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Nonlinear Static Stress Analysis Tutorial

2-D Cantilever Beam Model

Part Number 6700.420

Revision 12.04

June 1999


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Nonlinear Static Stress Analysis Tutorial, Revision 12.04printed locally from files supplied electronically. 2

June 18, 1999

ALGOR, INC.

150 Beta Drive

Pittsburgh, PA 15238-2932 USAPhone: +1 (412) 967-2700

FAX: +1 (412) 967-2781

Product/Services E-mail:

[email protected]

Technical Support E-mail:

[email protected]

Internet Address:

www.algor.com

Please refer to Appendix B to see a list of the Algor software programs and version numbers used in this tutorial. If you have

any problems running this tutorial, please contact your account representative or technical support.

Copyright 1999 Algor, Inc.

All rights reserved. This publication may not be reproduced in any form, by any method, for any purpose, either in part or in

its entirety, without the expressed written permission of Algor, Inc.

This publication describes the state of Algor software at the time of its printing and may not reflect the software at all times in

the future. This publication may be changed without notice. This publication is not designed to transmit any engineering

knowledge relating specifically to any company or individual engineering project. In providing this publication, Algor does

not assume the role of engineering consultant to any user of this publication and hereby disclaims any and all responsibility

for any errors or omissions arising out of any engineering activity in which this publication may be utilized.

This document has been designed to be printed on the customer's local computer and printer. Algor cannot be held

responsible for any errors incurred in the printing of this document.


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The Purpose of this Tutorial

Welcome to the Algor Design and Finite Element Analysis (FEA) Systemthe best value in desktop computer FEA. This

Nonlinear Static Stress Analysis Tutorial provides an introduction to the system in general and the Accupak/NLM software inparticular.

Note: You must have Algors Accupak/NLM or Accupak/VE software installed on your computer to complete the

demonstration model in this tutorial. The tutorial specifically demonstrates use of Accupak/NLM, and, if you use

Accupak/VE instead, some of the keystrokes, text and figures will differ.

After working through the tutorials demonstration model of a two-dimensional cantilever beam, you should have a basic

understanding of how the system works. You should also have a good appreciation for some of the advanced modeling tools

included in the Algor Design and FEA System.

For additional information about FEA, see Appendix A. For complete product and purchasing information, please contact

your account representative at Algor, Inc., by calling +1 (412) 967-2700.


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Tutorial Conventions

To make this tutorial easy to use, the following conventions will be employed. For the command conventions, the item (or an

example of one) that you need to perform is noted in bold on the left. To the right of the item is a short description of the

action and/or results of the action.

User Input Notation Conventions

1.04 Enter "1.04" using the keyboard. Text that you need to enter is noted in bold type using a Courier font.

Press the key (or choose "Esc" from the current menu if using Superview). Some of the other keys

expressed in this manner are , and the function keys, for example .

-c Press and the letter "c" simultaneously. Keys to be pressed at the same time are shown with a

hyphen between them.

"Enclose" Select the "Enclose" option. The names of pop-up menus, options and buttons are enclosed in quotation

marks and shown as they are on the screen.

"Modify: Select the MODIFY pull-down menu and choose the "Copy" option. Then, choose "Rotate Last"

Copy...: from the "Copy Options" pop-up window. Commands in sequences are separated by colons.

Rotate Last"

Mouse Use the mouse to click on the specified location. Algor software is designed for a two-button mouse.

Where "click" or "left click" is used, you should press the left mouse button. "Right click" means you

should press the right mouse button. The left mouse button is used for entering new points and making

menu selections. The right mouse button is used to "snap" to the nearest point in Algor graphics programs

or to access certain help screens in Superdraw. If you have a three-button mouse, you will not use your

middle button for Algor software.

In the tables throughout this tutorial, input instructions using toolbars and pull-down menus are in the two left columns.

Descriptions or more detailed instructions are given in the right column. For example:

Selection

Tools"Select:All" Access the SELECT menu and click on "All" to select all points in

the model.

OtherNotation Conventions

sd3.reb, an .esdfile Filenames and file extensions are lowercase and italic.

filename.doc Filenames that are user-supplied are in bold, lowercase italics.

\modeldirectory Directory names may appear in Courier type and be followed by the term "directory". (The directory

where all your Algor software is stored is usually referred to as the algor directory, where "algor" is

in bold, lowercase italics.)

FILE menu Menu names are shown in uppercase characters.

The rest of "The Basics" section provides introductory information about Algor software, particularly Superdraw III. If you

would prefer to immediately begin the tutorial's demonstration model, skip ahead to the "Preprocessing" section.


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Starting Algor Software

Algor software may be started by:

Selecting "Algor FEA" from your windows environment. Typing a program name from a command line prompt (e.g., sd3)and pressing .

For this tutorial, you will be starting Algor software by selecting "Algor FEA". Windows 95/98 and Windows NT 4.0 users

will find it from the "Start" button under "Programs:Algor Software".Navigating the Superdraw III InterfaceThe Superdraw III interface allows you to access program functions through pull-down menus and toolbars. Superdraw III

displays the "Add CAD Objects", "File Utilities", "Selection Tools" and "View Utilities" toolbars on default startup.

Displaying Toolbars

You can display or hide toolbars or adjust the icon size by selecting the SETTINGS menu and choosing "Toolbars...". Todisplay the toolbars used in the tutorial but not displayed by default, follow these steps:

"Settings:Toolbars..." Click on "Settings" in the menu bar and then choose "Toolbars" from the pull-downmenu. A pop-up window will appear displaying all of the toolbar titles.Mouse Locate the toolbars you wish to display. Click on each so it is highlighted.Note:If you want to turn a toolbar off, click on the title so it is not highlighted."Close" Click on "Close" to exit the "Toolbars" pop-up.

