1. Product failure analysis using Explicit dynamics using ANSYS
Workbench
1 ABSTRACT
To estimate the various mechanical properties that are changed when the object is beenfreely displaced under
the gravity, which are the taken into consideration in the field of Industrial designand Product design and
Quality Control section in the industries and designer’s studios. This is usually made by the drop test equipment
which are automatic and semi‐ automatic in nature. This is made virtually with help of simulation method.
Electronic devices are being displaced by the height of 50 mm and the concrete floor is taken for the case
study. The explicit solver named as AUTODYN is used to simulate the iterations and the hexagonal meshing is
taken for the accurate resulting of the structuralobjectives. The basic objects are crack detection and facture
detection .
Case study objects
1) Phones (iPhone 6)
2) Tablets (iPad mini)
3) MP3 Devices (iPod Shuffle)
Members of the project
Batch no:
Name Id number Mail‐ id
SOMSAI KUMAR .K 13007265 Somasai.kompalli@gmail.com
ANWAR HUSSAIN 13007270 Sk.anwarhyssain@gmail.com
NAGA SAI RAM .GOPISETTI 13007293 Nagasairam11@gmail.com
HARIESWAR. A 13007295 Harueswar751995@gmail.com
ARUN KUMAR.N.J 13007297 Arunkumarak97@gmail.com

2. Introduction to Finite Element Analysis.
In mathematics, the finite element method (FEM) is a numerical technique for finding approximate solutions
to boundary value problems for partial differential equations. It uses subdivision of a whole problem domain into
simpler parts, called finite elements, and vibrational methods from the calculus of variations to solve the problem
by minimizing an associated error function. Analogous to the idea that connecting many tiny straight lines can
approximate a larger circle, FEM encompasses methods for connecting many simple element equations over many
small subdomains, named finite elements, to approximate a more complex equation over a larger domain.
The subdivision of a whole domain into simpler parts has several advantages:
• Accurate representation of complex geometry
• Inclusion of dissimilar material properties
• Easy representation of the total solution
• Capture of local effects.
A typical work out of the method involves (1) dividing the domain of the problem into a collection of subdomains,
with each subdomain represented by a set of element equations to the original problem, followed by (2)
systematically recombining all sets of element equations into a global system of equations for the final calculation.
The global system of equations has known solution techniques, and can be calculated from the initial values of the
original problem to obtain a numerical answer.
In the first step above, the element equations are simple equations that locally approximate the original complex
equations to be studied, where the original equations are often partial differential equations (PDE). To explain the
approximation in this process, FEM is commonly introduced as a special case of Galerkin method. The process, in
mathematical language, is to construct an integral of the inner product of the residual and the weight functions and
set the integral to zero. In simple terms, it is a procedure that minimizes the error of approximation by fitting trial
functions into the PDE. The residual is the error caused by the trial functions, and the weight functions
are polynomial approximation functions that project the residual. The process eliminates all the spatial derivatives
from the PDE, thus approximating the PDE locally with
• a set of algebraic equations for steady state problems,
• a set of ordinary differential equations for transient problems.
These equation sets are the element equations. They are linear if the underlying PDE is linear, and vice versa.
Algebraic equation sets that arise in the steady state problems are solved using numerical linear algebra methods,
while ordinary differential equation sets that arise in the transient problems are solved by numerical integration
using standard techniques such as Euler's method or the Runge-Kutta method.
In step (2) above, a global system of equations is generated from the element equations through a transformation of
coordinates from the subdomains' local nodes to the domain's global nodes. This spatial transformation includes
appropriate orientation adjustments as applied in relation to the reference coordinate system. The process is often
carried out by FEM software using coordinate data generated from the subdomains.

3. FEM is best understood from its practical application, known as finite element analysis (FEA). FEA as applied
in engineering is a computational tool for performing engineering analysis. It includes the use of mesh
generation techniques for dividing a complex problem into small elements, as well as the use of software program
coded with FEM algorithm. In applying FEA, the complex problem is usually a physical system with the
underlying physics such as the Euler-Bernoulli beam equation, the heat equation, or the Navier-Stokes
equations expressed in either PDE or integral equations, while the divided small elements of the complex problem
represent different areas in the physical system.
FEA is a good choice for analyzing problems over complicated domains (like cars and oil pipelines), when the
domain changes (as during a solid state reaction with a moving boundary), when the desired precision varies over
the entire domain, or when the solution lacks smoothness. For instance, in a frontal crash simulation it is possible
to increase prediction accuracy in "important" areas like the front of the car and reduce it in its rear (thus reducing
cost of the simulation). Another example would be in numerical weather prediction, where it is more important to
have accurate predictions over developing highly nonlinear phenomena (such as tropical cyclones in the
atmosphere, or eddies in the ocean) rather than relatively calm areas.
Methods and solvers used in the case study.
Well out of many methods the following methods are in the commercial and widely used methods where changed
into solvers too.
1. AEM
2. Generalized finite element method
3. hp-FEM
4. hpk-FEM
5. XFEM
6. S-FEM
7. Spectral element method
8. Meshfree methods
9. Discontinuous Galerkin methods
10. Finite element limit analysis
11. Stretched grid method
As above we can see that solvers are those which are algorithms which take control of situation and problem
specification along with initial conditions. Solvers play important role in solution solving. Well this are
computational techniques which has numerical set of procedures mainly matrix computation and manipulation.
But there are multiple and complicated solvers which have wide variety of parameter control and complicated
analyzation pipeline so the following are the solvers used in this case study this may be in RADIOSS solver too but
jointly coded by ANSYS too.
The solver used in this case study is AUTODYN which is an explicit dynamic solver in ANSYS WORKBENCH.

