INDEX

1. Overview of FEA and its application in automotive.............................................1

1.1. Basic definition...................................................................................................1

1.2. Types of applied elements for structural strength problems and its problem
in automotive of Finite element analysis.................................................................1

1.2.1. 1-D (Line) Elements:.....................................................................................1

1.2.2. 2-D (Plane) Elements:...................................................................................2

1.2.3 3-D (Solid) Elements:.....................................................................................3

1.2.4. Applied problems in automotive FEA:..........................................................4

1.3 Application of FEA in Automotive Industry....................................................8

2. ANSYS - a general-purpose FEA program..........................................................10

2.1 Useful definitions...............................................................................................10

2.2 ANSYS analysis approach................................................................................11

2.2.1 Preprocessor.................................................................................................11

2.2.2 Solution processor........................................................................................12

2.2.3 General postprocessor..................................................................................12

2.2.4 Time History Postprocessor.........................................................................12

2.3 File Structure.....................................................................................................12

2.3.1 Database File...............................................................................................12

2.3.2 Log File........................................................................................................13

2.4 Using the ANSYS Help System........................................................................13

3. Linear and nonlinear in structural analysis.........................................................14

3.1 Linear structural analysis.................................................................................14

3.1.1 Static analysis...............................................................................................14

3.1.2 Assumptions of linear analysis.....................................................................14

 3.2 Nonlinear structural analysis...........................................................................15

3.2.1 Geometric Nonlinearity................................................................................15

3.2.2 Differences between linear and nonlinear analysis.....................................16

3.2.3 Purpose of nonlinear analysis......................................................................16

4. Solving problem......................................................................................................17

4.1 Solving problem by Graphical User Interface ( GUI )..................................17

4.1.1 Nonlinear analysis........................................................................................17

4.1.2 Linear analysis.............................................................................................31

4.2 Solving problem by ANSYS Parametric Design Language ( APDL)...........41

4.2.1 Code for Linear Analysis of Cantilever Beam:............................................42

4.2.2. Code for Nonlinear Analysis of Cantilever Beam.......................................43

5. Comparison the results and conclusion between Linear and Nonlinear Analysis
......................................................................................................................................44

5.1 The deformed shape:.........................................................................................44

5.2 The deflection contour plot...............................................................................45

5.3 List horizontal displacement:...........................................................................47

1. Overview of FEA and its application in automotive

1.1. Basic definition

Finite Element Analysis (FEA) is a powerful computational technique used to

predict how structures and materials will respond to external forces, thermal
conditions, vibrations, and other physical effects. By breaking down a complex system
into smaller, manageable elements, FEA allows for precise analysis of stress, strain,
and deflection within materials and structures. Each element represents a small portion
of the larger system, connected at nodes, which form a mesh that approximates the
geometry of the analyzed object.

1.2. Types of applied elements for structural strength problems and its problem
in automotive of Finite element analysis

1.2.1. 1-D (Line) Elements:

1D elements are used for structures that have one significant dimension along
which the behavior is analyzed. These elements are ideal for analyzing structures
where only length is a major factor.

- Truss (or Link) Elements:

○ Used for axial forces (tension/compression).
 ○ Application: Structural frameworks, bridges.
- Beam Elements:
○ Handle axial forces, bending moments, and shear forces.
○ Application: Chassis, control arms, building frames.

1.2.2. 2-D (Plane) Elements:

2D elements are used for structures where two dimensions are significant, and
the third dimension is negligible. These are primarily used for analyzing flat or shell-
like structures.
 - Plane Stress Elements:
○ Used for thin structures with stress in the plane.
○ Application: Thin plates, membranes.
- Plane Strain Elements:
○ Used for long structures with uniform cross-section.
○ Application: Dams, tunnels.
- Shell Elements:
○ Handle bending and membrane actions in thin, curved surfaces.
○ Application: Vehicle bodies, aircraft fuselage.
- Plate Elements:
○ Used for flat, thin structures that bend.
○ Application: Floor slabs, roof panels.
- Membrane Elements:
○ Handle in-plane forces but negligible bending stiffness.
○ Application: Tents, airbags.

