FEA 2 MARKS AND ANSWERS

7/23/2019 FEA 2 MARKS AND ANSWERS

http://slidepdf.com/reader/full/fea-2-marks-and-answers 1/20

2 Marks

Unit-I

1. What is meant by finite element?

A small units having definite shape of geometry and nodes is called finite element.

2. What is meant by node or joint?

Each kind of finite element has a specific structural shape and is inter- connected with the

adjacent element by nodal point or nodes. At the nodes, degrees of freedom are located. The

forces will act only at nodes at any others place in the element.

3. What is the basic of finite element method?

Discretiation is the basis of finite element method. The art of subdividing a structure in

to convenient number of smaller components is known as discretiation.

4. What are the types of boundary conditions?

• !rimary boundary conditions

• "econdary boundary conditions

5. tate the methods of en!ineerin! analysis?

• E#perimental methods

• Analytical methods

• $umerical methods or appro#imate methods

". What are the types of element?

• %D element

• &D element

• 'D element

#. tate the three phases of finite element method.

• !reprocessing

• Analysis

• !ost !rocessing

$. What is structural problem?Displacement at each nodal point is obtained. (y these displacements solution stress and

strain in each element can be calculated.

%. What is non structural problem?

Temperature or fluid pressure at each nodal point is obtained. (y using these values

properties such as heat flow fluid flow for each element can be calculated.

1



2 Marks

1&. What are the methods are !enerally associated 'ith the finite element analysis?

• )orce method

• Displacement or stiffness method.

11. ()plain stiffness method.

Displacement or stiffness method, displacement of the nodes is considered as the

unknown of the problem. Among them two approaches, displacement method is desirable.

12. What is meant by post processin!?

Analysis and evaluation of the solution result is referred to as post processing.

!ostprocessor computer program help the user to interpret the result by displaying them in

graphical form.

13. *ame the +ariation methods.• *it method.

• *ay-+eigh *it method.

14. What is meant by de!rees of freedom?

hen the force or reaction act at nodal point node is subjected to deformation. The

deformation includes displacement rotation, and or strains. These are collectively known as

degrees of freedom

15. What is meant by discreti,ation and assembla!e?

The art of subdividing a structure in to convenient number of smaller components is

known as discretiation. These smaller components are then put together. The process of uniting

the various elements together is called assemblage.

1". What is aylei!h-it, method?

t is integral approach method which is useful for solving comple# structural problem,

encountered in finite element analysis. This method is possible only if a suitable function is

available.

1#. What is spect ratio?

t is defined as the ratio of the largest dimension of the element to the smallest dimension.

n many cases, as the aspect ratio increases the in accuracy of the solution increases. The

conclusion of many researches is that the aspect ratio should be close to unity as possible.

2



2 Marks

1$. What is truss element?

The truss elements are the part of a truss structure linked together by point joint which

transmits only a#ial force to the element.

1%. What are the h and p +ersions of finite element method?

t is used to improve the accuracy of the finite element method. n h version, the order of

polynomial appro#imation for all elements is kept constant and the numbers of elements are

increased. n p version, the numbers of elements are maintained constant and the order of

polynomial appro#imation of element is increased.

2&. *ame the 'ei!hted residual method.

• !oint collocation method

• "ub domain collocation method

• +est suares method

• /alerkins method.

21. /ist the t'o ad+anta!es of post processin!.

*euired result can be obtained in graphical form. 0ontour diagrams can be used to

understand the solution easily and uickly.

22. 0urin! discreti,ation mention the places 'here it is necessary to place a node?

• 0oncentrated load acting point

• 0ross-section changing point

• Different material interjections point

• "udden change in point load•

23. What is the difference bet'een static and dynamic analysis?

Static analysis: The solution of the problem does not vary with time is known as static

analysis

E#ample1 stress analysis on a beam

Dynamic analysis: The solution of the problem varies with time is known as dynamic

analysis

E#ample1 vibration analysis problem.

24. *ame any four ( soft'ares.

• A$"2"

• $A"T*A$

• 03"43"

• D2A$A

3



2 Marks

25. 0ifferentiate bet'een !lobal and local a)es.

+ocal a#es are established in an element. "ince it is in the element level, they change with

the change in orientation of the element. The direction differs from element to element.

/lobal a#es are defined for the entire system. They are same in direction for all the

elements even though the elements are differently oriented.

2". 0istin!uish bet'een potential ener!y function and potential ener!y functional

f a system has finite number of degree of freedom 5%, &, and '6, then the potential

energy e#pressed as,

7 8 f 5%, &, and '6

t is known as function. f a system has infinite degrees of freedom then the potential

energy is e#pressed as

2#. What are the types of loadin! actin! on the structure?

• (ody force 5f6

• Traction force 5T6

• !oint load 5!6

2$. 0efine the body force

A body force is distributed force acting on every elemental volume of the body

9nit1 )orce per unit volume.