You can also adjust the toolbar size while in the "Toolbars" pop-up menu by clicking on one of the display choices on the

right under "Icon Size".

As you build your model, you may find that the toolbars prevent you from seeing the whole model. You can move or resizethe toolbars at your convenience.


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Moving ToolbarsTo move a toolbar, click and hold on the toolbars title bar as shown below. Drag it to the desired location and then release.

Click on the title bar and drag to a new location.

Resizing Toolbars

To adjust the size of a toolbar, position the cursor on the side of the toolbar that you want to change. As shown below, thecursor will become a two-headed arrow. Click and hold. Drag the mouse so that the outline of the toolbar changes to the

shape you want and then release the mouse button.

Click on the appropriate side and adjust the toolbar shape.

Making Corrections

You can make changes or corrections to your model in a variety of ways using Superdraw III. The following are threemethods to try if you find a flaw in your model:

or "Undo": In the status bar, an "Undo" button is located on the left-hand side of the screen. If the"Undo" button is green, the last command can be undone. Just click on "Undo" or press on the keyboard.

"Select:Point:Add Mode": Suppose you find that you have added too many boundary conditions. You canselect each individual condition in succession. (The same applies to the "Subtract Mode", except you are

deselecting conditions.) Then, use "Modify:Delete" to eliminate the unwanted conditions.

"Add:Line...": Suppose you accidentally erase a line in the model. You can redraw the line by bringing up the"Line" pop-up window. Right click on the end of the line you want to connect to and then right click again on the

other connecting line. (You must right click for the new line to "snap" to the existing lines.) You can replace the

missing line without redrawing the whole model.


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The Superdraw III Interface

Figure 1 shows the Superdraw III interface.

Interface Legend

A. Title Bar:Displays the program name, the active model name, the current analysis type and the current unit system.

B. Menu Bar:The menu bar is located just below the title bar and contains the pull-down menus.

C. "Live" Area:This region is where modeling activity is displayed. Also referred to as themodel display.

D. Floating Toolbars:These give you quick access to many of Superdraw IIIs commands.

E. Miniaxis:Indicates your viewpoint in relation to the three-dimensional "live" area.

F. Status Bar:Displays important messages and pertinent information and provides coordinates and various measurements.

G. Dialog Bar:Provides a text bar to enter values.

Figure 1: An Overview of the Superdraw III Interface


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Overview of Nonlinear Analysis

What is the difference between linear and nonlinear analysis and why should you consider the need to perform a nonlinear

analysis on your model?

Linear analysis is only accurate for a model in which the relationship between the forces and stresses/deflections is a linear

function. The classic example of this type of behavior is a simple linear spring that is fixed at one end and has an axial force

at the free end. If the magnitude of the force is increased, the deflection of the spring will increase in proportion. If the

relationship is linear and the force is plotted against the displacement, the resulting curve will be a straight line (see Figure 2).

Hooke's law is then defined as F=Kx, where the spring stiffness (K) is the slope of the line.

Figure 2:Force-Displacement Curve for Linear Spring

With nonlinear analysis, forces do not display a linear relationship with displacements and/or stresses. There are three major

causes of nonlinear behavior that can be classified as follows:

Material Nonlinearity

Material nonlinearity is caused by materials that do not have a linear stress-strain curve. An example of this type of material

is carbon steel that is loaded past the point of yield. Up to the yield point, steel is elastic in nature and has a linear stress-strain curve as depicted in Figure 3. The slope of this line is commonly referred to as the Modulus of Elasticity or Youngs

Modulus. In the plastic region beyond the point of yield, the stress-strain curve becomes nonlinear. When loading steel

materials into the plastic region, a nonlinear analysis is required to obtain accurate results.

Figure 3:Typical Stress-Strain Curve for Carbon Steel


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Geometric Nonlinearity

Geometric nonlinearity occurs in models that are subjected to relatively large deformations or strains. In these cases, the

severe deformation of the model has an appreciable impact on the geometric characteristics of the model. Simply stated, a bar

that is severely deformed will behave differently under load than when the bar was initially straight at the onset of theanalysis. The Accupak/NLM program can account for this behavior by incrementing the load and updating the geometric

stiffness matrix during the course of the analysis.

Element Nonlinearity

Element nonlinearity is characterized by situations where the stiffness matrix of an element will change as a function of some

specified variable. A good example of this is a contact element, which can be used to model the contact between different

surfaces. When the surfaces are in contact, the stiffness matrix of the contact element is positive and the contact forces are

transferred through the contact element. When the surfaces are not in contact, the stiffness matrix of the contact element is

zero and no forces are transferred. The Accupak/NLM program can account for this type of behavior by incrementing the

load and updating the element stiffness matrix during the course of the analysis.

The following is the sequence of steps that you will typically follow in performing a nonlinear stress analysis with the AlgorAccupak/NLM program. (Figure 4 shows a graphical flowchart of these steps.)

Figure 4:Flowchart of Modeling Steps for Nonlinear Stress Analysis


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Create the geometry of the model using the Superdraw III program to quickly and easily construct a finite elementmesh. Superdraw III is also used to designate areas of the model with different materials and to apply boundary

conditions and nodal loadings to the model. Use Superdraw IIIs data input screens and pull-down menus to easily enter material properties, choose element types

and define load cases. Superdraw III then compiles all of the geometry, material and loading data and generates an

input file for the processor. To assure good results and before committing to a processor run, the model is loaded into Superview to visually check

the geometry, boundary conditions and loading. If errors are found, they must be corrected in Superdraw III before the

model is processed further. The input file created by Superdraw III is then submitted to the nonlinear processor for the finite element analysis. Upon completion of a successful processor run, the results of the analysis are checked in Superview. If the results are

not satisfactory, modifications are made to the model in Superdraw III and the model is processed again.