1.2.3 3-D (Solid) Elements:

3D elements are used for structures where all three dimensions are significant.
These elements are essential for analyzing the complete volumetric behavior of
structures.
 - Solid (or Continuum) Elements:
○ Handle complex loading conditions including bending, shear, and axial
loads.
○ Application: Engine components, structural foundations.
- Axisymmetric Elements:
○ Used for structures symmetrical around an axis.
○ Application: Pressure vessels, rotational components like gears.
- Thermal Elements:
○ Model heat transfer (conduction, convection, radiation).
○ Application: Heat exchangers, engine cooling systems.

1.2.4. Applied problems in automotive FEA:

In automotive engineering, Finite Element Analysis (FEA) is crucial for

designing and analyzing various components to ensure their structural integrity,
performance, and safety. Here are the primary types of finite elements used for
structural strength problems and their applications in the automotive industry:

1.2.4.1 Truss Elements

Truss elements are 1D elements that can only carry axial forces, either tension
or compression. They are typically used to model structures like frameworks that are
composed of interconnected straight members.

Applications in Automotive:

- Vehicle Frames and Spaceframes: Used in the design and analysis of

lightweight frames and spaceframes, ensuring efficient load distribution and
structural stability.
- Suspension Systems: Helps in analyzing the load paths in suspension linkages
and control arms.

Problems Addressed:

- Ensuring the structural integrity of frame designs under various loading

conditions.
- Optimizing material usage while maintaining strength and rigidity.

1.2.4.2 Beam Elements

Description: Beam elements are also 1D elements but can handle axial forces, bending
moments, and shear forces. They are ideal for analyzing components that are primarily
subjected to bending.

Applications in Automotive:

- Chassis and Structural Members: Analysis of longitudinal and lateral beams in

the chassis, optimizing stiffness and reducing weight.
- Anti-Roll Bars and Control Arms: Evaluating the performance of these
components under dynamic loading conditions.
Problems Addressed:

- Ensuring components withstand bending and shear forces without failure.

- Enhancing the stiffness and strength of critical structural members.

1.2.4.3 Shell Elements

Description: Shell elements are 2D elements that can model structures with a
significant surface area compared to their thickness. They handle both in-plane and
out-of-plane loads.

Applications in Automotive:

- Body Panels and Roofs: Analysis of the vehicle's exterior panels for impact
resistance and durability.
- Crashworthiness Analysis: Simulating the behavior of vehicle bodies during
crashes to improve safety features.

Problems Addressed:

- Evaluating the structural integrity and durability of thin-walled components.

- Optimizing the design for weight reduction while maintaining strength.

1.2.4.4 Solid (Continuum) Elements

Description: Solid elements are 3D elements used to model volumetric

structures. They can simulate complex stress states and are suitable for detailed
analysis.

Applications in Automotive:

- Engine Components and Mounts: Analyzing stresses and deformations in

engine blocks, pistons, and mounting brackets.
- Transmission Housings and Gearboxes: Evaluating the performance and
durability of drivetrain components under operational loads.

Problems Addressed:
 - Ensuring components can withstand complex loading conditions and high-
stress concentrations.
- Enhancing the reliability and performance of critical mechanical parts.

1.2.4.5 Plane Stress/Strain Elements

Description: Plane stress elements are used for thin structures with negligible
thickness, while plane strain elements are used for long structures with a uniform
cross-section.

Applications in Automotive:

- Brake Discs and Pads: Plane stress elements analyze the stress distribution in
thin brake components.
- Longitudinal Members: Plane strain elements are used for analyzing long,
straight members like rails or beams.

Problems Addressed:

- Predicting the stress distribution in thin components to prevent failure.

- Ensuring the structural integrity of long components under various loading
conditions.

