Fem Ppt Introduction Sachin New

A L - F A L A H S C H O O L O F E N G I N E E R I N G A N D T E C H N O L O G Y

D E P A R T M E N T O F M E C H A N I C A L E N G I N E E R I N G

M A S T E R O F T E C H N O L O G Y

( M A C H I N E D E S I G N )

Introduction to theFinite Element Method

BY: SACHIN CHATURVEDI

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M. Tech (FEM - Syllabus)

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Paper Code: M-847-A

Theory: 100 Marks

Sessional: 50 Marks

FEM - BOOKS3


1. Introduction to Finite Elements in Engineering Analysis by Tirupathi R.Chandruipatala and Ashok R. Belagundu. Prentice Hall.

2. The Finite Element Method in Engineering by S.S.Rao, Peragamon Press,Oxford.

3. Finite Element Procedures, by Klaus Jurgen Bathi, Prentice Hall.

4. The Finite Element Method by Zienkiewicz published by Mc Graw Hill.

5. An Introduction to Finite Element Method by J.N. Reddy published by McGraw Hill.

6. Fundamentals of the Finite Element Method for Heat and Fluid Flow byRoland W. Lewis, Perumal Nithiarasu, Kankanhalli N. Seetharamu by JohnWiley.

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Basic Concepts

The finite element method

(FEM), or finite element

analysis (FEA), is based on the

idea of building a complicated

object with simple blocks, or,

dividing a complicated object

into small and manageable

pieces. Application of this simple

idea can be found everywhere in

everyday life, as well as in

engineering.


Examples

Best Example Of Fem

Blades in turbine engines are typical examples

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FEM Examples6


1. Introduction to FEM7


Numerical Methods:

1.1 Applications8


A diversity of specializations under the union of the mechanical engineering

discipline (such as aeronautical, biomechanical, and automotive industries)

commonly use integrated FEM in design and development of their products.

Several modern FEM packages include specific components such as thermal,

electromagnetic, fluid, and structural working environments. In a structural

simulation, FEM helps tremendously in producing stiffness and strength

visualizations and also in minimizing weight, materials, and costs.

ApplicationsCont……

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FEM allows detailed visualization of where structures bend or twist, and

indicates the distribution of stresses and displacements. FEM software provides

a wide range of simulation options for controlling the complexity of both

modeling and analysis of a system. Similarly, the desired level of accuracy

required and associated computational time requirements can be managed

simultaneously to address most engineering applications. FEM allows entire

designs to be constructed, refined, and optimized before the design is

manufactured.

ApplicationsCont……

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This powerful design tool has significantly improved both the standard of

engineering designs and the methodology of the design process in many

industrial applications. The introduction of FEM has substantially decreased the

time to take products from concept to the production line. It is primarily through

improved initial prototype designs using FEM that testing and development have

been accelerated. In summary, benefits of FEM include increased accuracy,

enhanced design and better insight into critical design parameters, virtual

prototyping, fewer hardware prototypes, a faster and less expensive design cycle,

increased productivity, and increased revenue.

1.2 Visualization (Applications)11


Visualization of how a car deforms in an asymmetrical crash using finite element analysis

1.3 Structural Analysis12


1.4 Thermal System Analysis13


1.5 Flow Analysis14


1.6 Thermomechanical Process Analysis

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B. Forging

A. Rolling

C. Injection Molding

Research Work On16


IndustryAcademics

B. Tech R&D Department

ConferencesJournals

International Journals

National Journals

International Conferences

National Conferences

M. Tech Phd

Research

Concepts, Designs, Developments, Manufacturing, Renovation, Innovations

2 General Procedure of FEM17


General Procedure of FEM18


General Procedure of FEM19


2.1 Finite Element Formulations

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2.1.1 Direct approach for discrete systems

Direct approach has the following features:

• It applies physical concept (e.g. force equilibrium, energy conservation,mass conservation, etc.) directly to discretized elements. It is easy in itsphysical interpretation.

• It does not need elaborate sophisticated mathematical manipulation orconcept.

• Its applicability is limited to certain problems for which equilibrium orconservation law can be easily stated in terms of physical quantities onewants to obtain. In most cases, discretized elements are self-obvious inthe physical sense.


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2.1.2 Coordinate Transformation approach

In many cases, one can introduce a local coordinate system associated witheach element in addition to a global coordinate system. A local coordinatesystem can be defined in many cases in a self-obvious way inherent to theelement itself. It is much easier to determine the stiffness matrix withrespect to the local coordinate system of an element than with respect to theglobal coordinate system. The stiffness matrix with respect to the localcoordinate system is to be transformed to that with respect to the globalcoordinate system before the assembly procedure.

i) Vector Transformation in 2-D.

ii) Transformation of stiffness matrix.


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2.1.3 Direct approach for Elasticity Problem (plane stress, plane strain)

In this section, we are concerned about an elastic deformation problem intwodimensional continuous media (therefore, not a discrete system).

2.1.4 Assembly Procedure

The assembly procedure is based on compatibility and conservation law(e.g. force balance, mass conservation and energy conservation).

2.1.5 Variational Approach in Finite Element Formulation

Differential formulation, physical phenomena can be described in termsof minimization of total energy (or functional) associated with theproblem, which is called “variational formulation”.


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2.1.6 Principle of Minimum Total Potential Energy

There is a very important physical principle to describe a deformationprocess of an elastic body, namely Principle of Minimum Total PotentialEnergy, which can be summarized as below:

Finite Element Method versus Rayleigh-Ritz Method

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One of the historically famous approximate methods for this kind of problem isRayleigh-Ritz Method, and the other modern method is the Finite Elementmethod. Here we will discuss both methods with the comparison in mind.

i) Rayleigh-Ritz Method: This method is very simple and easy tounderstand. However, it is not easy to find a familyof trial functions for the entire domain satisfyingthe essential boundary conditions when geometryis complicated.

ii) Finite Element Method: In this case, the shape functions can be foundmore easily than the trial functions withouthaving to worry about satisfying the essentialboundary conditions, which makes FEM muchmore useful than Rayleigh-Ritz Method. In thisregard, the Finite Element Method is amodernized approximation method suitable forcomputer environment.

3 Shape Functions And Discretization

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We will discuss the element types, shape functions and discretization in thissection. It is important to be able to select an element type which is most suitablefor the problem of interest, and to determine the shape functions for the chosenelement type. Finally, automatic mesh generation techniques are, in practicalsense, also important to finite element analysis applications.

3.1 Element Types

i) One-dimensional Elements


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ii) Two-dimensional Elements


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iii) Three-dimensional Elements

4 Natural Coordinates

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Note that N (x, y) in our current form is represented in terms of the nodalcoordinates (xi , yi ) and a global coordinate (x, y). One can have a better form interms of so-called “Natural Coordinate”, in particular for triangular type ofelements (or “Normalized Coordinate” for a quadrilateral type of elements ).

1) One-dimensional case

4 Natural Coordinates

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2) Two-dimensional case

3) Three-dimensional case

5 Normalized coordinate

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6 Shape functions (Examples)

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Shape functions for several quadrilateral elements are summarized below:


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7 Exercise

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QUESTIONS

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