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2-D Cantilever Beam Model

In this tutorial, you will use Algor's nonlinear static stress analysis capabilities to model and analyze a two-dimensional (2-D)

cantilever beam.

You will perform the following steps:

I. Preprocessing Create the model, add the necessary boundary conditions and add properties to the geometry using

Superdraw III. Visually check the geometry and boundary conditions using Superview.

II. Processing Analyze the model using the Accupak/NLM analysis processor. (Note: Accupak/VE can also be used, but

some keystrokes, text and figures will differ from what is shown in this tutorial, which specifically demonstrates use of

Accupak/NLM.)

III. Postprocessing View the analysis results with Superview.

I. Preprocessing

In the preprocessing phase, you will create a two-dimensional model of the cantilever beam. Using Superdraw III, you will

generate the geometry and add boundary conditions and a nodal force loading. You will select an element type, specify

material properties, define loading conditions and cases and convert the drawing to nodes and elements. Then, using

Superview, you will visually check the geometry, boundary conditions and forces.

1. Problem Description

Because mechanical design should be driven by engineering analysis, Algor provides design modeling tools with the ability to

make models which are ideal for the engineering analysis of all design model classes. For every model class, one or morepowerful, easy-to-use suites of engineering design tools are available.

In this tutorial, we will use a two-dimensional solid design scenario to create a simple model of a carbon steel cantilever beam

with a circular cutout (see Figure 5).

Figure 5:Engineering Drawing of the Cantilever Beam


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Due to the in-plane loading, any stresses through the thickness of the beam will occur from Poisson's effect and will have no

variation through the thickness. The model can then be classified as a plane stress analysis, which warrants the use of the 2-D

solid nonlinear element using the plane stress option.

The beam is to be loaded with a 3250-pound force, which has been predetermined to cause some of the material in the beamto go plastic in the region of the stress-strain curve beyond the point of yield. The load will then be taken off of the model

completely so that the plastic deformation and residual stresses caused by yielding can be analyzed.

As a result of this type of complex loading and unloading, it is important to input a stress-strain curve for the material that

adequately represents the behavior of the material in both the elastic and plastic regions. For this example, a von Mises

material option will be used to characterize the stress-strain behavior with a bilinear curve as shown in Figure 6. The slope of

the line up to the point of yield is the Modulus of Elasticity or Youngs Modulus (E). The slope of the line after the point of

yield is known as the strain hardening modulus (Et).

Figure 6:Typical Von Mises Material Model for Carbon Steel

2. Creating the Model with Superdraw

Create the geometry of the two-dimensional cantilever beam model with Superdraw.

Starting Superdraw III

Every Algor software package includes Superdraw III, Algor's finite element model-building tool. Superdraw III provides

access to all preprocessing, processing and postprocessing functions.

Start Superdraw III from the Windows taskbar.

Note:Alternatively, at the Windows desktop, you could double click on the "Algor FEA" icon, .

"Start:Programs:

Algor Software:

Algor FEA"

In the Windows taskbar, click on the "Start" button. Use the mouse to drag

the cursor to "Programs" and then "Algor Software". Click on "Algor

FEA".


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The initial Superdraw III screen will now appear. (It will look similar to Figure 1.) From this screen, you have a variety of

tasks available to you. You can start a new model, choose an existing model and perform any complete engineering analysis.

The Superdraw III interface allows you to access program functions through pull-down menus and toolbars. You will be

using commands contained in the following toolbars:

Add CAD Objects Add FEA Objects Common Utilities Construct Objects File Utilities Modify Existing Objects Selection Tools

View UtilitiesSuperdraw III displays the "Add CAD Objects", "File Utilities", "Selection Tools" and "View Utilities" toolbars on default

startup. See "The Basics" section for more information on how to display, move and adjust toolbars.

Just below the title bar, the menu bar contains the pull-down menus for accessing key modeling and analysis functions as well

as displaying help and accessing DocuTech (Algors CD-based documentation and information resource). Help is available at

all times by clicking the mouse on the "Help" button and then choosing the item for which you want additional information.

For more detailed information about the features of Superdraw III, refer to the Superdraw Reference Division available

through DocuTech.

Specifying the Analysis Type

Make sure that the "Model Data Control" window is open. If it is not open, then do the following:

"Tools:

Model Data Control"

Click on the TOOLS pull-down menu and select the "Model Data

Control" option to access the "Model Data Control" pop-up window.

(See Figure 7.)

Note:Alternatively, you could click on the "Model Data" button in the

status bar.


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Figure 7: Accessing the "Model Data Control" Pop-Up Window

Specify the analysis type using the "Model Data Control" pop-up window. (Alternatively, you could use the "Analysis Type"

command under the ANALYZE pull-down menu.)

"Analysis Type" Click on the "Analysis Type" field in the "Model Data Control" pop-up

window."Nonlinear Stress withNonlinear Material Models"

Select the "Nonlinear Stress with Nonlinear Material Models" option. (SeeFigure 8.)Note:If you have Accupak/VE installed instead of Accupak/NLM, then youwill not see "Nonlinear Stress with Nonlinear Material Models" as an option

for the analysis type. Rather, you should choose "MES with Nonlinear

Material Models".

Figure 8: Specifying the Analysis Type

Notice that the analysis type is now shown in the title bar.