4. Engineering simulation can help Improve the survivability of buildings, vehicles, soldiers and police personnel.
Using ANSYS Autodyn engineers can design and virtually test simple and complex active armor to protect troops
in battle from improvised explosive devices (IED), rocket-propelled grenades, shaped charges and other threats.
This same software used to model space debris impact on satellites, can also be used to design common liquid
containers such as water and detergent bottles. Using ANSYS Autodyn can help us to improve a wide variety of
products, reduce their cost and most importantly decrease time to market. ANSYS Autodyn software is a versatile
explicit analysis tool for modeling the nonlinear dynamics of solids, fluids, gases and their interactions. The product
has been developed to provide advanced capabilities within a robust, easy-to-use software tool. Simulation projects
can be completed with significantly less effort, less time and lower labor costs than with other explicit programs.
This high productivity is a result of the easy-to-use, quick-to-learn, intuitive, interactive graphical interface
implemented. Time and effort are saved in problem setup and analysis by automatic options to define contact, by
coupling interfaces and by minimizing input requirements using safe logical defaults.
1) The solver technology in ANSYS Autodyn provides:
2) Finite element solvers for computational structural dynamics (FE)
3) Finite volume solvers for fast transient computational fluid dynamics (CFD)
4) Mesh-free particle solvers for high velocities, large deformation and fragmentation (SPH)
5) Multi-solver coupling for multi physics solutions including coupling between FE, CFD and SPH
6) A wide suite of material models incorporating constitutive response and coupled thermodynamics
7) Serial and parallel computation on shared and distributed memory systems
The problem time magnitude is of 0.1s which is completely nonlinear and explicit method. The following is simple
visualization of the algorithm framed in RADIOSS and FEA solver. The following is time dependent which is
explicit time integration.
[M][u’’ ] =[ F ] + [ Rc ]………………………………………(1)
Where
[ M ] is mass matrix which is diagonal matrix.
[ u’’ ] is the nodal displacements matrix.
[ F ] is the force matrix
[ Rc ] is the reaction matrix which is unknown.
But [ F ] = [ FINT ] +[ FEXT ] – [ C ] [u’]………………………(2)
Where
[FINT ] is force acting on interior if the body generally taken as 0
[ FEXT ] is the force acting on the body generally impact force.
[ C ] is the damping matrix for this case this is taken as 0 since the material are not elastic in nature.
[u’] is the time derivation .
The above equation is sent into nodal displacement derivative quantization following iteration is made as follows
u’t + Δt
- u’ t
+ [( 1 + Ψ )t
u’’+ Ψ t +Δt
u’’] Δt…………………..(3)
The iteration steps is taken by special procesure called as N-R iterative process

5. [ K]i
[ Δu ] = [ F ]i
+ Rc
i+1
…………………………………....…( 4)
where [ K ] is called as stiffness matrix or can be taken as mass vector.
And the N R iteration is
ui+1
= ui
+ Δu …………………………………………………….( 4i)
the following is the basic eularaian algorithm with a custom change for differential time based solution solver.
ut’’ =
1
∆𝑡𝑡2 [ u t + Δt - 2ut + u t + Δt ]
the above equational solution is sent in to equation ( 1 ) and the R C values are computed in the iteration which are
the impact forces of the object and their manipulations result in deformation.
The final deformation analysis made bt autodyne is as follows.
Ut +Δt = Δt2
M-1
[ [ FEXT ]t – [FINT]t+ Rt + Δt] + 2ut – ut – Δt …………..(5).
This final equation is used in the numerical simulation of the explicit dynamic module in ANSYS workbench.
MODEL’S USED FOR THE ANALYSIS AND INVESTIGATION
As we see craze of innovation and increase of structural optimization exploration employed by many product
designers and consumer based electronics companies, now employing this techniques in recent years by Apple the
product line of iPhone 6S and iPad mini and beginning of structural optimization with iPod nano many rumors have
creeped into market that product failed structurally and impact condition for the higher nominal velocities the
analysis is conducted by 50 m/s. the CAD test models are show as follows
As the above we can see the solid structural models of the various devices, so following gives us the mesh model
of the above CAD test models. The mesh used in the test procedure is given in following table.
object name Mesh
physics preferences Explicit
Element size
Smoothing High
Minimum edge length 1.e-003 m
Figure 2 showing the iPod nano Figure 3 showing the iPhone 6sFigure 1 showing the iPad mini

