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MATERIAL NONLINEAR

ANALYSISusing SolidWorks 2010 Simulation

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Learning Module

Non-Linear Analysis

Title Page Guide

What is a Learning Module?

A Learning Module (LM) is a structured, concise, and self-sufficient learning resource. An

LM provides the learner with the required content in a precise and concise manner, enabling

the learner to learn more efficiently and effectively. It has a number of characteristics that

distinguish it from a traditional textbook or textbook chapter:

An LM is learning objective driven, and its scope is clearly defined and bounded. Themodule is compact and precise in presentation, and its core material contains only

contents essential for achieving the learning objectives. Since an LM is inherently

concise, it can be learned relatively quickly and efficiently.

An LM is independent and free-standing. Module-based learning is therefore non-sequential and flexible, and can be personalized with ease.

Presenting the material in a contained and precise fashion will allow the user to learneffectively, reducing the time and effort spent and ultimately improving the learning

experience. This is the first module on Non-linear analysis and covers a material non-

linearity study in FEM. It goes through all of the steps necessary to successfully complete an

analysis, including geometry creation, material selection, boundary condition specification,meshing, solution, and validation. These steps are first covered conceptually and then worked

through directly as they are applied to an example problem.

Estimated Learning Time for This Module

Estimated learning time for this LM is equivalent to three 50-minute lectures, or one week of

study time for a 3 credit hour course.

How to Use This Module

The learning module is organized in sections. Each section contains a short explanation and a

link to where that section can be found. The explanation will give you an idea of what

content is in each section. The link will allow you to complete the parts of the module you

are interested in, while being able to skip any parts that you might already be familiar with.The modularity of the LM allows for an efficient use of your time.

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1. Learning Objectives

The objective of this module is to introduce the user to the process of material non-linearanalysis using FEM. Upon completion of the module, the user should have a good understanding

of the necessary logical steps of an FEM analysis, and be able to perform the following tasks:

Creating the solid geometry Assigning material properties Imposing displacement boundary conditions Applying external forces Meshing Running the analysis Verifying model correctness Processing needed results

2. Prerequisites

In order to complete the learning module successfully, the following prerequisites are required:

By subject area:o Statics;o Mechanics of Materials or Elasticityo Plasticity

By topic:Knowledge of

o force balanceo statically equivalent force systemso elastic deformationo plastic deformationo Youngs moduluso Tangent moduluso Plastic stress and straino Poissons ratioo displacemento straino stresso von Mises stresso Yield criteriao Strain hardeningo Work hardeningo Plastic flowo Types of nonlinearitieso Stress concentration factoro Tension and bending loading modes

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3. Pre-test

The pre-test should be taken before taking other sections of the module. The purpose of the pre-test is to assess the user's prior knowledge in subject areas relevant to static structural analysis

such as Mechanics of Materials. Questions are focused towards fundamental concepts including

stress, strain, displacement, kinematic relationship, constitutive relationship, equilibrium, andmaterial properties.

4. Tutorial Problem Statements

A good tutorial problem should focus on the logical steps in FEM modeling and demonstrate asmany aspects of the FEM software as possible. It should also be simple in mechanics with an

analytical solution available for validation. Three tutorial problems are covered in this learning

module.

Tutorial Problem 1

A rectangular beam of 1 inch x 0.25 inch x 0.04 inch is restrained at one end as shown in the

below figure. A Load of 315 lbf is applied as shown in the figure. The beam is made up of plaincarbon steel (consider a Tangential modulus of 31e6 psi).

Find the von-Mises stress. Compare the FEM result with analytic result.

Figure 1:Tutorial Problem 1

Tutorial Problem 2

A rectangular beam of 2 inches x 0.05 inches x 0.25 inches is fixed at one end as shown in the

below figure. A Load of 10 lbf is applied at the other end vertically upwards. The beam is made

up of plain carbon steel (consider a Tangential modulus of 31e6 psi).

Find the von-mises stress. Find the plastic moment.

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Figure 2:Tutorial problem 2

Tutorial Problem 3

A rectangular plate of 1 inch x 0.3 inches x 0.025 inches with a hole of radius 0.05 inches at its

center is fixed at one end as shown in the below figure. A Load of 100 lbf is applied as shown inthe figure. The beam is made up of plain carbon steel (consider a Tangential modulus of 31e6

psi).

Find the von-Mises stress. Find the stress concentration factor.

Figure 3:Tutorial problem 3

5. Conceptual Analysis

Conceptual analysis is the abstraction of the logical steps in performing a task or solving a

problem. Conceptual analysis for FEM simulation is problem type dependent but software-

independent, and is fundamental in understanding and solving the problem.

Conceptual analysis for static structural analysis reveals the following general logical steps:

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1. Pre-processingo Geometry creationo Material property assignmento Restraint and applied load specificationo Mesh generation

2.

Solution3. Post-processing4. Validation

8. Post-test

The post-test will be taken upon completion of the module. The first part of the post-test is fromthe pre-test to test knowledge gained by the user, and the second part is focused on the FEM

simulation process covered by the tutorial.

9. Assessment

The assessment is provided as a way to receive feedback about the module. The user evaluates

several categories of the learning experience, including interactive learning, the module format,

its effectiveness and efficiency, the appropriateness of the sections, and the overall learningexperience. There is also the opportunity to give suggestions or comments about the module.