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Defining the Unit System

Use the "Model Data Control" pop-up window to define the unit system for the model. (Alternatively, you could use the"Unit System" command under the SETTINGS pull-down menu.)

"Units" In the "Model Data Control" pop-up window, click on the "Units" button to

access the Units Definition pop-up window.You will be prompted to enter a new model name at this time because unit information is stored separately with every model.

"OK" Click on "OK".nlbeam Choose a file location and type a new file name next to "File name". (See

Figure 9.) In this example, the model will be saved in a file callednlbeam

in a folder called "tutorial" on the C: drive. The name and location of your

file may vary according to your preferences.

or"Save" Press or click on the "Save" button to save the new filename.

Figure 9: Entering a Filename for the New Model

Notice that the filename and location you entered are now shown in the title bar.

Make sure that the unit system is set to English (in). If it is not, then do the following:

Mouse Click on the arrow to the right of the "Unit System" field.

"English (in)" Select the "English (in)" option. (See Figure 10.)


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Figure 10: Defining the Unit System

"OK" Click on the "OK" button to accept the entered data and close the "Units

Definition" pop-up window.

"Close" Close the "Model Data Control" window so that you may easily view your

model during construction.

Defining Initial View Settings

For convenient viewing, define the following settings:

Common

Utilities"Settings:Miniaxis Display" Choose the SETTINGS pull-down menu and then the "Miniaxis Display"

option to access the "Miniaxis Display" pop-up window.

"At Fixed Location" Click on "At Fixed Location". A checkmark will appear in the box to the

left, indicating that this option is active.

"Done" Close the "Miniaxis Display" pop-up menu.

View

Utilities"View:Pre-Defined Views:

YZ Right"

Select the YZ view by opening the VIEW pull-down menu and selecting

"Pre-Defined Views" and then "YZ Right". Models with

2-D elements must be constructed in the YZ plane.

"Options:Display Model

Using"

Choose the OPTIONS pull-down menu and then "Display Model Using"

to access the "Model Display" pop-up window.

"Layer Number" Specify that the model will be displayed by layer number.


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Drawing a Rectangle

Draw a 4"x4" rectangle to begin the definition of the end of the cantilever beam with the cutout.

Add CADObjects

"Add:Rectangle" Select the "Rectangle" command from the ADD pull-down menu.

Press the key to input the first corner point at (0,0,0).

44 Enter the other corner point of the rectangle as (0,4,4).

View

Utilities"View:Enclose" Use the "Enclose" command to automatically scale the viewing area so that

all geometry is visible. Your screen should now look like Figure 11.

Figure 11:Enclosed View of Rectangle

Saving the Model

File

Utilities"File:Save" In general, periodically save your work when building a model.

Adding the Cutout

Add CAD

Objects"Add:Circle:

Center and Point"

Click on the "Circle" option in the ADD pull-down menu, then on "Center

and Point".

22 Enter the centerpoint of the circle at (0,2,2).

32 Enter a point on the diameter of the circle at (0,3,2). Your model should

now look like Figure 12.


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Figure 12:Model with the Circle Added

Dividing the Circle and Meshing

Divide the circle into four arcs and mesh the region.

Construct

Objects"Construct:Divide" Choose the CONSTRUCT pull-down menu and then "Divide" to access

the "Divide" pop-up window.

"Number" Use the "Number" command to change the number of divisions.

4 In the dialog bar, enter 4 as the number of sections.

"To Lines" Deactivate this option (remove the checkmark) so that the circle will bedivided into arcs.

"Divide" The circle is now divided into 4 arcs.

Rotate the arcs so that each arc is aligned with a side of the rectangle.

Modify

Existing

Objects

"Modify:Rotate" Choose the MODIFY pull-down menu and then "Rotate" to access the

"Rotate" pop-up window.

"About X Axis" Choose the X axis as the axis of rotation.

"Angle" Specify the angle of rotation.

45 In the dialog bar, enter a rotation angle of 45 degrees.

22 Enter the center of the rotation at (0,2,2).

"Rotate" The four arcs are now rotated by 45 degrees.


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Construct a mesh between each arc and the line of the rectangle with which it is aligned.

FEA

Mesh

Tools

"FEA Mesh:Automatic Mesh:

Between 2 Objects"

Choose the FEA MESH pull-down menu and then "Automatic Mesh" and

"Between 2 Objects" to access the "Mesh" pop-up window.

"Division Values" Specify the density of the mesh in the AB and BC directions.

6 Enter 6 for the density in the AB direction (tangential). The density in the

BC direction (radial) will remain at the default value of 4.

Mouse Position the cursor above the P1-P3 arc very near P1 in Figure 13 and click

the left mouse button. (Annotation was added to the figure to label items.)

Then position the cursor above the P2-P4 edge very near P2 in Figure 13

and click the left mouse button. Your model should now look like Figure

14. If it doesn't, you can click on the "Undo" status button or use the

"Edit:Undo Last Operation" command or press to undo the mesh and

then try again.

Figure 13:Annotated Selection Points for Meshing Between Objects


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Figure 14:Mesh Created with First Use of the "FEA Mesh:Automatic Mesh:Between 2 Objects" Command

Meshing the Three Remaining Sections

Mouse Using the left mouse button, repeat this procedure for the three remaining

arcs and lines using the "P3-P4", "P5-P6" and "P7-P8" point combinations

in Figure 13. When you have finished, your model should look like Figure

15.

Figure 15:Completed Mesh


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Defining the Rest of the Cantilever Beam


Spacing"

Access the "Spacing" pop-up window.

