DESIGN AND STRUCTURAL ANALYSIS OF HIGH
SPEED HELICAL GEAR USING ANSYS
ABSTRACT
Marine engines are among heavy-duty machineries, which need to be taken care of in the best
way during prototype development stages. These engines are operated at very high speeds which
induce large stresses and deflections in the gears as well as in other rotating components. For the
safe functioning of the engine, these stresses and deflections have to be minimized.
In this project, static-structural analysis on a high speed helical gear used in marine engines,
have been performed. The dimensions of the model have been arrived at by
theoretical methods. The stresses generated and the deflections of the tooth have been
analyzed for different materials. Finall y the results obtained by theoretical anal ysis
and Finite Element Anal ysis are compared to check the correctness. A conclusion
has been arrived on the material which is best suited for the marine engines based on the results.
TABLE OF CONTENTS
CHAPTER
DESCRIPTION
Abstract
Acknowledgment
1.
Introduction
1
1.1
Advantages of Gear Drives
2
1.2
Disadvantages of Gear Drives
2
1.3
General classifications of gears
3
1.3.1
According to position of axes of shafts
3
1.3.2
According to the peripheral velocity of the gears
3
1.3.3
According to the type of gearing
3
1.3.4
According to the position of teeth on gear surface
3
1.3.5
According to the position of axes of the shafts
3
Marine engines
7
Reciprocating Diesel Engines
7
Finite Element Methods
9
2.
2.1
3.
3.1
Terms commonly used in Finite Element Method
11
3.2
General Description of FEM
14
3.3
Advantages of FEM
17
3.4
Limitation
19
3.5
Basic Approach to FEA Software
21
3.5.1
Pre Processor
21
3.5.1.1
Building of Model
21
3.5.1.2
Creation of Finite Element Model for Meshing
21
3.5.2
Solver
23
3.5.3
Post Processor
24
FEA software-ANSYS
25
4.1
Introduction to ANSYS program
25
4.2
Evolution of ANSYS Program
25
4.3
Overview of the Program
26
4.4
Reducing design, manufacturing costs using Ansys
29
4.5
Types of Structural Analysis
31
4.5.1
Structural Static Analysis
32
4.6
Procedure for Ansys Analysis
32
4.6.1
Build the model
32
4.6.2
Obtain the solution
33
4.6.2.1
Pre-processor
34
4.6.2.2
Solution
38
4.6.2.3
Post processor
38
Theoretical Design calculations
39
4.
5.
5.1
Calculations for Steel
39
5.1.1
Design of Hole
46
5.2
Calculations for Aluminium Alloy
47
5.2.1
Design of Hole
54
Definition of Problem
55
6.1
Element considered for static analysis
55
6.2
Assumptions and Restrictions
56
6.3
Materials Used
57
6.4
Mesh Generation
57
6.5
Boundary conditions
58
Experimental Results
59
7.1
Results for Steel
59
7.2
Results for Ceramics
67
Discussion of Results
71
8.1
Results for Steel as Material
71
8.2
Results for Ceramics as Material
72
8.3
Results Comparison for Steel
74
8.4
Results Comparison for Ceramics
75
Conclusion
77
10.
Future Scope of Work
78
11.
References
79
6.
7.
8.
9.
CHAPTER 1
INTRODUCTION
Gears are most commonly used for power transmission in all the modern devices. These
toothed wheels are used to change the speed or power between input and output. They have
gained wide range of acceptance in all kinds of applications and have been used extensively in
the high-speed marine engines.
In the present era of sophisticated technology, gear design has evolved to a high
degree of perfection. The design and manufacture of precision cut gears, made from
materials of high strength, have made it possible to produce gears which are capable of
transmitting extremely large loads at extremely high circumferential speeds with very
little noise, vibration and other undesirable aspects of gear drives.
A gear is a toothed wheel having a special tooth space of profile enabling it to mesh
smoothly with other gears and power transmission takes place from one shaft to other by means
of successive engagement of teeth.