10. Practice Problems

The user should be able to solve practice problems after taking the module. The practiceproblems provide a good reinforcement of the knowledge and skills learned in the module, and

can be assigned as homework problems in teaching, or self study problems to enhance learning.

These problems are similar to the tutorial problem worked in the module, but they involvedifferent geometries and loading modes, stress concentration, and statically indeterminate beams.

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Attachment C. SolidWorks-Specific FEM Tutorial

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Pre-test

1. When a stress in the material exceeds the yield stress, the material is said to be in :O plastic loading

O elastic loading

O fixedO Torsion

2. The basic fundamental principles of elasticity are applicable to plastic modelsO True

O False

3. Which of the following are Yield criteria?O Mohr-CoulombO Tresca

O Drucker-Prager

O All the above

4. Yield stress is dependent onO Temperature

O size

O strain rateO All the above

5. Which of these are the effects of work hardening?O decrease of density in material

O formation of dislocationsO elongation of material length

O None of the above

6. Which of the following statements about von Mises stress is correct?O von Mises stress is a scalar.O von Mises stress is maximum along a principal direction.

O von Mises stress has 6 independent components.

O von Mises stress is equal to yield strength of the material.

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7. Hookes law holds good even after the material is loaded beyond its yield limit.O True

O False

8. For a bar of uniform cross-section under axial loading in x direction, the Youngsmodulus is equal to

O The ratio of the axial displacement to the axial normal stress

O The ratio of the x-normal stress to the x-normal strain

O The ratio of the xy-shear stress to the x-normal stressO The ratio of the xy-shear stress to the xy-shear strain

9. For a square plate of uniform thickness under unequal bi-axial loading in x and ydirections, the shear modulus is equal to

O The ratio of the x-normal stress to the x-normal strainO The ratio of the y-normal stress to the y-normal strain

O The ratio of the xy-shear stress to the xy-shear strain

O The ratio of the x-displacement to the x-normal stress

10. If the von Mises stress of material point A is equal to the von Mises stress of materialpoint B, then each of the six stress components (i.e.,

xx,

yy,

zz,

xy,

yz, and

zx) ofpoint A is equal to the corresponding stress component of point B.

O True

O False

Conceptual Analysis

Conceptual Analysis of Nonlinear analysis:

Conceptual analysis for a static structural problem using finite element analysis revealsthat the following logical steps and sub-steps are needed:

1. Pre-processing (building the model)1. Geometry creation2. Material property assignment3. Boundary condition specification

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o Prescribed displacement boundary condition (holding the model)o Applied force boundary condition (loading the model)

4. Mesh generation2. Solution (running the simulation)3. Post-processing (getting results)4.

Validation (checking)

The above steps are explained in some detail as follows.

1. Pre-processing

The pre-processing in FEM simulation is analogous to building the structure or making

the specimen in physical testing. Several sub-steps involved in pre-processing are

geometry creation, material property assignment, boundary condition specification, andmesh generation.

The geometry of the structure to be analyzed is defined in the geometry creation step.After the solid geometry is created, the material properties of the solid are specified in the

material property assignment step. The material required for the FEM analysis depends

on the type of analysis. For example, in the elastic deformation analysis of an isotropic

material under isothermal condition, only the modulus of elasticity and the Poissonsratio are needed.

For most novice users of FEM, the boundary condition specification step is probably themost challenging of all pre-processing steps. Two types of boundary conditions are

possible. The first is prescribed displacement boundary condition which is analogous to

holding or supporting the specimen in physical testing. The second is applied force

boundary condition which is analogous to loading the specimen. Several factorscontribute to the challenge of applying boundary conditions correctly:

1) Prescribed displacement boundary conditions expressed in terms such asconstu

aboundary or const

x

u

bboundary

are mathematical simplifications, and

frequently only represent supports in real structures approximately. As a result,choosing a good approximate mathematical representation can be a challenge.

2) How a boundary is restrained depends also on the element type. For example, forthe "clamped" or "built-in" support, a boundary should be restrained as having

zero nodal displacement if solid element is used, while for the same support, the

boundary should be restrained as having zero nodal displacement and zero nodalrotation if shell element is used.

3) Frequently, the structure to be analyzed is not fully restrained from rigid bodymotion in the original problem statement. In order to obtain an FEM solution,

auxiliary restraints become necessary. Over-restraining the model, however, leads

to spurious stress results. The challenge is then adding auxiliary restraints toeliminate the possibility of rigid body motion without over-restraining the

structure.

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Because of the above challenges, one learning module will be devoted to boundary

condition specification.

Mesh generation is the process of discretizing the body into finite elements and

assembling the discrete elements into an integral structure that approximates the originalbody. Most FEM packages have their own default meshing parameters to mesh the modeland run the analysis while providing ways for the user to refine the mesh.

2. Solution

The solution is the process of solving the governing equations resulting from the

discretized FEM model. Although the mathematics for the solution process can be quite

involved, this step is transparent to the user and is usually as simple as clicking a solutionbutton or issuing the solution command.

3. Post-processing

The purpose of an FEM analysis is to obtain wanted results, and this is what the post-

processing step is for. Typically, various components or measures of stress, strain, and

displacement at any given location in the structure are available for putout. Additionalquantities for output may include factory of safety, energy norm error, contact pressure,

reaction force, strain energy density, etc. The way a quantity is outputted depends on the

FEM software.