"AB Spacing" Activate the "AB Spacing" option so that the aspect ratio of the elementswill vary in the AB direction. Notice that the default settings are for

"Arithmetic" and "Ratio" and the dialog bar indicates "Longest/Shortest

3, Number of Divisions 6". (This will result in elements that are 3 times

longer at point B than they are at point A.)FEA

Mesh

Tools


4 Point"

Activate the "4 Point" option to define a mesh for the rest of the

cantilever beam by specifying 4 points in order A,B,C,D.

"Division Values" Specify the density of the mesh in the AB and BC directions.

186 Enter 18 for the density in the AB direction and 6 for the density in the BC

direction. Note that the density in the BC direction is set to 6 so that the

nodes and elements will align with the existing geometry.Mouse Place the cursor near the lower right corner of the model and click the right

mouse button once to define point A.

24 Enter point B at (0,24,0).

244 Enter point C at (0,24,4).

Mouse Place the cursor near the upper right corner of the model and right click to

define point D.View

Utilities"View:Enclose" Enclose all geometry on the screen.

Notice that, by keeping track of and specifying the correct mesh densities, the nodes and elements all align correctly. This is avery important concept when creating a valid finite element mesh for your model.

Cleaning Duplicate Lines

Modify

Existing

Objects

"Modify:Clean:Duplicate" Click on the MODIFY pull-down menu and then select "Clean Duplicate"

to access the "Duplicate" pop-up menu.

"Perform Cleaning" Remove any duplicate lines that were created during the meshing process.

The status bar will indicate that 450 lines were kept while 22 lines were

deleted from the model. (See Figure 16.) In general, it is recommended

practice to check for duplicate lines after you have modeled the geometry.


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Figure 16: Model after Use of the "Modify:Clean:Duplicate" Command

"Done" Close the "Duplicate" pop-up menu.

Adding Boundary Conditions and a Force

In this section, you will add boundary conditions (points of constraint) and a force to the model.

Zoom in on the left end of the cantilever beam.

View

Utilities"View:Zoom:In" Access the "Zoom In" pop-up menu.

Mouse Use two clicks of the left mouse button to form a windowing box around the

left end of the cantilever beam as shown in Figure 17.


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Figure 17: Windowing Box for the "Zoom:In" Command

"Done" Close the "Zoom In" pop-up menu.

Change to a new layer before adding the boundary conditions.

"Options:

Current Object Parameters:

Layer Number"

Activate the "LAYER" pop-up table. (Alternately, you can access the

"Layer" pop-up table by clicking on the "L=n" button in the status bar.) It is

not a requirement to change layers before adding boundary conditions in

Superdraw III. However, the use of different layers is helpful in Superdraw

III in case the boundary conditions later need to be modified or deleted.

2 Set the current layer to be 2 (red).

Add boundary conditions to the model.

Add FEA

Objects"FEA Add:

Stress and Vibration Analysis:

Boundary Conditions"

Activate the "Boundary Conditions" pop-up menu. Notice in the dialog

area that the default boundary condition (represented by an "@" symbol) is

fully constrained in all directions. (You can further verify this by

examining the settings under the "Change Values" option.)

Note:If desired, you can change the text height by using the "Text

Attributes:Height" command and entering a value such as .25.

"Box Apply" Use this option to apply boundary conditions to all nodes (endpoints of the

lines) that are fully enclosed within a selection window.

Mouse Use two clicks of the left mouse button to form a windowing box around the

entire left boundary of the cantilever beam as shown in Figure 18.

Boundary condition symbols will appear at the selected nodes.


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Figure 18: Selection Box for the "Box Apply" Command

"Done" Close the "Boundary Conditions" pop-up menu.

View

Utilities"View:Enclose" Enclose the model on the screen.

Change the layer before adding the force.

"Options:

Current Object Parameters:

Layer Number"

Activate the "Layer" pop-up table. (Alternately, you can access the "Layer"

pop-up table by clicking on the red "L=2" button in the status bar.)

3 Change the current layer to 3 (yellow).

Add a nodal force to the model.

Add FEA

Objects"FEA Add:

Stress and Vibration Analysis:

Nodal Forces"

Access the "Nodal Forces" pop-up menu. Notice that the default magnitude

for the force is set to 100 in the dialog area. We will use this default value

and then specify a load curve later in the "Model Data Control" window to

vary our load up to the full 3,250 lbs and then back to no load.

"Vector" Define the vector along which the force will act.

"Z Direction" Specify the Z direction.

"Negate" Use this command so that the force will act in the negative Z direction.

Note:If you want to specify the length of force arrows, you can use the

"Length" command and enter a value such as 1."Done" Close the "Vector" pop-up and return to the "Nodal Forces" pop-up.

Note:If you want to specify the size of force arrows, you can use the

"Arrow Size" command and enter a value such as .25.

Mouse Place the cursor close to the upper right corner of the model and right click

to add the force to the upper right node of the model.


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View

Utilities"View:Enclose" Enclose the model on the screen. Your model should now look like Figure

19.

Figure 19: Model after Applying the Nodal Force

"Done" Close the "Nodal Forces" pop-up menu.

From this vantage point, you may notice that the text string associated with the force has been converted to a line. This is

normal behavior and will occur if you view the model from a distance. If you again zoom in on the force, the text will

become legible.

Saving the Model

File

Utilities"File:Save" Save your changes to the Superdraw model.

3. Using the "Model Data Control" Window

Once you have constructed your model using Superdraw III, you will use the "Model Data Control" window to:

Choose an element type Specify material properties Define loading conditions and cases Convert the Superdraw III geometry mesh into nodes and elements

"Tools:

Model Data Control"

Open the "Model Data Control" pop-up window.


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Enter data for element group 1.