Gears operate in pairs, the smallest of the pair being called “pinion” and the larger one
“gear”. Usually the pinion drives the gear and the system acts as a speed reducer and torque
converter.
1.1 ADVANTAGES OF GEAR DRIVES:
The following are the advantages of the gear drives compared to other drives.
 Gear drives are more compact in construction due to relatively small centre distance.
 Gears are used where the constant velocity ratio is desired.
 Gears can be operated at higher speeds.
 It has higher efficiency.
 Reliability in service.
 It has wide transmitted power range due to gear shifting facility.
 Gear offers lighter loads on the shafts and bearings.
 Gear can change the direction of axis of rotation.
1.2 DISADVANTAGES OF GEAR DRIVES:
 Not suitable for the shafts which are at longer center distance.
 Manufacturing is complex. It needs special tools and equipment.
 Require perfect alignment of shafts.
 Requires more attention to lubrication.
 The error in cutting teeth may cause vibration and noise during operation.
1.3 GENERAL CLASSIFICATION OF GEARS:
Although the types and the modalities of gear design vary widely for mechanical power
transmission, gears are generally categorized into the following types.
1.3.1 ACCORDING TO THE POSITION OF AXES OF THE SHAFTS:
The axes of the two shafts between which the motion is to be transmitted, may be
( a) Parallel, (b) Intersecting, and (c) Non-Intersecting and Non-parallel
1.3.2 ACCORDING TO THE PERIPHERAL VELOCITY OF THE GEARS:
The gears, according to the peripheral velocity of the gears, may be classified as: (a) Low
Velocity, (b) Medium Velocity and (c) High Velocity.
1.3.3 ACCORDING TO TYPE OF GEARING:
The gears, according to the type of gearing may be classified as (a) External Gearing, (b)
Internal Gearing, (c) Rack and Pinion.
1.3.4 ACCORDING TO THE POSITION OF THE TEETH ON THE GEAR SURFACE:
The teeth on the gear surface may be (a) Straight (b) Inclined (c) Curved.
1.3.5 ACCORDING TO THE POSITION OF AXES OF THE SHAFTS:
Spur Gears: Spur gears are the simplest and most common type of gear. Their general form is
a cylinder or disk. The teeth project radially, and with these "straight-cut gears", the leading
edges of the teeth are aligned parallel to the axis of rotation. These gears can only mesh correctly
if they are fitted to parallel axles. Spur gears on non-parallel shafts can mesh, but only point
contact will be achieved, not line contact across the full width of the tooth; also the length of the
path of contact may be too short. This causes impact stress and noise. Spur gears make a
characteristic whine at high speeds and can not take as much torque as helical gears because their
teeth are receiving impact blows.
Fig: 1.1
Helical Gears: Helical gears offer a refinement over spur gears. The leading edges of the teeth
are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this
angling causes the tooth shape to be a segment of a helix. The angled teeth engage more
gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly
than spur gears. Helical gears also offer the possibility of using non-parallel shafts.
With parallel helical gears, each pair of teeth first makes contact at a single point at one side
of the gear wheel; a moving curve of contact then grows gradually across the tooth face. It may
span the entire width of the tooth for a time. Finally, it recedes until the teeth break contact at a
single point on the opposite side of the wheel. Thus force is taken up and released gradually.
.
Fig: 1.2
Double Helical Gears:
Double helical gears, also known as herringbone gears, overcome the problem of axial thrust
presented by 'single' helical gears by having teeth that set in a 'V' shape. Each gear in a double
helical gear can be thought of as two standards, but mirror image, helical gears stacked. This
cancels out the thrust since each half of the gear thrusts in the opposite direction. They can be
directly interchanged with spur gears without any need for different bearings.
Bevel Gears:
Bevel gears are essentially conically shaped, although the actual gear does not extend all the
way to the vertex (tip) of the cone that bound it. With two bevel gears in mesh, the vertices of
their two cones lie on a single point, and the shaft axes also intersect at that point. The angle
between the shafts can be anything except zero or 180 degrees. Bevel gears with equal numbers
of teeth and shaft axes at 90 degrees are called miter gears.