4. Validation

Although validation is not a formal part of the FEM analysis, it is important to beincluded. Blindly trusting a simulation without checking its correctness can be dangerous.

The validation usually involves comparing FEM results at one or more selected positions

with exact or approximate solutions using classical approaches such as elasticity ormechanics of materials. Going through validation strengthens conceptual understanding

and enhances learning.

Conceptual Analysis of the Given Problem

The goal of the FEM simulation is to analyze the behavior of the solid with the given

forces acting on it. The problem shows a rectangular steel beam in the vertical plane

which is fixed at one end and has a force of 315 lbf acting at the other end. The modulusof elasticity is 30 Mpsi and Poissons ratio is 0.28. Conceptual analysis of the current

problem is described as follows.

1. Pre-processing (building the model)The geometry of the structure is first created using the design feature of the FEMpackage. Next, a material is assigned to the solid model. In the given problem, the

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material of the beam is given as steel. Depending on the software, the material is either

directly selected as steel from the material library, or the properties of the material given

in the problem are inputted directly.

After assigning the material properties, the boundary conditions are specified. The end

that is attached to the wall will need a fixed restraint, which means zero displacement forall boundary nodes due to the solid mesh. The load is applied on the other end

The next step is to mesh the solid to discretize it into finite elements. Generally,

commercial FEA software has automatic default meshing parameters such as averageelement size of the mesh, quality of the mesh, etc. Here the default parameters provided

by the software is used.

2. Solution (running the simulation)The next step is to run the simulation and obtain a solution. Usually the software provides

several solver options. The default solver usually works well. For some problems, aparticular solver may be faster or give more accurate results.

3. Post-processing (getting results)After the analysis is complete, the post-processing steps are performed. Results such as

von Mises stress, various stresses, displacements, and strains can be viewed.

4. Validation (checking)Validation is the final step in the analysis process. In this step, the stresses acting on the

beam are calculated by hand. These analytical solutions are compared with the softwaregenerated results to check the validity of the analysis.

This completes the Conceptual Analysis section. Click the link below to continue withthe learning module.

SolidWorks-Specific FEM Tutorial 1

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Overview: In this section, three tutorial problems will be solved using the commercial

FEM software SolidWorks. Although the underlying principles and logical steps of an

FEM simulation identified in the Conceptual Analysis section are independent of anyparticular FEM software, the realization of conceptual analysis steps will be software

dependent. The SolidWorks-specific steps are described in this section.

This is a step-by-step tutorial. However, it is designed such that those who are familiarwith the details in a particular step can skip it and go directly into the next step.

Tutorial Problem 1. A rectangular beam subjected to tensile loading

0. Launching SolidWorks

SolidWorks Simulation is an integral part of the SolidWorks computer aided design

software suite. The general user interface of SolidWorks is shown in Figure 8.

Figure 8:general user interface of SolidWorks.

In order to perform FEM analysis, it is necessary to enable the FEM component,

called SolidWorks Simulation, in the software.

Step 1: Enabling SolidWorks Simulation

Main menu Frequently used command icons Help icon

Roll over todisplay

File,

Tools and

other menus

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o Click "Tools" in the main menu. Select "Add-ins...". The Add-ins dialogwindow appears, as shown in Figure 9.

o Check the boxes in both the Active Add-ins and Start Up columnscorresponding to SolidWorks Simulation.

o Checking the Active Add-ins box enables the SolidWorks for thecurrent session. Checking the Start Up box enables the SolidWorks forall future sessions whenever SolidWorks starts up.

Figure 9:Location of the SolidWorks icon andthe boxes to be checked for adding it to the panel.

1. Pre-Processing

Purpose: The purpose of pre-processing is to create an FEM model for use in the next

step of the simulation, Solution. It consists of the following sub-steps: Geometry creation Material property assignment Boundary condition specification Mesh generation.

1.1 Geometry Creation

The purpose of Geometry Creation is to create a geometrical representation of the solid

object or structure to be analyzed in FEM. In SolidWorks such a geometric model is

called apart. In this tutorial, the necessary part has already been created in SolidWorks.

The following steps will open up the part for use in the FEM analysis.

Step 1: Opening the part for simulation. One of the following two options can be

used.

o Option1: Double click the following icon to open the embedded part file,tensile load.SLDPRT, in SolidWorks.

Check

SolidWorks

Simulation boxes

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Click SolidWorks part file icon to open it ==>tensile load.SLDPRT

o Option 2: Download the part file tensile load.SLDPRT from the web sitehttp://www.femlearning.org/. Use the File menu in SolidWorks to open thedownloaded part.

The SolidWorks model tree will appear with the given part name at the top. Above the

model tree, there should be various tabs labeled Features, Sketch, etc. If the

Simulation tab is not visible, go back to steps 1 and 2 to enable the SolidWorksSimulation package.

Step

2: Creating a Study

o Click the Simulation tababove the model tree

o Click on the drop downarrow under Study andselect New Study as in

Figure 10

o In the Name panel, give thestudy the name Tensile

Loading

o Select Nonlinear in theType panel to study theNonlinear behavior of the

part under the loado In the options bar present at

the bottom select static

o Click OK to accept andclose the menu Figure 10:The SolidWorks Study

menu.

1.2 Material Property Assignment

The Material Property Assignment sub-step assigns materials to different components of

the part to be analyzed. All components must be assigned with appropriate materialproperties.