Mouse Use the mouse to click on the "Element" field for group 1. This will

activate the "Group 1" data entry screen. Notice, in the status bar, that the

group number button is now highlighted.

"2-D" Under "Element Type", click on "2-D". A dot will appear, highlighting the

selected element type.

"Tag:" Click on the "Tag:" field to specify a text string which can be used to keep

track of your element groups.

Cantilever Beam Type any identifying text description, such as "Cantilever Beam". (See

Figure 20.)

Figure 20: The "Group 1" Data Entry Screen

or"OK" Press or click on the "OK" button to accept the information entered

in the "Group 1" data entry screen and return to the "Model Data Control"

window. You should now see that the "Element" field shows "2-D" and the

"Tag" field contains the entered text string.

Specify the analysis formulation and material model for element group 1.

Mouse Use the mouse to click on the "Data" field for group 1. This will invoke the

"Element Definition" data entry screen.

"von Mises with Isotropic

Hardening"

Make sure that the "General" tab is active. Under "General Settings", click

on the arrow to the right of the "Material Model" field and select "von

Mises with Isotropic Hardening". Notice that a red dot appears to the left ofthe "Thickness" field, indicating that this field is required input.

"Thickness" Highlight the "Thickness" field.

-1.0 Type -1.0as the value.

"OK" Click on the "OK" button to accept the entered data. A pop-up window will

appear with a message to notify you that thickness must be greater than

zero.

"OK" Click on "OK" to close the message window.

1.0 Enter 1.0as the value. (See Figure 21.)


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Figure 21: The "Element Definition" Data Entry Screen

"OK" Click on the "OK" button to accept the entered data and return to the

"Model Data Control" window.

You will now see that the "Data" field for group 1 in the "Model Data Control" pop-up window is checkmarked, indicating a

successful conversion of the inputted data.

Define material properties for element group 1.

Note:You can create a custom material library by selecting "Tools:Manage Material Library", or use Algors

default Material Property Library to apply material properties to a model.

Mouse Click on the "Material" field for group 1. This will open the "Element

Material Selection" data entry screen.

"[Customer Defined]" In the "Select Material" list, click on "[Customer Defined]".

"Edit Properties" Click on the "Edit Properties" button to access the "Element Material

Specification" data entry screen.

"Mass Density" Highlight the "Mass Density" field.

0.000732 Type 0.000732as the value.

"Modulus of Elasticity" Highlight the "Modulus of Elasticity" field.

30e6 Type 30e6as the value.

"Poisson's Ratio" Highlight the "Poisson's Ratio" field.

0.30 Type0.30as the value.

"Yield Stress" Highlight the "Yield Stress" field.30000 Type 30000as the value.

"Strain Hardening Modulus" Highlight the "Strain Hardening Modulus" field.

5e6 Type 5e6as the value. Your screen should look like Figure 22.


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Figure 22: Entering Material Properties for the Cantilever Beam

"OK" Click on the "OK" button to accept the material property information.

"OK" Click on the "OK" button to return to the "Model Data Control" window.

Note:For two-dimensional models, the user can specify the thickness of the model. For axisymmetric and

three-dimensional models, the thickness is ignored.

You should now see that the "Material" field for group 1 in the "Model Data Control" pop-up window lists the material as

"[Customer Defined]".

Use the "Model Data Control" window to define global data for the model. (Alternatively, you could use the "Global

Settings" command under the ANALYZE pull-down menu.)

"Global" Click on the "Global" button to access the "Global Data" entry screen.

Mouse Under "Event", notice that the "Duration" and "Capture rate" fields are

highlighted by red dots, indicating that these fields are required input.

Highlight the "Duration" field.1.0 Type 1.0as the value for the duration.

Mouse Highlight the "Capture rate" field.

40.0 Type 40.0as the number of steps per second.

Make sure that the "Analysis type - automatic setup" field is set to "Non-Linear Static (NLS)". If it is not, then do the

following.

Mouse Click on the arrow to the right of the "Analysis Type - automatic setup"

field.

"Non-Linear Static (NLS)" Select "Non-Linear Static (NLS)".


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Next, input a load curve for the model.

Mouse On the "Load Curves" tab, highlight the "Description" field.

beam Type beamas an identifying text description.

"Add Row" Click on the "Add Row" button. This will leave time = 0.0 and multiplier =

0.0 for index 1.

Mouse Double click on the "Time" field for index 2. This will highlight the field.

0.532.5 Input 0.5for time and 32.5for multiplier.

"Add Row" Click on the "Add Row" button.

Mouse Double click in the "Time" field for index 3.

1.0 Input 1.0for time. Your screen should look like Figure 23.

"OK" Click "OK" to save the entered load curve data and return to the "Model

Data Control" window.

Figure 23: Load Curve Spreadsheet Information

Notice that the ending time of the curve is 1, which is equal to the duration of the event. Also notice that the value of 32.5 is

multiplied times the 100-pound force that was added in Superdraw III, which will result in a 3250-pound force acting on the

model. The function of this loading curve is depicted in Figure 24.


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Figure 24: Loading Curve Function for the Model

Next, you will use Superview to check your model before processing it.

4. Using Superview to Check the Cantilever Beam Model

In this section, you will check your design for modeling errors by using Superview, Algor's visualization software. A visual

inspection of the model can confirm whether the nodes, elements and boundary conditions are correctly defined.

Starting Superview

Execute the Superview program from Superdraw.

"Check" In the "Model Data Control" window, click on the "Check" button to enter

Superview.

After the software verifies the geometry and finite element data, the beam model appears in the display window as shown inFigure 25. Red triangles indicate the boundary conditions on the fixed end.