E#ample1 "elf weight due to gravity

2%. 0efine traction force

Traction force is defined as distributed force acting on the surface of the body.

9nit1 )orce per unit area.

E#ample1 )rictional resistance, viscous drag, surface shear

3&. What is point load?

!oint load is force acting at a particular point which causes displacement.

4



2 Marks

U*I 2

1. What are the basic steps in+ol+ed in the finite element modelin!?

• Discretiation of structure.

• $umbering of nodes.

2. Write do'n the !eneral finite element e6uation.

{ F } = [ K ]{u}

where

{ F } = )orce vector

[ K ] = "tiffness 4atri#

{u} = Displacement 4atri#

3. What is discreti,ation?

The art of subdividing a structure in to a convenient number of smaller components is

known as discretiation.

4. What are the classifications of coordinates?

• /lobal coordinates

• +ocal coordinates

• $atural coordinates

5. What is 7lobal coordinates?

The points in the entire structure are defined using coordinates system is known as global

coordinate system.

". What is natural coordinates?

A natural coordinate system is used to define any point inside the element by a set of

dimensionless number whose magnitude never e#ceeds unity. This system is very useful in

assembling of stiffness matrices.

#. 0efine shape function.Appro#imate relation : 5#,y6 8 $% 5#,y6 :% ; $& 5#,y6 :& ; $' 5#,y6 :'

here :%, :&, and :' are the values of the field variable at the nodes $ %, $&, and $' are

the interpolation functions.$%, $&, and $' are also called shape functions because they are used to

e#press the geometry or shape of the element.

5



2 Marks

$. What are the characteristic of shape function?

t has unit value at one nodal point and ero value at other nodal points. The sum of shape

function is eual to one.

%. Why polynomials are !enerally used as shape function?

Differentiation and integration of polynomial are uite easy. The accuracy of the result

can be improved by increasing the order of the polynomial. t is easy to formulate and

computerie the finite element euations

1&. 8o' do you calculate the si,e of the !lobal stiffness matri)?

/lobal stiffness matri# sie 8 $umber of nodes < Degrees of freedom per node.

11. Write do'n the e)pression of stiffness matri) for one dimensional bar element.

12. tate the properties of stiffness matri)

• t is a symmetric matri#

• The sum of elements in any column must be eual to ero

• t is an unstable element. "o the determinant is eual to ero.

13. Write do'n the e)pression of stiffness matri) for a truss element.

14. Write do'n the e)pression of shape function * and displacement u for one dimensional

bar element.

U = N 1u1+N 2u2

N 1 = 1-X / l

N 2 = X / l

15. 0efine total potential ener!y.

Total potential energy, 7 8 "train energy 596 ; potential energy of the e#ternal forces56

6



2 Marks

1". tate the principle of minimum potential ener!y.

Among all the displacement euations that satisfied internal compatibility and the

boundary condition those that also satisfy the euation of euilibrium make the potential energy

a minimum is a stable system.

1#. Write do'n the finite element e6uation for one dimensional t'o noded bar element.

1$. What is truss?

A truss is defined as a structure made up of several bars, riveted or welded together.

1%. tate the assumption are made 'hile findin! the forces in a truss

• All the members are pin jointed.

• The truss is loaded only at the joint

• The self weight of the members is neglected unless stated.

2&. tate the principles of +irtual ener!y?

A body is in euilibrium if the internal virtual work euals the e#ternal virtual work for

the every kinematically admissible displacement field.

21. What is essential boundary condition

!rimary boundary condition or E(0 (oundary condition which in terms of field variable

is known as !rimary boundary condition.

22. *atural boundary conditions

"econdary boundary natural boundary conditions which are in the differential form of

field variable is known as secondary boundary condition.

7



2 Marks

U*I - 3

1. 8o' do you define t'o dimensional elements?

Two dimensional elements are define by three or more nodes in a two dimensional plane.

The basic element useful for two dimensional analysis is the triangular element.

2.What is 9 element?

Three noded triangular elements are known as 0"T. t has si# unknown displacement

degrees of freedom 5u%, v%, u&, v&, u', v'6. The element is called 0"T because it has a constant

strain throughout it.

3. What is / element?

"i# nodded triangular elements are known as +"T. t has twelve unknown displacement

degrees of freedom. The displacement function for the elements are uadratic instead of linear as

in the 0"T.

4. What is : element?

Ten nodded triangular elements are known as =uadratic strain triangle. t is also called as

cubic displacement triangle.

5. What meant by plane stress analysis?

!lane stress is defined to be a state of stress in which the normal stress and shear stress

directed perpendicular to the plane are assumed to be ero.

". 0efine plane strain analysis.

!lane strain is defined to be state of strain normal to the #y plane and the shear strains are

assumed to be ero.

#. Write do'n the stiffness matri) e6uation for t'o dimensional 9 elements.

"tiffness matri# [ K ] = [ B]T [ D][ B] At

[ B]T -"train displacement

[ D] -"tress strain matri#

8



2 Marks

$. Write do'n the stress strain relationship matri) for plane stress conditions.