6. Table 1.1 showingthe mesh data of iPad mini test model made in ANSYS.
Objective Data
Material Aluminum with concrete contact
Mesh type Triangular
Number of nodes for test objective 13554
Number of elements for test objectives 53706
Transition Slow
Figure 2.2 showing the mesh data of iPod nano test model made in ANSYS.
Objective Data
Material Alumium with concrat contact
Mesh type Triangular
Number of nodes for test object 13554
Number of elements for test objective 53706
Transition Slow

7. Objective Data
Material Aluminum with concrete contact
Mesh type Triangular
Number of nodes in test objective 9842
Number of elements in test objective 37940
Transition Smooth
Figure 3.3 showing the mesh data of iPhone 6S test model made in ANSYS.
Test procedure for explicit dynamic analysis in ANSYS workbench 12.1
The following tree diagram gives the procedure of the conducting explicit dynamic analysis in ansys workbench.

8. ANSYS Procedure
Drage explicit dynamics ( ANSYS ) from the Analysis systems.
Double tap on engineering data
Double tap on general materials
Add alumium and concreat by pressing + sign
Update the project by clicking lighting bolt and return to the project.
Right click on geometry and click import .
Browse for the file say IGES or .para or some other file formats understood by the
Double tap on the geometry after importing
This will open DESIGN MODELER
Select some plane that is exact bottom of the object I choose XY plane
and draw the rectangle
This will be the base
Select the extrude command
In detail view select the dimensions and direction as both side symmetrical and
generate by clicking the lighting bolt and click close and return to project.
Double tap on model
Under project tree in outline, update mesh by clicking the lighting bolt in
mesh icon.
Click on geometry to expand and click on first solid and apply the
material.
Repeat the same for solid 2
The connections and coordinate system are predefined by the system
itself.
Close the window and return to the project main page

9. Double tap on setup
Click on initial conditions and select the velocity
In details tab select the geometry and set the magnitude and direct by click the plane in
downward
Click on analysis settings and edit maximum number of cycles as
100 and end time as 1e-003 s
In same tab select the inertia select the standard earth gravity and
select the direction of the gravity basically along -y axis And under
same tab supports click fixed support and select the solid 2 upper face
by face selection tool.
Double tap on solution
Click on deformation and directional deformation
In details tab of directional deformation select geometry select solid 1
and orientation in axis of impact
Run the solution by clicking the lighting bolt with solve icon The
solution serpents upon the number of cycles and processing power of the
computer.
In graphics area select the report preview and publish for getting
the reports
Exit by saving the project

10. Test results and discussions.
The following are the test results made on the test objectives the results include only deformation which is the main
aim of this case study.
Figure 1.0 showing the deformation contors of iPad mini in y axis.
Figure 1.1 showing the isosurface and propagation of deformation in iPad mini.

11. figure 2.0 showing the directional deformation contors of iPod nano in Z axix.
Figure 2.1 showing the directional deformation isosurface propagation of iPod mini

12. figure 3.0 showing the deformation contors of iPhone 6S in the direction of the y axix .
figure 3.1 showing the isosurfae propagation in the direction of the y axis
the comparitive analysis of the above test results are done I following discussions.

13. Graph 1.0 showing the test results of the objects.
From the above graph we can see that minimum and maximum results of the test objectives and the point line in
the maximum deformation made by the test objectives have no change and approximately line on same line and the
design is that the maximum deformation that can allow is of the range between -0.000001m to -0.0000005m which
is very negligible but for the minimum values this there is a lot of data interpretation. The iPod Nano and iPhone
6S shows the approximately equal and adjacent incremental relationships but for the iPad mini it shows the
minimum value of -1.1608e-05 which altered the trend of the deformation results. But the maximum and minimum
values of the iPad mini have the difference relation that to attain the maximum value.
From all the above we can summarize that the smaller the deformation greater the safety of the object or the design
so the average value of the all the objects is lesser in iPad mini so this design structure holds good in the test
conditions. The least in design is iPod Nano and iPhone 6S this also justifies the rumors around the iPhone 6S.

14. REFERENCES:
1) Introduction to Finite Element Analysis https://en.wikipedia.org/wiki/Finite_element_method
2) “Insight into an implicit time integration scheme for structural dynamics” by Klaus-Jürgen Bathe ,
Gunwoo Noh from Massachusetts Institute of Technology Cambridge, MA 02139, United States from
journal of Computers and Structures , ELSEVIER
3) “2nd European Hyperworks Technology Conference (EHTC 2008), Sept 30–Oct 1, 2008, Strasbourg,
France” by Zhi-Qiang Feng, Jean-Michel Cros, Christine Renaud Laboratoire de Mécanique et
d’Énergétique d’Évry Université d’Évry - Val d’Essonne, France. With collaboration with Altair
HyperWorks.
4) Introduction to AUTODYN
http://www.ansys.com/Products/Simulation+Technology/Structural+Analysis/Explicit+Dynamics/ANSY
S+Autodyn from ANSYS TECHNICAL DOCUMENTATION.