1.2.4.6 Challenges in Automotive FEA

- Complex Geometries: Automotive components often have intricate geometries,
making meshing and analysis challenging.
- Material Properties: Accurate characterization of advanced materials (e.g.,
composites, high-strength steels) is essential for reliable analysis.
- Nonlinear Behavior: Many automotive components exhibit nonlinear behavior
under load, requiring advanced nonlinear analysis techniques.
- Dynamic Loading: Vehicles are subjected to dynamic loads such as vibrations,
impacts, and varying operational conditions, necessitating robust dynamic
analysis.
1.3 Application of FEA in Automotive Industry

Finite Element Analysis is a cornerstone of modern automotive engineering,

offering detailed insights into the behavior of vehicle components under various
conditions. Its ability to simulate real-world scenarios and optimize designs
contributes significantly to the development of safer, more efficient, and innovative
vehicles. By harnessing the power of FEA, the automotive industry continues to push
the boundaries of what is possible in vehicle design and performance.

FEA is indispensable in the automotive industry for several key applications:

- Structural Analysis:

Crash Simulations: FEA is used to simulate vehicle crashes, helping engineers

understand how different materials and structures deform under impact. This is crucial
for improving safety features and designing crumple zones that absorb energy during a
collision.

Durability Testing: Automotive components like chassis, frames, and

suspension systems are analyzed to ensure they can withstand long-term use and
repeated loads without failure.

- Thermal Analysis:

Engine Components: FEA helps in predicting temperature distributions and

thermal stresses in engine components, ensuring they operate efficiently under varying
thermal conditions.

Cooling Systems: The analysis aids in optimizing the design of radiators and
cooling passages to prevent overheating and maintain optimal engine performance.

- Vibration and Noise Analysis:

NVH (Noise, Vibration, and Harshness) Optimization: FEA is used to analyze

and minimize vibrations and noise within the vehicle cabin, leading to a more
comfortable driving experience.
 Dynamic Analysis: This includes studying the behavior of components under
dynamic loading conditions, such as suspension systems during driving over rough
terrain.

- Material Analysis:

Lightweight Materials: With the industry's shift towards lightweight, fuel-

efficient vehicles, FEA is crucial in evaluating the performance of advanced materials
like composites and high-strength alloys.

Fatigue Analysis: It helps predict the lifespan of materials subjected to cyclic

loading, preventing premature failures and optimizing material selection.

- Optimization and Innovation:

Design Optimization: Engineers use FEA to iterate and optimize designs for
better performance, weight reduction, and cost efficiency.

Innovation in Manufacturing: FEA supports the development of innovative

manufacturing techniques, such as additive manufacturing, by predicting the
performance of 3D-printed components under real-world conditions.
2. ANSYS - a general-purpose FEA program

2.1 Useful definitions

Before exploring the details of the procedures associated with the ANSYS
program, we first define the following terms:

Jobname A designated name for the files generated during an ANSYS session,
which can be assigned either prior to or following the launch of the ANSYS program.

Working Directory A dedicated folder (directory) for ANSYS to store all files
generated during a session. The Working Directory can be specified either before or
after launching the ANSYS program.

Interactive Mode This is the primary mode of interaction between users and the
ANSYS program. It utilizes a platform known as the Graphical User Interface (GUI),
which consists of menus, dialog boxes, buttons, and various windows. Interactive
Mode is ideal for beginner ANSYS users as it offers an excellent learning
environment and is particularly effective for postprocessing tasks.

Batch Mode This method enables the use of the ANSYS program without
launching the GUI. It relies on an Input File written in ANSYS Parametric Design
Language (APDL), which supports parameters and common programming constructs
like DO loops and IF statements. These features make Batch Mode a highly powerful
tool for analysis. One notable advantage of Batch Mode is its efficiency in addressing
errors or mistakes during model generation. Users can simply modify the relevant
portion of the Input File and reload it, significantly saving time.