Step 3: Opening the material property manager

o In the upper left hand corner, click Apply Material.o The Material window appears as shown in Figure 11.

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Figure 11:The Material window.

This will apply one material to all components. If the part is made of several componentswith different materials, open the model tree and apply this process to individual

components.

SolidWorks has a built-in material library that can be directly selected for the part.However, in this tutorial, material properties are defined using user input option.

Step 4: Defining custom material properties

o In the Material window, on the left panel under Select Material Source,select Custom definedo On the right panel, select PlasticityVon Mises in Model Typeo Select English (IPS) under Unitso Max von Mises Stress is selected for Default failure criteriono In the lower half of the panel, enter 30e6 for Elastic modulus, 31994.45

for Yield Strength, 31e6 for Tangent Modulus, 7.22e-006 forThermal expansion coefficient, 0.28 for Poissons ratio, 0.281793 for

Mass densityand 0 for Hardening factor.

1.3 Boundary Condition Specification

In the Boundary Condition Specification sub-step, the restraints and loads on the part aredefined. Here, the face of the beam attached to the wall needs to be restrained, and the

force in the proper direction needs to be applied on the other end of the beam.

Step 5: Opening the fixtures property manager

o Right click on Fixtures in the model tree and select Advanced Fixtures

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o Move the cursor into the graphic window.And constrain the part as shown in the below figures.

Figure 12 (a):Applying an immovable restraint to the plate

Figure 12 (b):Applying an immovable restraint to the beam.

Once the desired face is visible, select the face on which to apply the restraint. Note that

in the display panel, within the second box in the Type panel, Face appears,

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indicating that one surface is being selected. Clicking on this face in the graphics panel

would deselect the face and select the other face for direction.

Step 6: Restraining the member

o Select the face as in Figure 13o

Once the face has been selected, click the green check mark to close theFixture menu

The next step is to load the beam with the applied force. The total force applied is 315 lbf

acting towards right side of the beam as shown in the figure 6.

Figure 13:Applying the tensile force.

Step 7: Applying the Forceo Right click on External Loads in the model tree and select Force.o Under the Force/Torque tab, click the Faces, Edges, Vertices, Reference

Points for Force input field box to activate it, if not already active.

o Click on the face on which the force is applied in the graphics window. Makesure the face is highlighted (turns blue) and appears in the input field box.

o Choose Normal. Click the Face, Edge, Plane, Axis for Direction inputfield box to activate it.

o Then click on Reverse direction to apply the force upwards.o Variation with time is left unchanged (linear).o Click OK to close the menu.

1.4 Mesh Generation

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Purpose: The purpose of the Mesh Generation sub-step is to discretize the part into

elements. The mesh consists of a network of these elements.

Step 9: Creating the mesh

o Right click Mesh in themodel tree and select Createmesh

o Leave the mesh bar on itsdefault value

o Drop down the Advancedmenu and make sure the

mesh is high quality, not draft

quality, by making sure the

Draft Quality Meshcheckbox is not clicked

which is shown in the figure

14.o Click OK to close the

menu and generate the mesh.

o Figure 15 shows thecompleted mesh

Figure 14:Basic Mesh

properties.

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Figure 15:A completed mesh.

Mesh Control in SolidWorks may be used to refine the mesh locally. The guiding

principle is to refine mesh at locations of high stress gradient, such as regions aroundstress concentrators and locations of geometric changes. For the current problem, local

mesh refinement is not pursued.

1.5 Setting the static study properties

Purpose: The purpose of defining the static study properties is to define the iteration typeand the parameters like the tolerances and the stepping options for solver and various

other parameters.

o Various parameters are defined as shown in the following figures 16 (a) & (b).

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Figures 16 (a) & 9 (b):Static study parameters.

2. Solution

Purpose: The Solution is the step where the computer solves the simulation problem and

generates results for use in the Post-Processing step.

Step 1: Running the simulation

o At the top of the screen, click Runo When the analysis is finished, the Results icon will appear on the model tree

3. Post-Processing

Purpose: The purpose of the Post-Processing step is to process the results of interest. Forthis problem, the von Mises stress is the parameter of interest. From that we will calculate

the bending moment of the beam.

Step 1: Creating a stress plot

o Right click Results on the model tree and select Define Stress Ploto Select von Mises as the stress type and psi as the unito Unclick the Deformed Shape box and click OK to close the menu

Figure 17 shows the resulting stress plot.

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Figure 17:The von Mises stress plot.

We can observe that the von mises stress that is obtained exceeds the yield strength of thematerial. This shows that the material is subjected to a plastic deformation.

Step 2: Plotting the resultant deformation

o The deformation due to the plastic loads can be plotted like the below figure

Figure 18. Plot displaying the plastic deformation

Step 3: Plotting plastic strain

o To plot the plastic strain, click edit definition for strain plot.

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o Then select plastic as shown in the figure 19.o Then the resulting figure can be obtained like in figure 20.o These results can now be compared to analytical solutions for validation.

Figure 19.Selecting plastic strain

Figure 20:Plot for plastic strain

Note: If you want to view the stress at a particular point, right click on the stress plot andselect Probe. Also in Chart Options, you can choose to display the minimum and

maximum stress on the figure.

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4. Validation

Purpose: The purpose of the Validation step is to compare FEM solutions with analyticalsolutions, or known published results, to validate the correctness of the FEM model.