Fig: 1.3
Fig: 1.4
Worm Gears:
Worm gear is a special case of a spiral gear in which the larger wheel usually has hollowed or
concave shape such that a portion of the pitch diameter of the other gear is enveloped on it. The
smaller of the two wheels called the worm which also has a large spiral angle. The shafts may
have any angle between them, but normally it is 90°.The system can be non-throated, single
throated, double throated types.
Hypoid Gears:
These are similar to spiral bevel gears, but have non-intersecting axes i.e. the axes of pinion is
offset relative to the gear axis. However the plane containing the two axes is usually at right
angles to each other.
CHAPTER 2
MARINE ENGINES
2.1 RECIPROCATING DIESEL ENGINES:
The engine used in 99% of modern ships is diesel reciprocating engines. The rotating
crankshaft can power the propeller directly for slow speed engines, via a gearbox for medium
and high speed engines, or via an alternator and electric motor in diesel-electric vessels.
The reciprocating marine diesel engine first came into use in 1903 when the diesel electric
rivertanker Vandal was put in service by Branobel. Diesel engines soon offered greater
efficiency than the steam turbine, but for many years had an inferior power-to-space ratio.
Diesel engines today are broadly classified according to

Their operating cycle: two-stroke or four-stroke

Their construction: Crosshead, trunk, or opposed piston

Their speed
o
Slow speed: any engine with a maximum operating speed up to 300 revs/minute,
although most large 2-stroke slow speed diesel engines operate below 120
revs/minute. Some very long stroke engines have a maximum speed of around 80
revs/minute. The largest, most powerful engines in the world are slow speed, two
stroke, and crosshead diesels.
o
Medium speed: any engine with a maximum operating speed in the range 300-900
revs/minute. Many modern 4-stroke medium speed diesel engines have a
maximum operating speed of around 500 rpm.
o
High speed: any engine with a maximum operating speed above 900 revs/minute.
Most modern larger merchant ships use either slow speed, two stroke, crosshead engines, or
medium speed, four stroke, trunk engines. Some smaller vessels may use high speed diesel
engines.
The size of the different types of engines is an important factor in selecting what will be
installed in a new ship. Slow speed two-stroke engines are much taller, but the area needed,
length and width, is smaller than that needed for four-stroke medium speed diesel engines. As
space higher up in passenger ships and ferries is at a premium, these ships tend to use multiple
medium speed engines resulting in a longer, lower engine room than that needed for two-stroke
diesel engines. Multiple engine installations also give redundancy in the event of mechanical
failure of one or more engines and greater efficiency over a wider range of operating conditions.
As modern ships' propellers are at their most efficient at the operating speed of most slow
speed diesel engines, ships with these engines do not generally need gearboxes. Usually such
propulsion systems consist of either one or two propeller shafts each with its own direct drive
engine. Ships propelled by medium or high speed diesel engines may have one or two
(sometimes more) propellers, commonly with one or more engines driving each propeller shaft
through a gearbox.
CHAPTER 3
FINITE ELEMENT METHODS
The finite element method is numerical analysis technique for obtaining approximate
solutions to a wide variety of engineering problems. Because of its diversity and flexibility as an
analysis tool, it is receiving much attention in engineering schools and industries. In more and
more engineering situations today, we find that it is necessary to obtain approximate solutions to
problems rather than exact closed form solution.
It is not possible to obtain analytical mathematical solutions for many engineering problems.
An analytical solutions is a mathematical expression that gives the values of the desired
unknown quantity at any location in the body, as consequence it is valid for infinite number of
location in the body. For problems involving complex material properties and boundary
conditions, the engineer resorts to numerical methods that provides approximate, but acceptable
solutions.
The finite element method has become a powerful tool for the numerical solutions of a wide
range of engineering problems. It has developed simultaneously with the increasing use of the
high-speed electronic digital computers and with the growing emphasis on numerical methods
for engineering analysis. This method started as a generalization of the structural idea to some
problems of elastic continuum problem, started in terms of different equations or as an extrinum
problem.