Combined Mode This method combines Interactive and Batch Modes, enabling
the user to activate the GUI while utilizing an Input File. Typically, the Input File is
used to generate the model and obtain the solution, while the GUI's Postprocessor is
employed to review the results. This approach leverages the key advantages of both
Interactive and Batch Modes.
2.2 ANSYS analysis approach

There are three main steps in a typical ANSYS analysis:

- Model generation:
 Simplifications, idealizations.
 Define materials/material properties.
 Generate finite element model (mesh).
- Solution:
 Specify boundary conditions.
 Obtain the solution.
- Review results:
 Plot/list results.
 Check for validity.

Each of these steps corresponds to a specific processor or processors within the

Processor Level in ANSYS. In particular, model generation is done in the
Preprocessor and application of loads and the solution is performed in the Solution
Processor. Finally, the results are viewed in the General Postprocessor and Time
History Postprocessor for steady-state (static) and transient (time-dependent)
problems, respectively. There are several other processors within the ANSYS
program. These mostly concern optimization and probabilistic-type problems. The
most commonly used processors are described in the following subsections.

2.2.1 Preprocessor

Model generation takes place in this processor, involving material definition,

solid model creation, and meshing. Key tasks within this processor include:

- Specify element type.

- Define real constants (if required by the element type).
- Define material properties.
 - Create the model geometry.
- Generate the mesh.

Although the boundary conditions can also be specified in this processor, it is

usually done in the Solution Processor.

2.2.2 Solution processor

This processor is used for obtaining the solution for the finite element model
that I generated within the Preprocessor. Crucial tasks within this processor are:

- Define analysis type and analysis options.

- Specify boundary conditions.
- Obtain solution.

2.2.3 General postprocessor

In this processor, the results at a specific time (if the analysis type is transient)
over the entire or a portion of the model is reviewed. This includes the plotting of
contours, vector displays, deformed shapes, and listings of the results in tabular
format.

2.2.4 Time History Postprocessor

This processor is used to review results at specific points in time (if the analysis
type is transient). Similar to the General Postprocessor, it provides graphical
variations and tabular listings of results data as functions of time.

2.3 File Structure

Several files are created during a typical ANSYS analysis. Some of these files
are in ASCII format while the others are binary. Brief descriptions of common file
types
are given below.
2.3.1 Database File
During a typical ANSYS analysis, input and output data reside in memory until
they are saved in a Database File, which is saved in the Working Directory. The
syntax
for the name of the Database File is jobname.db. This binary file includes the element
type, material properties, geometry (solid model), mesh (nodal coordinates and
element connectivity), and the results if a solution is obtained. Once the Database File
is saved, the user can resume from this file at any time. There are three distinct ways
to save and resume the Database File:
- Use the Utility Menu.
- Click on SAVE_DB or RESUM_DB button on the ANSYS Toolbar.
- Issue the command SAVE or RESUME in the Input Field.

2.3.2 Log File

The Log File is an ASCII file, which is created (or resumed) immediately upon
entering ANSYS. Every action taken by the user is stored sequentially in this file in
command format (ANSYS Parametric Design Language (APDL)). The syntax for the
name of the Log File, which is also saved in the Working Directory, is jobname.log. If
jobname.log already exists in the Working Directory, ANSYS appends the newly
executed actions instead of overwriting the file. The Log File can be utilized to:
- Understand how an analysis was performed by another user.
- Learn the command equivalents of the actions taken within ANSYS.

2.4 Using the ANSYS Help System

Information on ANSYS procedures, commands, and concepts can be found in
the ANSYS Help System. The importance of knowing how to use the Help System
cannot be overemphasized. It can be accessed within the Graphical User Interface
(GUI) in three ways:
- By choosing the Help menu item under Utility Menu.
- By pressing the Help button within dialog boxes.
- By entering the HELP command directly in the Input Field.
 The Help System is also available as a stand-alone program outside of ANSYS.
The user can bring up the desired help topic by choosing it from the system’s table of
contents or index, through a word search, or by choosing a hypertext link. The Help
System is built on the HTML platform in the form of web pages. There are three tabs
on the left of the Help Window: Contents, Index, and Search. The help pages are
displayed on the right side of the Help Window.