%.0ra' the shape functions of a 9 element.

1&. What are the differences bet'een 2 0imensional scalar +ariable and +ector +ariable

elements?

Two dimensional scalar variable elements have only one direction independent variable

per node. Two dimensional triangular element stiffness matri# sie is ' # '. Two dimensional

vector variable elements have direction dependent variable at each node. The element stiffness

matri# of a triangular element is of sie >#>.

11. Write do'n the !o+ernin! differential e6uation for a t'o dimensional steady-state heattransfer problem.

9



2 Marks

12. What is rea coordinates?

L1 = A1 /A

L2 = A2 /A

L3 = A3 /A

13.Write the applications of 9 element?

• 9se in areas where the strain gradient is small.

• 9se in mesh transition areas 5fine mesh to coarse mesh6.

• Avoid using 0"T in stress concentration or other crucial areas in the structure, such as

edges of holes and corners.

• *ecommended for uick and preliminary )E analysis of &-D problems.

14.Write do'n the strain displacement matri) for 9 element.

15. ()plain the important properties of 9 element.

%. The strain components are constant throughout the volume of the element.

&. t has si# unknown displacement degrees of freedom.

1". What is a)isymmetric element?

4any three dimensional problem in engineering e#hibit symmetry about an a#is of

rotation such type of problem are solved by special two dimensional element called the

a#isymmetric element

1#. What are the conditions for a problem to be a)isymmetric?

• The problem domain must be symmetric about the a#is of revolution

• All boundary condition must be symmetric about the a#is of revolution

• All loading condition must be symmetric about the a#is of revolution

1$. 7i+e the stiffness matri) e6uation for an a)isymmetric trian!ular element.

"tiffness matri# [ K ] = [ B]T [ D][ B]&t rA

10



2 Marks

1%. 0istin!uish bet'een plane stress and plane strain problems.

;lane stress<

A state of plane stress is said to e#ist when the elastic body is very thin and there is no

load applied in the coordinate direction parallel to the thickness. E#ample1 A ring press - fitted on

a shaft is a plane stress problem. n plane stress problem ?, @y and @y are ero.

;lane strain<

A state of plane strain occurs in members that are not free to e#pand in the direction

perpendicular to the plane of applied loads. E#ample1 n a long body of uniform cross-section,

subjected to transverse loading along its length, a small thickness in the loaded area can be

treated as plane-strain problem. ere e ,By , By , are ero.

2&.What are conditions for a problem to be a)i-symmetric?

%. The problem domain must be symmetric about the a#is of revolution

&. All the boundary conditions must be symmetric about the a#is of revolution

'.All the loading conditions must be symmetric about the a#is of revolution

21.What are the 'ays in 'hich a 30 problem can be reduced to a 20 problem?

1.;lane tress< 3ne dimension is too small when compared to other dimensions

()ample< /ear thickness is small

2.;lane strain< 3ne dimsensional problem is too large when compared to other two

dimensions

()ample< +ong !ipe

'.)isymmetric< /eometry is symmetric about a#is

()ample< 0ooling tower

22. Write do'n the constituti+e relationship for the a)i-symmetric problem.

The 0onstitutive +aw relates the stresses in a loaded solid to the strains developed.

{ ? }=[ D]{e }

? - "tress

e - "train

D- "train displacement matri#)or a#i-symmetric problems

11



2 Marks

23. 0istin!uish bet'een /a!ran!e and 8ermition interpolation functions.

At the inter element boundary the displacements are continuous in the case of +agrange

interpolation function whereas in addition to displacements, slopes are continuous in the case of

ermition interpolation functions

24. 0efine super parametic element.

f the order of the shape functions for describing the geometry is more than that for

describing field variable, then the element is said to be super parametric.

25. Write do'n the strain displacement matri) for a)i-symmetry element.

2". What is the purpose of Isoparametric element?

t is difficult to represent the curved boundaries by straight edges finite elements. A large

number of finite elements may be used to obtain reasonable resemblance between original body

and the assemblage.

2#. Write do'n the shape functions for 4 noded rectan!ular elements usin! natural

coordinate system.

2$. Write do'n =acobian matri) for 4 noded 6uadrilateral elements.

12



2 Marks

2%. Write do'n stiffness matri) e6uation for 4 noded isoparametric 6uadrilateral elements.

"tiffness matri#

3&. 0efine super parametric element.

f the number of nodes used for defining the geometry is more than of nodes used for the

displacement is known as super parametric element.

13



2 Marks

U*I 4

14



2 Marks

15



2 Marks

16



2 Marks

17



2 Marks

18



2 Marks

19



2 Marks

15. What are the different modes of heat transfer?• 0onduction

• 0onvection

• *adiation

20

FEA 2 MARKS AND ANSWERS

Documents

Transcript of FEA 2 MARKS AND ANSWERS