The fundamental areas that have to be learned for working capability of finite element method
include:
 MATRIX ALGEBRA.
 SOLID MECHANICS.
 VARIATION
METHODS.
 COMPUTER SKILLS.
Matrix techniques are definitely most efficient and systematic way to handle algebra of finite
element method. Basically matrix algebra provides a scheme by which a large number of
equations can be stored and manipulated. Since vast majority of literature on the finite element
method treats problems in structural and continuum mechanics, including soil and rock
mechanics, the knowledge of these fields became necessary. It is useful to consider the finite
element procedure basically as a Variation approach. This conception has contributed
significantly to the convenience of formulating the method and to its generality.
The term “finite element” distinguishes the technique from the use of infinitesimal
“differential elements” used in calculus, differential equations. The method is also distinguished
from finite difference equations, for which although the steps in to which space is divided into
finite elements are finite in size; there is a little freedom in the shapes that the discrete steps can
take. F.E.A is a way to deal with structures that are more complex than dealt with analytically
using the partial differential equations.
F.E.A deals with complex boundaries better than finite difference equations and gives
answers to the ‘real world’ structural problems. It has been substantially extended scope during
the roughly forty years of its use.
F.E.A makes it possible it evaluate a detail and complex structure, in a computer during the
planning of the structure. The demonstration in the computer about the adequate strength of the
structure and possibility of improving design during planning can justify the cost of this analysis
work. F.E.A has also been known to increase the rating of the structures that were significantly
over design and build many decades ago.
In the absence of finite element analysis (or other numerical analysis), development of
structures must be based on hand calculations only. For complex structures, the simplifying
assumptions are required to make any calculations possible can lead to a conservative and heavy
design. A considerable factor of ignorance can remain as to whether the structure will be
adequate for all design loads. Significant changes in design involve expensive strain gauging to
evaluate strength and deformation.
3.1 TERMS COMMONLY USED IN FINITE ELEMENT METHOD:
 DESCRITIZATION: The process of selecting only a certain number of discrete points in
the body can be termed as Descritization.
 CONTINUUM: The continuum is the physical body, structure or solid being analyzed.
 NODE: The finite elements, which are interconnected at joints, are called nodes or nodal
points.
 ELEMENT: Small geometrical regular figures are called elements.
 DISPLACE MODELS: The nodal displacements, rotations and strains necessary to specify
completely deformation of finite element.
 DEGREE
OF FREEDOM:
The nodal displacements, rotations and strains necessary to
specify completely deformation of finite element.
 LOCAL
COORDINATE SYSTEM:
Local coordinate system is one that is defined for a
particular element and not necessary for the entire body or structure.
 GLOBAL
SYSTEM:
The coordinate system for the entire body is called the Global
coordinate system.
 NATURAL
COORDINATE SYSTEM:
Natural coordinate system is a local system, which
permits the specification of point within the element by a set of dimensionless numbers,
whose magnitudes never exceeds unity.
 INTERPOLATION FUNCTION: It is a function, which has unit value at one nodal point and
a zero value at all other nodal points.
 ASPECT
RATIO:
The aspect ratio describes the shapes of the element in the assemblage
for two dimensional elements; this parameter is defined as the ratio of largest dimension
of the element to the smallest dimension.
 FIELD VARIABLES: The principal unknowns of a problem are called the field variables.
PROCESS OF FINITE ELEMENT ANALYSIS:
Physical
Problems
[Fig: 3.1]
Change of Physical
Problems
Mathematical Model
Governed by
Different Equations,
Assumptions In

Geometry

Kinematics

Material Law

Loading

Boundary
Improve Mathematical Model
Conditions
etc
Finite
Element
Solution Choice of





Finite Element
Mesh Density
Solution
Parametric
Representation
Loading
Boundary
Conditions
Assessment of
accuracy of Finite
Element Solution of
Mathematical
Model
Define Mesh
3.2 GENERAL DESCRIPTION OF FEM:
In the finite element method, the actual continuum of body of matter like solid, liquid or gas is
represented as an assemblage of sub divisions called Finite elements. These elements are
considered to be inter connected at specified points known as nodes or nodal points. These
nodes usually lie on the element boundaries where an adjacent element is considered to be
connected.