3. Linear and nonlinear in structural analysis

3.1 Linear structural analysis

A linear analysis is performed when a structure is anticipated to behave in a
linear manner. The deformation and load-bearing capacity can be assessed using one
of the available analysis types in ANSYS, either static or dynamic, depending on the
type of applied load. If the loading is part of the solution for structural stability, a
buckling analysis is carried out. For structures subjected to thermal loads, the analysis
is termed thermomechanical.

3.1.1 Static analysis

The behavior of structures under static loading can be analyzed by employing
different types of elements within ANSYS. The nature of the structure dictates the
type of elements utilized in the analysis. Discrete or framed structures are suitable for
modeling with rod- and beam-type elements. However, the modeling of continuous
structures usually require a three-dimensional model with solid elements. Under
certain types of loading and geometric conditions, the three-dimensional type of
analysis can be idealized as a two-dimensional analysis. If the component is subjected
to in-plane loading only and its thickness is small with respect to the other length
dimensions, it is idealized as a plane stress condition. If the component with a uniform
cross section is long in the depth direction and is subjected to a uniform loading along
the depth direction, it is idealized as a plane strain condition. If the component has a
circular cross section and is subjected to uniform and concentric loading, it possesses
axisymmetric. If thin structural components are subjected to lateral loading, the plate
and shell elements are suitable for analysis.

3.1.2 Assumptions of linear analysis

Linear structural analysis is based on two fundamental assumptions:
- Material linearity – i.e., the structures are composed of linear elastic material
( following the Hooke’s law)
- Geometric linearity implying that the structural deformations are so small that
the equations of equilibrium can be expressed in the undeformed geometry of
the structure.

3.2 Nonlinear structural analysis

A nonlinear structural analysis is required when the load-displacement
relationship is nonlinear, including cases where the stress-strain relationship is a
nonlinear function of stress, strain, and/or time. This also applies when large
displacements lead to changes in geometry, irreversible structural behavior occurs
upon removal of external loads, or there are changes in boundary conditions, such as
alterations in contact area or the influence of the loading sequence on the structure’s
behavior. Structural nonlinearities can be categorized into geometric nonlinearity,
material nonlinearity, and contact or boundary nonlinearity.
Nonlinear analyses typically demand more computational time. Therefore,
when addressing nonlinear static problems, it can be beneficial to first solve a
simplified version of the problem without considering nonlinearities. The results from
the linear solution can quickly reveal errors in modeling, meshing, and boundary
condition application. Additionally, the linear solution can highlight areas with high
stress gradients, helping the user refine the mesh in those regions.
In nonlinear analyses, it is crucial to apply all available simplifications to
enhance convergence and minimize computational costs. For instance, if the problem
can be approximated using plane stress or plane strain assumptions, the user should
take advantage of this simplification. In our project, we are concerned about geometric
nonlinearity only.

3.2.1 Geometric Nonlinearity

Geometric nonlinearities occur due to large strains, small strains with finite
displacements and/or rotations, and the loss of structural stability. Large strains,
exceeding 5%, can be found in rubber structures and metal forming. Slender structures
like bars and thin plates may experience significant displacements and rotations
despite having small strains. Structures that are initially stressed with small strains and
displacements can lose stability through buckling.

3.2.2 Differences between linear and nonlinear analysis

Nonlinear analysis still based on linear’s analysis assumptions, but the most
highlight differences are:

- Material nonlinearity - i.e., the material in more conditions ( buckling,

collapse ) instead of only elastic condition.
- Large deformation, the relationship between the applied forces and the
resulting displacements is nonlinear.
- Iterative Solution Process, due to the nonlinear nature of the problem, an
iterative solution process is required, such as the Newton-Raphson method, to
update the equilibrium state of the system at each step.

And there are many assumptions such as consider internal force,nonlinear

boundary conditions, finite displacements, change in geometry,...