For the current problem, closed form solutions based on elementary beam theory fromMechanics of Materials and plasticity are computed and compared with the FEM results.This will reveal whether or not the results of the finite element analysis are reasonable.

In this problem,

The beam is subjected to a tensile load. The stress equations from elementary beam

theory are:

Axial stress, =

= = 31500 psi

Elastic= 31500 psi

Elastic=

= = 0.00105

To find the plastic strain, we have considered a tangent modulus of 3.1e7 psi.So we can find the plastic stress at that particular tangent modulus and correspondingly

we can find out the plastic moment value.

Plastic=

x (Tangent Modulus)

= (0.00105) x (3.1e7)

= 32550 psi

The above plastic stress is the value at that particular tangent modulus.

Now we will consider the FEA value for plastic stress at the same Tangent Modulus.

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From FEA:

Plastic = 32921.9 psi

Stress Component SolidWorks Elementary Beam Theory % Error

32550 psi 32921.9 psi 1.13 %

The percent error is low for both stress components. The good agreement between theresults using elementary beam theory and the FEM results validates the correctness of the

FEM analysis.

Tutorial Problem 2. A rectangular cantilever beam under a vertical bending force.

1. Pre-Processing

Purpose: The purpose of pre-processing is to create an FEM model for use in the next

step of the simulation, Solution. It consists of the following sub-steps:

Geometry creation Material property assignment Boundary condition specification Mesh generation.


The purpose of Geometry Creation is to create a geometrical representation of the solid

object or structure to be analyzed in FEM. In SolidWorks such a geometric model is

called apart. In this tutorial, the necessary part has already been created in SolidWorks.The following steps will open up the part for use in the FEM analysis.


used.o Option1: Double click the following icon to open the embedded part file,

bend.SLDPRT, in SolidWorks.

Click SolidWorks part file icon to open it ==>bend.SLDPRT

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o Option 2: Download the part file bend.SLDPRT from the web sitehttp://www.femlearning.org/. Use the Filemenu in SolidWorks to open the

downloaded part.


model tree, there should be various tabs labeled Features, Sketch, etc. If theSimulation tab is not visible, go back to steps 1 and 2 to enable the SolidWorksSimulation package.

Step 2:Creating a Study

o Click the Simulation tababove the model tree

o Click on the drop downarrow under Study and

select New Study as in

Figure 23o In the Name panel, give the

study the name

Beambending

o Select Nonlinear in theType panel to study the

Nonlinear behavior of the

part under the load

o In the options bar present atthe bottom select static

o Click OK to accept andclose the menu Figure 23:The SolidWorks Study

menu.


The Material Property Assignment sub-

step assigns materials to different

components of the part to be analyzed.All components must be assigned with

appropriate material properties.Step 3: Opening the materialproperty manager

o In the upper left hand corner,click Apply Material.

o The Material windowappears as shown in Figure

24. Figure 24:The Material window.

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This will apply one material to all components. If the part is made of several components

with different materials, open the model tree and apply this process to individualcomponents.

SolidWorks has a built-in material library that can be directly selected for the part.

However, in this tutorial, material properties are defined using user input option.


o In the Material window, on the left panel under Select Material Source,select Custom defined

o On the right panel, select PlasticityVon Mises in Model Typeo Select English (IPS) under Unitso

Max von Mises Stress is selected for Default failure criteriono In the lower half of the panel, enter 30e6 for Elastic modulus, 31994.45

for Yield Strength, 31e6 for Tangent Modulus, 7.22e-006 for

Thermal expansion coefficient, 0.28 for Poissons ratio, 0.281793 for

Mass densityand 0 for Hardening factor.


In the Boundary Condition Specification sub-step, the restraints and loads on the part are

defined. Here, the face of the beam attached to the wall needs to be restrained, and the



o Right click on Fixtures in the model tree and select Fixed Geometryo Move the cursor into the graphic window.

As the cursor traverses the image of the model, notice a small icon accompany the cursor,and this icon change shapes when the cursor is at different locations. This indicates that

the SolidWorks is in graphical selection mode, and different shapes indicate different

identities would be selected: a square (icon) indicates the surface underneath the cursor

will be selected if the mouse is clicked, a line (icon) for an edge or a line, and a dot (icon)

for a point. In this tutorial problem, the entire end surface is restrained.

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Figure 25:Applying an immovable restraint to the beam.At the initial orientation, however, the end to be restrained is not visible, and could not be

selected. The model should be rotated to make the fixed end visible. To rotate the model

either hold down the scroll bar and rotate with the mouse or change the orientation by

clicking on the View Orientation icon in the top middle area of the workspace.


in the display panel, within the second box in the Type panel, Face appears,indicating that one surface is being selected. Clicking on this face in the graphics panel

would deselect the face.


o Select the face as in Figure 25o Once the face has been selected, click the green check mark to close the

Fixture menu

The next step is to load the beam with the applied force. The total force applied is 10 lbf

acting vertically upwards as shown in the figure 26.

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Figure 26:Applying the bending force.

Step 7: Applying the Force

o Right click on External Loads in the model tree and select Force.o Under the Force/Torque tab, click the Faces, Edges, Vertices, Reference

Points for Force input field box to activate it, if not already active.


o Choose Selected direction instead of Normal. Click the Face, Edge,Plane, Axis for Direction input field box to activate it.

o Then select the vertical edge of the face which is already selected for force tospecify the direction of force.