Since the actual variation of the field variables (like Displacement, stress,
temperature, pressure and velocity) inside the continuum are is not know, we assume that the
variation of the field variable inside a finite element can be approximated by a simple function.
These approximating functions (also called interpolation models) are defined in terms of the
values at the nodes. When the field equations (like equilibrium equations) for the whole
continuum are written, the new unknown will be the nodal values of the field variable. By
solving the field equations, which are generally in the form of the matrix equations, the nodal
values of the field variables will be known. Once these are known, the approximating function
defines the field variable throughout the assemblage of elements.
The solution of a general continuum by the finite element method always follows as orderly
step-by-step process. The step-by-step procedure for static structural problem can be stated as
follows:
Step 1:- DESCRITIZATION OF STRUCTURE (DOMAIN).
The first step in the finite element method is to divide the structure of solution region in to sub
divisions or elements.
Step 2:- SELECTION OF PROPER INTERPOLATION MODEL.
Since the displacement (field variable) solution of a complex structure under any specified
load conditions cannot be predicted exactly, we assume some suitable solution, within an
element to approximate the unknown solution. The assumed solution must be simple and it
should satisfy certain convergence requirements.
Step 3:- DERIVATION
OF ELEMENT STIFFNESS MATRICES (CHARACTERISTIC MATRICES) AND
LOAD VECTORS.
From the assumed displacement model the stiffness matrix [K(e)] and the load vector P(e) of
element ‘e’ are to be derived by using either equilibrium conditions or a suitable Variation
principle.
Step 4:- ASSEMBLAGE OF ELEMENT EQUATIONS TO OBTAIN THE EQUILIBRIUM EQUATIONS.
Since the structure is composed of several finite elements, the individual element stiffness
matrices and load vectors are to be assembled in a suitable manner and the overall equilibrium
equation has to be formulated as
[K]φ = P
Where [K]
is called assembled stiffness matrix,
Φ
is called the vector of nodal displacement and
P
is the vector or nodal force for the complete structure.
Step 5:- SOLUTION OF SYSTEM EQUATION TO FIND NODAL
VALUES OF DISPLACEMENT (FIELD
VARIABLE)
The overall equilibrium equations have to be modified to account for the boundary conditions
of the problem. After the incorporation of the boundary conditions, the equilibrium equations can
be expressed as,
[K]φ = P
For linear problems, the vector ‘φ’ can be solved very easily. But for non-linear problems,
the solution has to be obtained in a sequence of steps, each step involving the modification of the
stiffness matrix [K] and ‘φ’ or the load vector P.
Step 6:- COMPUTATION OF ELEMENT STRAINS AND STRESSES.
From the known nodal displacements, if required, the element strains and stresses can be
computed by using the necessary equations of solid or structural mechanics.
In the above steps, the words indicated in brackets implement the general FEM step-by-step
procedure.
3.3 ADVANTAGES OF FEM:
The FEM is based on the concept of discretization. Nevertheless as either a variational or
residual approach, the technique recognizes the multi dimensional continuity of the body not
only does the idealizations portray the body as continuous but it also requires no separate
interpolation process to extend the approximate solution to every point within the continuum.
Despite the fact that the solution is obtained at a finite number of discrete node points, the
formation of field variable models inherently provides a solution at all other locations in the
body. In contrast to other variational and residual approaches, the FEM does not require trail
solutions, which must all, apply to the entire multi dimensional continuum. The use of separate
sub-regions or the finite elements for the separate trial solutions thus permits a greater flexibility
in considering continuum of the shape.