3.2.3 Purpose of nonlinear analysis

- Save material: Nonlinear analysis can provide insights into the post-yield
behavior of structures, helping to understand how a structure behaves beyond
its elastic range, which is critical for safety and design under extreme
conditions.
 - Improved Prediction of Failure: Nonlinear analysis can better predict the point
at which a structure may fail due to excessive deformation, material yield, or
instability. Linear analysis typically fails to capture these failure modes
because it assumes elastic behavior.
- More Accurate for Real-World Applications: Nonlinear analysis is essential for
real-world engineering problems, where structures often experience large
displacements, complex material behavior, and other nonlinear effects that
linear analysis cannot accurately predict.

In summary, nonlinear analysis provides a more accurate and comprehensive

tool for understanding complex structural behaviors that linear analysis cannot
capture, especially in cases involving large deformations, material nonlinearity, and
instability.

4. Solving problem
- Problem statement: NonLinear Analysis of a Cantilever Beam
Follow a given file to solve a simple geometric nonlinear analysis of the beam:

To solve this problem, the load will be added incrementally. After each
increment, the stiffness matrix will be adjusted before increasing the load.
The solution will be compared to the equivalent solution using a linear
response.
- Units issues: we need to convert these parameters to solve this problem:
 Lengths: 5∈¿ 127 mm
  Beam section: H=0.125∈¿3.175 mm ; B=0.25∈¿ 6.35 mm
 Young’s modulus: 30e6 psi ¿206850 MPa
 Poisson's ratio: 0.3
 Element size of 10∈¿ 2.54 mm
 Load: 100 lb⋅∈¿ 11300 Nmm

4.1 Solving problem by Graphical User Interface ( GUI )

4.1.1 Nonlinear analysis

 Preprocessing: Defining the Problem

1. Give example a Title
Click File > Change Jobname > Enter the name

2. Define Element Types

Preprocessor > Element Type > Add/Edit/Delete…> Add…> Beam > 2 node 188
For this problem we will use the BEAM188. This element has 6 degrees of
freedom ( translation and rotation about X, Y, Z axis).
3. Define Element Material Properties
Preprocessor > Material Props > Material Models > Structural > Linear > Elastic >
Isotropic
In the window that appears, enter the following geometric properties for steel:
i. Young's modulus EX: 206850 MPa
ii. Poisson's Ratio PRXY: 0.3

4. Define the Section

Sections > Beam > Common Section > Enter the Name and Geometric parameters
 Because in Beam188, we can not enter Real constant, we add the geometric
properties in Sections

5. Create Keypoints
Preprocessor > Modeling > Create > Keypoints > In Active CS
We are going to define 2 keypoints (the beam vertices) for this structure to create a
beam with a length of 127 mm:

Keypoint Coordinates(x,y,z)

1 (0,0,0)
 2 (127,0,0)

6. Define Lines
 Preprocessor > Modeling > Create > Lines > Lines > Straight Line
Then we pick Keypoint 1 and Keypoint 2 to connect them by a line.

7. Define Mesh Size

Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines…
For this example we will specify an element edge length of 2.54 mm (50 element
divisions along the line).
8. Mesh the frame
Preprocessor > Meshing > Mesh > Lines > click 'Pick All'
  Solution: Assigning Loads and Solving
1. Define Analysis Type
Solution > New Analysis > Static

2. Set Solution Controls

Select Solution > Analysis Type > Sol'n Control...
The following image will appear:
Ensure the following selections are made (as shown above):
A. Ensure Large Static Displacements are permitted (this will include the
effects of large deflection in the results)
B. Ensure Automatic time stepping is on. Automatic time stepping allows
ANSYS to determine appropriate sizes to break the load steps into. Decreasing the
step size usually ensures better accuracy, however, this takes time. The Automatic
Time Step feature will determine an appropriate balance. This feature also activates
the ANSYS bisection feature which will allow recovery if convergence fails.
C. Enter 5 as the number of substeps. This will set the initial substep to 1/5 th
of the total load. The following example explains this: Assume that the applied load is
11300 Nmm. If the Automatic Time Stepping was off, there would be 5 load steps
(each increasing by 1/5 th of the total load)
Now, with the Automatic Time Stepping is on, the first step size will still be
2260 Nmm. However, the remaining substeps will be determined based on the
response of the material due to the previous load increment.
 D. Enter a maximum number of substeps of 1000. This stops the program if the
solution does not converge after 1000 steps.
E. Enter a minimum number of substeps of 1.
F. Ensure all solution items are written to a results file.