1.4 Mesh Generation

Purpose: The purpose of the Mesh Generation sub-step is to discretize the part intoelements. The mesh consists of a network of these elements.



o Leave the mesh bar on itsdefault value


mesh is high quality, not draft

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quality, by making sure the

Draft Quality Mesh

checkbox is not clickedwhich is shown in the figure

27.

oClick OK to close themenu and generate the mesh.



properties.


Mesh Control in SolidWorks may be used to refine the mesh locally. The guiding

principle is to refine mesh at locations of high stress gradient, such as regions around

stress concentrators and locations of geometric changes. For the current problem, localmesh refinement is not pursued.

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Purpose: The purpose of defining the static study properties is to define the iteration type

and the parameters like the tolerances and the stepping options for solver and various

other parameters.



2. Solution





3. Post-Processing

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Purpose: The purpose of the Post-Processing step is to process the results of interest. For

this problem, the von Mises stress is the parameter of interest. From that we will calculate



oRight click Results on the model tree and select Define Stress Plot

o Select von Mises as the stress type and psi as the unito Unclick the Deformed Shape box and click OK to close the menu



We can observe that the von mises stress that is obtained exceeds the yield strength of the

material. This shows that the material is subjected to a plastic deformation.



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o To plot the plastic strain,click edit definition for strain

plot.

oThen select plastic as shownin the figure 32.

o Then the resulting figure canbe obtained like in figure 33.

o These results can now becompared to analytical

solutions for validation.Figure 32.Selecting plastic

strain

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32


Note: If you want to view the stress at a particular point, right click on the stress plot and

select Probe. Also in Chart Options, you can choose to display the minimum and


4. Validation

Purpose: The purpose of the Validation step is to compare FEM solutions with analyticalsolutions, or known published results, to validate the correctness of the FEM model.

For the current problem, closed form solutions based on elementary beam theory fromMechanics of Materials and plasticity are computed and compared with the FEM results.

This will reveal whether or not the results of the finite element analysis are reasonable.

In this problem,

The beam is subjected to a bending load. The stress equations from elementary beamtheory are:

Moment M = (Force) x (length of the beam)

= (10 lbf) x (2 inches)

= 20 lbf-in

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We know that,

Elastic =

Where,

M = Bending Moment

C = distance from the neutral axis to the end of the beamI = Moment of inertia

Elastic= 38400 psi

Elastic=

=

= 0.00128

To find the plastic strain, we have considered a tangent modulus of 3.1e7 psi.So we can find the plastic stress at that particular tangent modulus and correspondingly

we can find out the plastic moment value.

Plastic = (Elastic ) x (Tangent Modulus)

= (0.00128) x (3.1e7)

= 39680 psi

The above plastic stress is the value at that particular tangent modulus.

Now we will consider the FEA value for plastic stress at the same Tangent Modulus.

From FEA:

Plastic = 37200.6 psi

Stress Component SolidWorks Elementary Beam Theory % Error

37200.6 psi 39680 psi 6.7 %

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ForM>Me the beam is in the elastic-plastic regime: the core of the beam (between

y=- c and y=c) is in the elastic regime, while the outer fibers are in the plastic regime

(=y).

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= (39680 x 0.05 x 0.252) / 4

= 24.99 lb-in

= (39680 x 0.05 x 0.252) / 6

= 16.6638 lb-in

Therefore, Mp= 1.5 MeThe above condition is also proved.

The percent error is low for both stress components. The good agreement between the

results using elementary beam theory and the FEM results validates the correctness of theFEM analysis.

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Tutorial Problem 3. A rectangular plate with a hole at its center subjected to

uniaxial loading.

1. Pre-Processing

Purpose: The purpose of pre-processing is to create an FEM model for use in the nextstep of the simulation, Solution. It consists of the following sub-steps:

Geometry creation Material property assignment Boundary condition specification Mesh generation.


The purpose of Geometry Creation is to create a geometrical representation of the solidobject or structure to be analyzed in FEM. In SolidWorks such a geometric model is

called apart. In this tutorial, the necessary part has already been created in SolidWorks.

The following steps will open up the part for use in the FEM analysis.


used.

o Option1: Double click the following icon to open the embedded part file, L-plate.SLDPRT, in SolidWorks.

Click SolidWorks part file icon to open it ==>plate.SLDPRT

o Option 2: Download the part file plate.SLDPRT from the web sitehttp://www.femlearning.org/. Use the File menu in SolidWorks to open the

downloaded part.


model tree, there should be various tabs labeled Features, Sketch, etc. If the

Simulation tab is not visible, go back to steps 1 and 2 to enable the SolidWorksSimulation package.

Step 2: Creating a Study

o Click the Simulation tab above the model treeo Click on the drop down arrow under Study and select New Study as in

Figure 36

o In the Name panel, give the study the name Stressconcentrationo Select Nonlinear in the Type panel to study theNonlinear behavior of the

part under the load

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o In the options bar present at the bottom select statico Click OK to accept and close the menu

Figure 36:The SolidWorks Study menu.


The Material Property Assignment sub-step assigns materials to different components of

the part to be analyzed. All components must be assigned with appropriate materialproperties.

Step 3: Opening the material property manager

o In the upper left hand corner, click Apply Material.o The Material window appears as shown in Figure 37.

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Figure 37:The Material window.