Some of the most important advantages of the FEM derive from the techniques of introducing
boundary conditions. This is another area in which the method differs from other variational or
residual approaches. Rather than requiring every trial solution to satisfy the boundary conditions,
one prescribes the conditions after obtaining the algebraic equations for assemblage.
No special techniques or artificial devices are necessary, such as the non-cantered difference
equations or factious external points often employed in the finite difference method.
The FEM not only accommodates complex geometry and boundary conditions, but it also has
proved successful in representing various types of complicated material properties that are
difficult to incorporate in to other numerical methods. For example, formulations in solid
mechanics have been devised for anisotropic, nonlinear, hysteretic, time dependant or
temperature dependant material behavior.
One of the most difficult problems encountered in applying numerical procedures of
engineering analysis is the representation of non-homogeneous continua. Nevertheless the FEM
readily accounts for non-homogeneity by the simple tactic of assigning different properties
within an element according to the pre selected polynomial pattern. For instance it is possible to
accommodate continuous or discontinuous variations of the constitutive parameters or of the
thickness of a two-dimensional body.
The systematic generality of the finite element procedure makes it a powerful and versatile tool
for a wide range of problems. As a result, flexible general-purpose computer programs can be
constructed. Primary examples of these programs are several structural analysis packages which
include a variety of element configurations and which can be applied to several categories of
structural problems. Among these packages are ASKA, STRUDL, SAP and NASTRAN &
SAFE. Another indicator of the generality of the method is that programs developed for one field
of engineering have been applied successfully to problems in different field with a little or no
modification.
Finally an engineer may develop a concept of the FEM at different levels. It is possible to
interpret the method in physical terms. On the other hand the method may be explained entirely
in mathematical terms. The physical or intuitive nature of the procedure is particularly useful to
the engineering student and practicing engineer.
3.4 LIMITATION:
One limitation of finite element method is that a few complex phenomenons are not
accommodated adequately by the method as its current state of development. Some examples of
such phenomenon form the realm of solid mechanics are cracking and fracture behavior, contact
problems, bond failures of composite materials, and non-linear material behavior with work
softening. Another example is transient, unconfined seepage problems. The numerical solution
of propagation or transient problem is not satisfactory in all respects. Many of these
phenomenon’s are presently under research and refinements of the methods to accommodate
these problems better can be expected.
The finite element method has reached a high level of development as a solution technique.
However the method yields realistic results only if the coefficients or material parameters, which
describe the basic phenomenon, are available. Material non-linearity in solid mechanics is a
notable example of a field in which our understanding of material behavior has lagged behind the
development of the analytical tool. In order to exploit fully the power of the finite element
method, significant effort must be direct towards the development of constitutive laws and the
evaluation of realistic coefficients and material parameters.
Even the most efficient finite element computer code requires a relatively large amount of
computer memory and time. Hence use of this method is limited to those who have access to
relatively large, high-speed computers. The advent of time-sharing, remote batch processing and
computer service bureaus or utilities ahs alleviated this restriction to some degree. In addition
the method can be applied indirectly to common engineering problems by utilizing tables, graphs
and other analysis aids that have been generated by finite element codes.
The most tedious aspects of the use of finite element methods are the basic processes of subdividing the continuum and of generating error free input data for the computer. Although these
processes may be automated to a degree they have been totally accomplished by computer
because some engineer judgement may be employed in the discretization. Error in the input data
may go undetected and erroneous result obtained there form may appear acceptable.
Consequently it is essential that the engineer/programmer provide checks to detect such errors.
In addition to check internal code, an auxiliary routine that reads the input data and generates a
computer plot of the discretized continuum is desirable. This plot permits a rapid visual check of
the input data.
Finally as for any approximate numerical method the results of the finite element analysis
must be interpreted with care. We must be aware of the assumptions employed in the
formulation, the possibility of the numerical difficulties and the limitations in the material
characterizations used. A large volume of solution information is generated by a finite element
routine but this data is worthwhile only when its generation and interpretation are tempered by
proper engineering judgment.