 Apply Constraints
Solution > Define Loads > Apply > Structural > Displacement > On Keypoints
Fix Keypoint 1 (ie all DOFs constrained).

3. Apply Loads
Solution > Define Loads > Apply > Structural > Force/Moment > On
Keypoints
Place a -11300 N moment in the FY direction at the right end of the beam
(Keypoint 2)
4. Solve the System
Solution > Solve > Current LS
 General Postprocessing: Viewing the Results
1. View the deformed shape
General Postproc > Plot Results > Deformed Shape... > Def + undeformed
2. View the deflection contour plot
General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF
solution, Y - Component of displacement
3. List Horizontal Displacement
General Postproc > List Results > Nodal Solution...> DOF solution, X-
Component of displacement
4.1.2 Linear analysis

Preprocessing: Defining the problem

1. Give example a Title
Click File > Change Jobname > Enter the name
2. Define Element Types
Preprocessor > Element Type > Add/Edit/Delete…> Add…> Beam > 2
node 188
For this problem we will use the BEAM188. This element has 6 degrees
of freedom ( translation and rotation about X, Y, Z axis).

3. Define Element Material Properties

Preprocessor > Material Props > Material Models > Structural > Linear
> Elastic > Isotropic
In the window that appears, enter the following geometric properties for
steel: i. Young's modulus EX: 206850 MPa
ii. Poisson's Ratio PRXY: 0.3
4. Define the Section
Sections > Beam > Common Section > Enter the Name and Geometric
parameters
Because in Beam188, we can not enter Real constant, we add the
geometric properties in Sections
5. Create Keypoints
Preprocessor > Modeling > Create > Keypoints > In Active CS
We are going to define 2 keypoints (the beam vertices) for this structure
to create a beam with a length of 127 mm:

Keypoint Coordinates(x,y,z)

1 (0,0,0)

2 (127,0,0)
6. Define Lines
Preprocessor > Modeling > Create > Lines > Lines > Straight Line
Then we pick Keypoint 1 and Keypoint 2 to connect them by a line.
7. Define Mesh Size
Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All
Lines…
For this example we will specify an element edge length of 2.54 mm (50
element divisions along the line).

8. Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'

 Solution: Assigning Loads and Solving

1. Define Analysis Type
Solution > New Analysis > Static.
2. Apply Constraints
Solution > Define Loads > Apply > Structural > Displacement > On Keypoints
Fix Keypoint 1 (ie all DOFs constrained).

3. Apply Loads
 Solution > Define Loads > Apply > Structural > Force/Moment > On
Keypoints
Place a −11300 N moment in the FY direction at the right end of the beam
(Keypoint 2)

Solve the System

Solution > Solve > Current LS
 General Postprocessing: Viewing the Results
1. View the deformed shape
General Postproc > Plot Results > Deformed Shape... > Def + undeformed
2. View the deflection contour plot
General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF
solution, Y - Component of displacement
3. List Horizontal Displacement
General Postproc > List Results > Nodal Solution...> DOF solution, X-
Component of displacement
4.2 Solving problem by ANSYS Parametric Design Language ( APDL)
APDL stands for ANSYS Parametric Design Language. It is a scripting
language to automate common tasks or even build your model in terms of parameters
(variables). APDL features macros, if-then-else branching, do-loops, and scalar,
vector and matrix operations. APDL is the foundation for sophisticated features such
as design optimization and adaptive meshing. In this chapter, we discuss some
important elements of Ansys-APDL.
To get the code from our GUI operation, we follow the steps:
List > File > Log File > Copy code
To enter the code to operate, we follow the steps:
 File > Read Input from > Select your code