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Figure 25: Initial Superview Screen

Commands are accessed by either mouse clicking on the command in a menu or by typing the different colored capital letter

of each command. Function keys such as and represent shortcuts to different menus. The previous menu can

always be accessed by pressing . The MAIN MENU can always be accessed by pressing .

The current settings are displayed in the status line, the bottom line of the screen. From left to right, you will see the filename,

snap status, current step number, current view and cursor coordinates. Changes can be made to the current screen setup by

choosing "Options" from the MAIN MENU.

Checking the Model Geometry with a Hidden Line Display

First, you will check the geometry for defects by displaying the finite element mesh.

"Options:General:MiniAxis:

Fixed"

Fix the location of the miniaxis so that it will not overlap the geometry.

"Stress-di:Hidden l" Perform a display of the model using the "Hidden l" option. This is one technique

to verify that the finite element mesh does not appear to contain defects or missing

elements. (See Figure 26.)


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Figure 26: Checking the Finite Element Mesh

Viewing the Element and Node Numbers

Examine the element and node numbers.

"Options:General:Ele num" Turn on the element numbering display option.

"Node num" Turn on the node numbering display option.

"Values" Use this command to change the color and size of the text for the element and

node numbers.

10 Use the key to clear the previous value in the field. Then change the

element numbers to color 10 (dark blue).

2 Tab over to the next field and change the node numbers to color 2 (red).75 Make the text smaller by setting the number of characters per line to 75. Your

model should now look like Figure 27.


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Figure 27: View of Model Showing Element and Node Numbers

At this point, the model has been visually checked and is ready to submit to the processor. You will now exit the Superview

program.

"donE" Exit the Superview program and return to the Superdraw.

You will now proceed to analyze the model.


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II. Processing

In the processing phase, you will analyze the cantilever beam model with the Accupak/NLM analysis processor.(Accupak/VE can also be used because it includes the capabilities of Accupak/NLM.)

1. Analyzing the Model with the Accupak/NLM Analysis Processor

"Analysis" In the "Model Data Control" window, under "FEA Model", click on the

"Analysis" button to access the analysis screen.

"Analyze" Select "Analyze" as shown in Figure 28 to begin analyzing the model with

the Accupak/NLM analysis processor.

Figure 28: The Analysis Screen

If you wish, you can "Pause" or "Stop" the analysis before it runs to completion.

When the analysis is finished, a pop-up window will appear telling you so.

"OK" Click on "OK" to close the pop-up window.

2. Viewing the Processor Statistics and Summary Files

After the analysis is complete or has been stopped, you can view the processor statistics and summary files.

In the analysis screen, under "Analysis Information", the "View Statistics" option is active.

Mouse Use the mouse to click on the scroll bar in the display window and scroll

through the statistics file.


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After viewing the statistics file, view the summary file.

"View Summary" In the "Analysis" screen, under "Analysis Information", click on "View

Summary" to display the summary file.

Mouse Use the mouse to scroll through the summary file.

"Done" After viewing the summary file, click on "Done" to close the "Analysis"

screen and return to the "Model Data Control" pop-up window.

Next, you will use Superview to view the analysis results.


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III. Postprocessing

In the postprocessing phase, you will view the analysis results using Superview.

Previously, you used Superview as a preprocessing tool to check the cantilever beam model. Superview is also a

comprehensive postprocessing tool, which can be used to view displacements, forces, moments and stresses.

1. Starting Superview

Execute the Superview program from Superdraw III.

"Results" In the "Model Data Control" pop-up window, under "FEA Model", click on

the "Results" button to start Superview.

2. Viewing Analysis Results

"Options:General:MiniAxis:

Fixed:Location"

Fix the location of the miniaxis so it will not overlap the model.

Mouse Place the cursor in the lower left-hand corner of the screen as shown in Figure 29

and click the left mouse button.

Figure 29: New Location of Miniaxis


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Viewing the Models Displaced Shape

To see the maximum stresses, the load step must be changed to load step 20 out of 40 (20/40), which is where the loading was

at its maximum.

"Mode/step" Use this command to change the current load step.

"sTep num" Use this option to type in the step number of the results that you wish to have

displayed.

20 Specify the step number as 20, where the force load was at its maximum.

"Displaced:Displ on" Make sure the "Displ on" option is activated (it will have an asterisk beside it

when activated) to view the displaced geometry.

"With undi" When this option is activated, a view of the original undisplaced geometry is

superimposed onto the displaced geometry.

"Calc scal" Use this command to automatically scale the deformed geometry to provide a

more reasonable view relative to the original geometry. Your model should now

look like Figure 30.

Figure 30: Displaced Model Superimposed on the Undisplaced Model

Viewing Stress Contours

"Stress-di:Post:S tensor" To isolate the stresses due to bending, use the "S tensor" option to look at the

stresses in only one direction.

"Normal:Y dir" This option is used to set the direction of the stresses that will be displayed. The

bending stresses are in the direction of the axis of the cantilever beam, which lies

along the Y axis.


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Because the model was drawn in terms of inches and all material properties and loadings were defined in terms of inches and

pounds, the stresses displayed will be in terms of pounds per square inch (psi).

"Stress-di" Return to the STRESS-DI menu.

"General" Go to the D GENERAL menu and make sure the "Solid-di" option is toggled on

(marked by an asterisk) so that all displays are filled with solid color. Your model

should now look like Figure 31.

Figure 31: Stress Tensor Display in the Y-Direction for Load Step 20 of 40

Notice that the legend box has values that are greater than 30,000 and less than -30,000. Recall, in the "Element Material

Specification" data entry screen, the yield stress was specified as 30,000. These results then indicate that portions of the

model have exceeded the yield stress in tension and compression.