3.5 BASIC APPROACH TO FEA SOFTWARE:
Basic approach for any finite element analysis (FEA) can be divided in to three parts
 Pre – processors
 Solver
 Post – Processor
3.5.1 PRE – PROCESSOR:
Pre – processor mainly contains building of model, meshing, assigning material properties
etc.
3.5.1.1 BUILDING OF MODEL:
Geometry is usually difficult to describe, as it has to be as close to as real. Since it has to take
real world loads and boundary conditions, it is equal to prototype simulated in computer.
3.5.1.2 CREATION OF FINITE ELEMENT MODEL FOR MESHING:
After assigning material properties and structural properties to the model, meshing is done.
Meshing is the process of dividing the model into finite number of finite sized elements.
FEA uses complex system of points called nodes, which make grid called MESH. This mesh
is programmed to contain material and structural properties, which define how the structure will
react to certain loading conditions. Nodes are assigned at a certain density throughout the
material depending on the anticipated stress levels of a particular area. Regions that will receive
large amounts of stress usually have a higher node density than those, which experience little or
no stress.
Points of interest may consist or fracture point of previously tested material, fillets, corners,
complex details and high stress areas.
The mesh acts like a spider web in that form each node, there extends a mesh element to each
of the adjacent nodes. The web of vectors is what carries the material properties to the object,
creating many elements.
Each FEA programs may came with an element library or one is constructed over time.
Elements are thought to fill the whole experiment; hence choice of elements very critical.
While meshing it has to be decided whether we have to go for finer mesh or coarser one. The
finer the mesh, the better is the result; but longer is the analysis time. Therefore a compromise
between accuracy and solution speed is usually made.
The mesh may be created manually or automatically. In the manually created mesh, we will
notice that the elements are similar at joints. This is known as mesh refinement and it enables
the stress to be captured at the geometric discontinuities (the junction).
Manual meshing is a tedious process for models with any degree of complications but inbuilt
mesh engine creates mesh automatically thus reducing the time. These automatic meshing has
imitations as to regards mesh quality and solution accuracy.
3.5.2 SOLVER:
Solvers are geometric task oriented. These are developed for specific
applications. Solvers are designed based on continuum approach where in construction of mass,
momentum and energy equation of state, thermodynamic equations as and when required for
each of the elements and the solution is obtained by interpreting these solutions. The solution to
these equations essentially depends on two methods
1. Implicit
2. Explicit
Choice of the method is based on the nature of problems.
The main goal of a finite element analysis is to examine a structure or a component response
to certain loading conditions. Therefore specifying the proper loading conditions is a key step in
the analysis. These loading conditions may be static, dynamic or transient whose nature may be
linear or non-linear.
The word loads in FEA includes the applied forcing functions externally or internally.
For example loads in structural are displacements, forces, pressures, temperatures and gravity.
In thermal analysis the applied loads are temperatures, heat flow rates convections and heat
generation.
Solver reads the model created by the pre-processor and formulates the mathematical
representation of the model. All the parameters defined in the pre-processing stage are used to do
this. If the model is correct the solver proceeds to form the element stiffness matrix for the
problem. After calculating the element stiffness matrix it calculates the results like
displacements, pressure, stresses, strains etc at each node within the component or continuum.
All these results are sent to a results file, which may be read by the Post-Processor.
3.5.3. POST – PROCESSOR:
Here the results of the analysis are read and interpreted. They can be presented in the form of
a table, a contour plot, deformed shape of the component to the mode shapes and natural
frequencies if frequencies are involved. Other results are available for fluids, thermal and
electrical analysis types.
Contour plots are usually more effective way of viewing for structural type problems. Slices
can be made through 3-D models to facilitate the viewing of internal stress patterns.
Post – Processor includes the calculations of stresses and strains I any of the x, y or z
directions or induced in a direction at an angle to the coordinate axis. The principal stresses and
strains may also be plotted or if required the yield stress and strains according to the main
theories if failure (von mises, st-venani, tresea etc) can be plotted.
Other information such as the strain energy, plastic strain and creep strain may be obtained
for certain types of analyses.