4.2.1 Code for Linear Analysis of Cantilever Beam:

/prep7 ! Start preprocessor
/title, Linear Analysis of Cantilever Beam

k,1,0,0,0 ! Define keypoints

k,2,127,0,0 ! 127 mm beam length

l,1,2 ! Define line

et,1,beam188 ! Beam element type

SECTYPE, 1, BEAM, RECT, beam, 0 ! Specifies the type of cross-section
for a beam element.
SECOFFSET, CENT ! Specifies that the cross-section is
centered at its geometric centroid.
SECDATA,6.35,3.175,0,0,0,0,0,0,0,0,0,0 ! Specifies the geometric properties
of the rectangular cross-section
mp,ex,1,206850 ! Young's Modulus (in MPa)
mp,prxy,1,0.3 ! Poisson's ratio

esize,2.54 ! Element size of 2.54 mm

lmesh,all ! Mesh the line

finish ! Stop preprocessor

/solu ! Start solution phase

dk,1,all ! Constrain all DOF on ground

 fk,2,fy,-11298.483 ! Applied moment in Nmm

solve ! Solve the problem

4.2.2. Code for Nonlinear Analysis of Cantilever Beam

/prep7 ! Start preprocessor
/title, NonLinear Analysis of Cantilever Beam

k,1,0,0,0 ! Define keypoints

k,2,127,0,0 ! 127 mm beam length

l,1,2 ! Define line

et,1,beam188 ! Beam element type

SECTYPE, 1, BEAM, RECT, beam, 0 ! Specifies the type of cross-section
for a beam element.
SECOFFSET, CENT ! Specifies that the cross-section is
centered at its geometric centroid.
SECDATA,6.35,3.175,0,0,0,0,0,0,0,0,0,0 ! Specifies the geometric properties
of the rectangular cross-section
mp,ex,1,206850 ! Young's Modulus (in MPa)
mp,prxy,1,0.3 ! Poisson's ratio

esize,2.54 ! Element size of 2.54 mm

lmesh,all ! Mesh the line

finish ! Stop preprocessor

/solu ! Start solution phase

antype,static ! Static analysis
nlgeom,on ! Turn on non-linear geometry analysis

autots,on ! Auto time stepping

nsubst,5,1000,1 ! Size of first substep = 1/5 of the total
load, max # substeps=10
outres,all,all ! Save results of all iterations

dk,1,all ! Constrain all DOF on ground

fk,2,fy,-11298.483 ! Applied moment in Nmm

solve ! Solve the problem

5. Comparison the results and conclusion between Linear and Nonlinear

Analysis:

5.1 The deformed shape:

 The linear analysis
  The nonlinearity analysis

After using ANSYS for simulation, we can see that the results align with the
theoretical predictions. Linear analysis assumes small deformations and a proportional
relationship between loads and displacements, which becomes inaccurate under high
loads or significant bending. Nonlinear analysis considers the changing geometry of
the structure during deformation, including effects like large rotations and stress
redistribution. As a result, it provides a more accurate representation of the beam's
behavior under substantial loads, capturing larger deflections that linear models
underestimate.

5.2 The deflection contour plot

  The Nonlinear analysis

 The Linear analysis

In Linear Analysis: The deflection appears smooth and uniform, with

deformation proportional to the applied load, consistent with small deformation
assumptions. The beam exhibits no significant geometric changes.
In Nonlinear Analysis: The deflection is more pronounced, showing large
deformation effects and curvature. The nonlinear model accounts for geometric
changes, resulting in a more realistic representation under high loads. This highlights
the significance of nonlinear analysis when large deflections are involved.

5.3 List horizontal displacement:

 The Nonlinear analysis:
  The Linear Analysis:

In a linear model, horizontal deflection is ignored because it assumes small

deformations and neglects geometric changes. Transverse loads only cause vertical
deflection, while axial stretching from bending is considered negligible. Horizontal
deflection appears only in nonlinear models that include large deformation effects.