This will apply one material to all components. If the part is made of several components

with different materials, open the model tree and apply this process to individual

components.

SolidWorks has a built-in material library that can be directly selected for the part.

However, in this tutorial, material properties are defined using user input option.


o In the Material window, on the left panel under Select Material Source,select Custom defined

o On the right panel, select PlasticityVon Mises in Model Typeo Select English (IPS) under Unitso Max von Mises Stress is selected for Default failure criteriono In the lower half of the panel, enter 30e6 for Elastic modulus, 31994.45

for Yield Strength, 31e6 for Tangent Modulus, 7.22e-006 forThermal expansion coefficient, 0.28 for Poissons ratio, 0.281793 for

Mass densityand 1/3 for Hardening factor.

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In the Boundary Condition Specification sub-step, the restraints and loads on the part aredefined. Here, the face of the beam attached to the wall needs to be restrained, and the



o Right click on Fixtures in the model tree and select Fixed Geometryo Move the cursor into the graphic window.

As the cursor traverses the image of the model, notice a small icon accompany the cursor,

and this icon change shapes when the cursor is at different locations. This indicates that

the SolidWorks is in graphical selection mode, and different shapes indicate different

identities would be selected: a square (icon) indicates the surface underneath the cursorwill be selected if the mouse is clicked, a line (icon) for an edge or a line, and a dot (icon)

for a point. In this tutorial problem, the entire end surface is restrained.

Figure 38:Applying an immovable restraint to the beam.

At the initial orientation, however, the end to be restrained is not visible, and could not be

selected. The model should be rotated to make the fixed end visible. To rotate the model

either hold down the scroll bar and rotate with the mouse or change the orientation byclicking on the View Orientation icon in the top middle area of the workspace.


in the display panel, within the second box in the Type panel, Face appears,indicating that one surface is being selected. Clicking on this face in the graphics panel

would deselect the face.

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o Select the face as in Figure 38o Once the face has been selected, click the green check mark to close the

Fixture menu

The next step is to load the beam with the applied force. The total force applied is 100 lbfas shown in the figure 39.

Figure 39:Applying the uniaxial tensile force.

Step 7: Applying the Force

o Right click on External Loads in the model tree and select Force.o Under the Force/Torque tab, click the Faces, Edges, Vertices, Reference

Points for Force input field boxto activate it, if not already active.


o Choose Normal. Click the Face, Edge, Plane, Axis for Direction inputfield box to activate it.


1.4 Mesh Generation

Purpose: The purpose of the Mesh Generation sub-step is to discretize the part into

elements. The mesh consists of a network of these elements.

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oLeave the mesh bar on itsdefault value


mesh is high quality, not draftquality, by making sure the

Draft Quality Mesh

checkbox is not clicked

which is shown in the figure40.

o Click OK to close themenu and generate the mesh.



properties.


Mesh Control in SolidWorks may be used to refine the mesh locally. The guidingprinciple is to refine mesh at locations of high stress gradient, such as regions around

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stress concentrators and locations of geometric changes. For the current problem, local

mesh refinement is not pursued.


Purpose: The purpose of defining the static study properties is to define the iteration typeand the parameters like the tolerances and the stepping options for solver and variousother parameters.



2. Solution





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3. Post-Processing

Purpose: The purpose of the Post-Processing step is to process the results of interest. Forthis problem, the von Mises stress is the parameter of interest. From that we will calculate



o Right click Results on the model tree and select Define Stress Ploto Select von Mises as the stress type and psi as the unito Unclick the Deformed Shape box and click OK to close the menu



We can observe that the von mises stress that is obtained exceeds the yield strength of thematerial. This shows that the material is subjected to a plastic deformation.



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o To plot the plastic strain,click edit definition for strain

plot.

oThen select plastic as shownin the figure 45.

o Then the resulting figure canbe obtained like in figure 46.

o These results can now becompared to analytical

solutions for validation.Figure 45.Selecting plastic

strain

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45


Note: If you want to view the stress at a particular point, right click on the stress plot and

select Probe. Also in Chart Options, you can choose to display the minimum and


4. Validation

Purpose: The purpose of the Validation step is to compare FEM solutions with analytical

solutions, or known published results, to validate the correctness of the FEM model.

For the current problem, closed form solutions based on elementary beam theory fromMechanics of Materials and plasticity are computed and compared with the FEM results.

This will reveal whether or not the results of the finite element analysis are reasonable.

In this problem,

The beam is subjected to a axial tensile load. The stress equations from elementary

beam theory are:

Within elastic range:

tK is defined by

nom

maxtK

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where the nominal stressdw

pw

t)dw(

pwt

A

F

net

nom

, t is the thickness of the plate.

The maximum normal stress max is the x normal stress at the top of the hole.

When the deformation is plastic:

For a nonhardening material, the stress concentration factor is (), whatever the yieldcriterion. When n = 1/3, the increases from ()to Y, the stress concentration factordecreases from 2 to a limiting value * = 1.35 for n = 1/3 and

*=

(

)

for other values of n.

In the plastic region (r c), the Mises criterion is identically satisfied by writing

r=

sin =

cos ( ), where (r c),

Where is an auxiliary angle. At the end of the hole r = a, the boundary condition

requires = 0, while at the plastic boundary r = c, the continuity of the stresses requires

to have the value

c= sin-1 { (

)}

Here in this case, * = 1.35, thenafter calculations are done,

= (Y) x (*)= (32) x (1.35)

= 43.2 ksi

c=

r= 43.2 ksi, here for this case it is uniaxial so = 0.

