite element analysis. Here you will find a simple account to give you the overall picture and get you started using the program. Once you have learned the basic concepts and operations, you will be ready to advance your skills with the more sophisticated features described in the companion Tutorials and Reference Guide.

1.1 Simple overview of the Finite Element MethodSuppose you want to solve a physical problem such as finding the stresses in an object when some prescribed forces are applied. This is a typical problem for FEA: some type of force is applied to an object and the response calculated subject to specified constraints. This is the usual structure:

In a mechanics problem the object might be a gear wheel, the force might be applied from another gear, the response might be the tensile and shear stresses throughout the gear wheel and on the supporting shaft. The constraint is that the gear must remain on the shaft.

In an electrostatic problem, the object might be a specially shaped capacitor, the force might be the voltage applied to the anode, the constraint that the cathode is earthed, and the response might be the stored charge and the polarization throughout the material.

The model you build must represent the object plus all these forces, constraints and materials. At the end of the calculation the software will display the results, and then you have to interpret them.

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The finite element method is a numerical technique for gaining an approximate answer to the problem by representing the object by an assembly of rods, plates, blocks, bricks the finite elements -- rather like a childs Lego model. Each of these building elements is given the appropriate material properties and is connected to adjacent elements at nodes special points on the ends, edges and faces of the element. Selected nodes will be given constraints to fix them in position, temperature, voltage, etc. depending on the problem. The physics of the situation is built into each element through a variational principle to minimize energy.

Mathematically the assemblage of nodes is represented as a very large matrix. The technique solves a matrix equation

[Node matrix describing object and constraints] [Response] = [Applied force]

The resulting [Response] matrix must then be converted into tables and graphs of values for the user to make use of.

Because the Lego bricks can easily be assembled into complicated shapes, FEA is a popular and powerful method for realistically predicting the behavior of many engineering structures and components. Computer graphics are used throughout the method to display the model and results.

The finite element method, therefore, has three main stages:1) build the model2) solve the model3) display the results

These can be broken down further: Build the model

o create nodes in positions to represent the objects shape either create in LISA or import from an existing CAD model refine as required.

o create finite elements (beams, plates, bricks, etc) between the nodeso assign material properties to the elementso assign constraints to selected nodeso assign applied forces to the appropriate nodes.

Solve the modelo define the type of analysis you want e.g. static linear, vibrational modes, dynamic

response with time, etc.o let LISAs Solver do the work.

Display the resultso open the results file and select which parameters you want to display e.g.

displacement, principal stress, temperature, voltage, o display as 2D or 3D contour plots, and/or as tables of numerical values,o before inferring anything from the results, they must first be validated,o validation requires confirming mesh convergence has occurred and that values are in

line with expectations from hand calculations, experiments or past experience,o mesh convergence requires refining the mesh repeatedly and solving until the results

no longer change appreciably.

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1.2 Basic operations in the graphics area

Because the graphics is so much a part of LISA, let us look first at a data file which displays a model and its solution.

1.2.1 Basic graphics tutorialStep 1File->Open, 1.2.1_basic_graphics_tutorial.liml in the tutorials folder where LISA has been installed. This is a contrived example merely to show the graphics features.

There are three parts to the screen the toolbars at the top, arranged into model-building tools and the graphics display options. the model structure and solution displayed in an outline tree in the left panel a graphic display area of the model

This sample is a beam with a T-shaped end and has already been solved. One end is totally fixed, as if built into a wall. At the free end a downwards force is applied at seven locations. The self-weight of the beam has been neglected.

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Step 2

Toggle the display of element surfaces.

Toggle element edge display.

Step 3

Select nodes

Drag over the model to see that nodes have been selected.

Click in an open space to deselect the nodes.Then left click a node to select it. Hold the Ctrl key down and click a couple of nodes to add to the selection set. If a node is already selected and it's clicked on while holding down the Ctrl key, it becomes deselected.

Left click to select a node, but keep the mouse button pressed and drag the node to a new location. Repeat the action on another node, but this time hold down the Shift key. You'll notice that the node is fixed and cannot be dragged.

Edit->Undo or Ctrl + Z to return the displaced node.

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Click in an open space to deselect the nodes.

Select faces. Drag over the model to see that only surfaces are selected.

Click in an open space to deselect the surfaces.

Select elements. Drag to see that only elements have been selected.

The Ctrl key has the same effect while selecting faces or elements as it does with selecting nodes.

Step 4The display of loads and constraints can be toggled off or on.

Step 5

Click the Z arrowhead of the triad at the bottom right corner of the graphics area to view the model parallel to the screen.

Left or right clicking the arrowheads will display the different views of the model parallel to the screen.

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Click the blue dot to return to an isometric view.

Step 6

Not all of a model's features can be displayed at the same time in the graphics area. Features hidden behind need to be rotated into view. To do this press down and hold the mouse middle button (the mouse middle button is the roller wheel between the left and right mouse buttons) and rotate the models display in the graphics area.

To see a small f