"Stress-di" Return to the MAIN MENU and then access the STRESS-DI menu.

"Aux post:Threshold" Use this option to color in only those elements that have a stress value that is

greater than the "Threshold".

30000 Specify a threshold of 30000 so any areas that have yielded (in tension) can be

easily identified.

Press the key to return to the STRESS-DI menu.

"Smoothed" Turn off this option so that results are not averaged across an element.

Notice that only those elements that have an "S tensor" value greater than the "Threshold" value are displayed. (See Figure

32.)


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Figure 32: Elements with Stress Greater than the Threshold Value

"Smoothed" Activate this option so that results are averaged across the elements to provide a

smoother display.

"Aux post:Threshold" Turn off the "Threshold" option.

Return to the STRESS-DI menu.

"Post:disp Vec" Use this option to display the displacements of the model. The displacement

magnitude results for step 20 of 40 are now displayed as shown in Figure 33.

The default option is "Magnitude", which will calculate the displacement values based on the square root of the sum of the

squares of the displacements in the X, Y and Z directions. Since all input was in terms of inches, the output of displacements

will also be in terms of inches.

Figure 33: Display of Displacement Magnitude for Load Step 20 of 40


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Notice that since the indicated displacements are actually quite small compared to the geometry, this model is not really

classified as being geometrically nonlinear. The nonlinearity in this case is being caused by loading the material into the

plastic realm beyond the yield point. It is important to realize that in the real world, large deformations are not necessarily

required to induce yielding of the material in a structure.

"Mode/step:sTep num" Use this command to change to the last load step in order to view residual stresses

and plastic deformations.

40 Specify the step number as 40. This is the last step and it has the force entirely

removed. The plastic deformation caused by yielding the material is now

displayed.

When a material is loaded up to the yield point and then unloaded, it will spring back to its original shape. When a material is

loaded beyond the yield point and then unloaded, the material will have a permanent "set" and will not return to its original

shape. A good example of this is a paper clip. If you pull on the free end a very small amount and let it go, it will return to its

original position. If you subject the paper clip to a large deformation, it will go plastic and will not return to its original

shape.


"Post:S tensor" Use this option to display the residual stresses in the model. The residual stresses

are now displayed.

"zoom In" Use this command to get a closer look at the residual stresses in the left end of the

cantilever beam.

Mouse Use two clicks of the left mouse button to form a windowing box around the left

end of the cantilever beam as shown in Figure 34. The residual stresses are again

displayed from a closer vantage point.

Figure 34: Windowing Box for the "zoom In" Command

Notice that although the legend has values for the color red, there is little red in the display. This is a result of the averaging

of values across nodes and elements. If one element reports a high stress to a node and another element reports low stress to

the same node, the average of these values will be in between.


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"Smoothed" Turn off this option so that no averaging is performed across the elements.

"maX abs" Turn on this option so that elements will be colored based on the highest value

reported at one of their nodes. The elements reporting the highest stresses are nowmore clearly displayed as depicted in Figure 35.

Figure 35: Residual Stress Tensor in the Y-Direction with the "maX abs" Option

The residual stresses indicate that the upper left corner of the beam is in residual compression and the lower left corner of the

beam is in residual tension. To understand these results, it is important to remember that only a small portion of the beam in

the corners went plastic. The rest of the beam stayed elastic and these regions want to return to their original undeformed

state. The upper left corner of the beam went plastic in tension, so its final state of deformation when unloaded will be longer

than its original state of deformation. When the elastic portions of the beam try to spring back, this area will be put into

compression. The lower left corner of the beam went plastic in compression, so its final state of deformation when unloaded

will be shorter than its original state of deformation. When the elastic portions of the beam try to spring back, this area will

be put into a tensile state of stress.


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3. Exiting Superview and Superdraw

You will now quit from Superview and return to Superdraw.

"donE" Press to return to the MAIN MENU of Superview and select "donE" to exit

Superview.

You return to Superdraw at this point.

"File:Exit" Exit Superdraw.

This brings the tutorial to an end. The Superdraw and Superview programs contain many features that were not discussed

here. You can experiment with these programs in order to learn about their additional capabilities. For help with any

command in either Superdraw or Superview, press the Help key and then select the command from the menu. A help

screen will then be displayed that provides additional information on the command.

Congratulations! You have completed the Nonlinear Static Stress Analysis Tutorial.


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Appendix A. Additional Information

Consult the following sources for more information about finite element analysis:

Suggested Reference Materials

Book I: Finite Element Modeling in Engineering Practice. Spyrakos, C.C. Pittsburgh, Pennsylvania: Algor Publishing

Division, 1994. Available as a reference textbook and multimedia CD-ROM.

Book II: Finite Element Analysis in Engineering Practice. Spyrakos, C.C. and Raftoyiannis, J. Pittsburgh, Pennsylvania:

Algor Publishing Division, 1997. Available as a reference textbook.

Finite Element Analysis in Action! Skaar, E.C. Pittsburgh, Pennsylvania: Algor, Inc. Publishing Division, 1995. Available

as a videotape and multimedia CD-ROM.

Other Reference Materials

First Course in Finite Element Method Using Algor. Logan, D. L. A. Boston, Massachusetts: PWS Publishing Company,

1997.


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Appendix B. Algor Software Reference

The following software version was used in this tutorial:

Algor FEA Release 12.00

Note:This tutorial specifically demonstrates use of Accupak/NLM. Accupak/VE can also be used because it

includes the capabilities of Accupak/NLM. If you use Accupak/VE, some of the keystrokes, text and figures will

differ.

nonlinear unlocked

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