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. Finally the results obtained by theoretical analysis

and Finite Element Analysis 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

2. Marine engines 7

2.1 Reciprocating Diesel Engines 7

3. Finite Element Methods 9

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

4. 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

5. Theoretical Design calculations 39

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

6. 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

7. Experimental Results 59

7.1 Results for Steel 59

7.2 Results for Ceramics 67

8. 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

9. Conclusion 77

10. Future Scope of Work 78

11. References 79

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: [Fig: 3.1]

Define Mesh

Improve Mathematical Model

Assessment of accuracy of Finite Element Solution of Mathematical Model

Finite Element Solution Choice of

Finite Element Mesh Density Solution

Parametric Representation

Loading Boundary

Mathematical Model

Governed by Different

Equations, Assumptions

In

Geometry

Kinematics

Material Law

Loading

Boundary

Conditions etc

Change of Physical ProblemsPhysical Problems

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 sub-

dividing 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.