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From FEA results:

r= 36 ksi. For a hardening factor of 1/3.

Stress Component SolidWorks Elementary Beam Theory % Errorr 36 ksi 43.2 ksi 16.6 %

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Attachment F. Assessment

48

Post-test

1. The internal force per unit area acting inside the body when a force is applied onthe body is called:

O Stress

O StrainO Displacement

O Other

2. What is limiting point?

3. Stress concentration factor is the ratio of :

O nominal stress / maximum stress.

O Elastic limit / stress acting.O Stress / strain.

O Force / area

4. xyrefers to:

O Shear stress in XY plane

O Normal stress in X directionO Sum of normal stress in X and Y direction

O Shear stress in YZ plane

5. What is perfect plasticity?

6. Bending moment induces:

O Tensile stress

O Compressive stress

O Both tensile and compressive stressO Shear stress

7. What is von Mises stress?

O The principle stress

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O The normal stress

O A scalar value that represents the total stress

O A stress vector

8. What is Poissons ratio?

O The ratio of the contraction strain to the axial strain

O The ratio of the shear stress to the normal stress

O The ratio of the displacement to the normal stressO The ratio of shear stress to shear strain

9. What is Youngs modulus?

O The ratio of the normal stress to the normal strain

O The ratio of the shear stress to the normal stressO The ratio of the displacement to the normal stress

O The ratio of shear stress to shear strain

10. What is the shear modulus?

O The ratio of the normal stress to the normal strainO The ratio of the shear stress to the normal stress

O The ratio of the displacement to the normal stress

O The ratio of shear stress to shear strain

11. What is Tangent Modulus?

12. What type of iterations is used in the non-linear analysis?

13. What is Geometric Nonlinearity?

14. For which type of materials, Von-Mises criterion is preferred?

15. What is the difference between elastic and plastic analysis?

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Assessment

1. Do you feel it was bad to not have a teacher there to answer any questions youmight have?

O It didnt matterO It would have been niceO I really wanted to ask a question

2. How did the interactivity of the program affect your learning?

O Improved it a lot

O Improved it someO No difference

O Hurt it some

O Hurt it a lot

3. The six levels of Blooms Taxonomy are listed below. Rank how well this

learning module covers each level. 5 meaning exceptionally well and 1 meaningvery poor.

1. Knowledge (remembering previously learned material)O 5

O 4

O 3

O 2O 1

2. Comprehension (the ability to grasp the meaning of the material and giveexamples)

O 5

O 4O 3

O 2

O 1

3.

Application (the ability to use the material in new situations)O 5

O 4

O 3O 2

O 1

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4. Analysis (the ability to break down material into its component parts so thatits organizational structure may be understood)

O 5O 4

O 3

O 2O 1

5. Synthesis (the ability to put parts together to form a new whole)O 5O 4

O 3

O 2

O 1

6. Evaluation (the ability to judge the value of the material for a given purpose)O 5O 4

O 3

O 2

O 1

4. Do you think the mixed text and video format works well?

O Yes

O Indifferent

O No

5. Do you think the module presents an affective method of learning FEA?

O Yes

O IndifferentO No

6. Did you prefer this module over the traditional classroom learning experience?

Why or why not.

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7. How accurate would it be to call this module self-contained and stand-alone?

O Very accurateO Accurate

O Indifferent

O InaccurateO Very inaccurate

8. What specifically did you like and/or dislike about the module.

9. How useful were the practice problems?

O Very helpful

O Helpful

O IndifferentO Unhelpful

O Very unhelpful

10. Was there any part of the module that you felt was unnecessary of redundant?

Was there a need for any additional parts?

11. Please list any suggestions for improving this module.

12. Overall, how would you rate your experience taking this module?

O Excellent

O FairO Average

O Poor

O Awful

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Attachment G. Practice Problems

53

Practice Problems

1. A rectangular beam of 1 inch x 0.25 inch x 0.04 inch is restrained at one end asshown in the below figure. A Load of 315 lbf is applied as shown in the figure. The

beam is made up of plain carbon steel (consider a Tangential modulus of 33e6 psi). Find the von-Mises stress. Compare the FEM result with analytic result.

2. A circular beam of 1 inch length and 0.05 inch diameter is restrained at one end asshown in the below figure. A Load of 100 lbf is applied as shown in the figure. The

beam is made up of plain carbon steel (consider a Tangential modulus of 31e6 psi).

Find the von-Mises stress. Compare the FEM result with analytic result.

3. A rectangular beam of 2 inches x 0.05 inches x 0.25 inches is fixed at one end asshown in the below figure. A Load of 10 lbf is applied at the other end vertically

upwards. The beam is made up of plain carbon steel (consider a Tangential modulusof 33e6 psi).

Find the von-Mises stress. Find the plastic moment.

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Attachment G. Practice Problems

54

4. A rectangular plate of 1 inch x 0.3 inches x 0.025 inches with a hole of radius 0.05inches at its center is fixed at one end as shown in the below figure. A Load of 100

lbf is applied as shown in the figure. The beam is made up of plain carbon steel(consider a Tangential modulus of 33e6 psi).

Find the von-Mises stress.

Find the stress concentration factor.

LM6

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