SEM-6 6th

Semester – B.E. / B.Tech.

BR-114

Department of Mechanical Engineering

ME86

92 Finite Element Analysis

Part-A (10 x 2 = 20 Marks)

UNIT – I

No Question Level Competence Mark

1.1 What are the types of boundary condition? L1 Understanding 2

1.2 Mention the basic steps of Rayleigh-Ritz method L2 Remembering 2

1.3 Name any four FEA software‟s L1 Evaluating 2

1.4 What is meant by Finite Element modeling? L2 Understanding

2

1.5 Mention the basic steps of Rayleigh-Ritz method? L3 Remembering 2

1.6 State the methods of Engineering analysis L4 Analyzing 2

1.7 What is meant by Finite element? L5 Understanding 2

1.8 What is meant by node or joint? L1 Understanding 2

1.9 Define shape functions. L1 Evaluating 2

1.10 What is meant by higher order elements? L2 Understanding 2

2.1 Name the variational methods. L1 Remembering 2

2.2 Give examples for the finite element. L2 Remembering 2

2.3 State the three phases of finite element method. L5 Remembering 2

2.4 Name the weighted residual methods. L3 Evaluating 2

Nadar Saraswathi College of Engineering and Technology,

Vadapudupatti, Theni - 625 531

(Approved by AICTE, New Delhi and Affiliated to Anna University, Chennai)

Format No. NAC/TLP-07a

Rev. No. 03

Date 29-11-2019

Total Page 01

Question Bank for the Units – I to V

2.5 What is truss element? L4 Understanding 2

2.6 What is “Aspect ratio”? L1 Understanding 2

2.7 List the two advantages of post-processing. L6 Remembering 2

2.8 What are structural and non-structural problems? L4 Understanding 2

2.9 Explain force method and stiffness method? L4 Understanding 2

2.10 What is the difference between static and dynamic

analysis?

L4 Analyze 2

3.1 What are types of loading acting on the structure? L4 Understanding 2

3.2 Define body force (f). L2 Remembering 2

3.3 What is point load (P). L4 Analyze 2

3.4 State the properties of a stiffness matrix. L5 Analyze 2

3.5 What is truss? L2 Understanding 2

3.6 Define heat transfer. L3 Remembering 2

3.7 Define Dynamic analysis. L3 Remembering 2

4.1 What are types of Eigen value problems? L6 Understanding 2

4.2 What are methods used for solving transient vibration

problems?

L4 Analyze 2

4.3 State the principles of virtual work. L4 Analyze 2

4.4 Define transaction force(T). L6 Remembering 2

4.5 What is the classification of Co-ordinates? L5 Understanding 2

4.6 Give the generations L4 Analyze 2

4.7 What are methods used for solving transient

problems?

L1 Understanding 2

5.1 How do you define two dimensional elements? L4 Analyze 2

5.2 What is CST element? L5 Understanding 2

5.3 What is LST element? L4 Understanding 2

5.4 What is QST element? L3 Understanding 2

5.5 What is meant by plain stress analysis? L1 Understanding 2

5.6 What is meant by plain stress analysis? L1 Understanding 2

5.7 Write a displacement function equation for CST

element.

L1 Understanding 2

5.8 State the assumption in the theory of pure torsion. L4 Analyze 2

6.1 Write down the finite element for tensional triangular

element.

L4 Analyze 2

6.2 Write down the shape function for two-dimensional

transfer.

L4 Analyze 2

6.3 Define path line. L1 Remembering 2

6.4 Define stream line. L1 Remembering 2

6.5 Write down the expression for stiffness matrix in two-

dimensional heat conduction and convection.

L2 Evaluating 2

6.6 Write down the governing equation for two

dimensional heat conduction.

L4 Analyze 2

6.7 Write down the stiffness matrix equation for one

dimensional heat transfer conduction element.

L4 Analyze 2

7.1 What is axisymmetric element? L4 Understanding 2

7.2 What ate the conduction for a problem to be

axisymmetric?

L2 Understanding 2

7.3 Write down the displacement equation for an

axisymmetric triangular element.

L4 Analyze 2

7.4 Give the stiffness matrix equation for an axisymmetric

triangular element.

L1 Remembering 2

7.5 What are the advantages of shell element? L2 Understanding 2

7.6 What are the assumption used in thick plate element? L1 Understanding 2

7.7 What are the assumption used in thin plate element? L2 Understanding 2

8.1 What are the ways in which a three dimensional

problem can be reduced to a two dimensional

approach?

L2 Understanding 2

8.2 Write down the stress-strain relationship for an

axisymmetric triangular element.

L4 Analyze 2

8.3 Give the strain-Displacement matrix for an

axisymmetric triangular element.

L1 Remembering 2

8.4 Define plate element. L1 Remembering 2

8.5 What are the assumptions for thin shell theory? L4 Analyze 2

8.6 Define dynamic analysis. L3 Remembering 2

8.7 Define normal modes. L3 Remembering 2

9.1 What is the purpose of Isoparametric element. L1 Understanding 2

9.2 Write down the shape function for 4 noded

rectangular elements using natural co-ordinate system.

L4 Analyze 2

9.3 Write down the jacobian matrix for four noded

quadrilateral element.

L4 Analyze 2

9.4 Write down the stiffness matrix equation for four

noded isoparametric quadrilateral element.

L3 Evaluating 2

9.5 Write down the element force vector equation for four

noded quadrilateral element.

L4 Analyze 2

9.6 Write down the Gaussian quadrature expression for

numerical integration.

L1 Evaluating 2

9.7 Define streamline. L2 Remembering 2

10.1 Define the stream function for a two dimensional

incompressible flow.

L2 Remembering 2

10.2 Define element capacitance matrix for unsteady state

transfer problem.

L2 Remembering 2

10.3 List the method of describing motion of fluid. L3 Remembering 2

10.4 Mention two natural boundary conditions as applied to

thermal problems.

L5 Evaluating 2

10.5 Define resonance. L1 Remembering 2

10.6 What are methods used for solving transient vibrations

problems?

L2 Understanding 2

10.7 Define linear dependence and independence of

vectors.

L3 Remembering 2

10.8 What are the types of Eigen value problems? L1 Understanding 2

10.9 What are the types of non-linearity? L2 Understanding 2

10.10 Is beam element an isoparametric element? L3 Evaluating 2

Part – B ( 5 x 13 = 65 Marks)

UNIT- I

11.a-1 The following differential equation is available for a

physical phenomenon, d2y/dx

2 – 10x

2 =5, 0≤x≤1 with

boundary conditions as y (0) = 0 and y (1) = 0.Find

L1 Knowledge

(13)

an approximate solution of the above differential

equation by using Galerkin‟s method of weighted

residuals and also compare with exact solution.

11.a-2 Solve differential equation for a physical problem

expressed as d2y/dx

2)+100=0, 0< x< 10 with Boundary

condition as y(0)=0, y(10)=0. using

(i)Point collocation (ii) Subdomain collocation

(iii) Least squares

(iv)Galerkin‟s method

L4 Analyzing (13)

11.a-3 Solve differential equation for a physical problem

expressed as d2y/dx

2)+60=0, 0< x< 10 with Boundary

condition as y(0)=0, y(10)=0. Trial function y=a1x(10-

x)using

(i)Point collocation (ii) Subdomain collocation

(iii) Least squares

(iv)Galerkin‟s method.

L3 Applying (13)

11.b-1 The differential equation of a physical phenomenon is

given by (d2y/dx

2)+500x

2=0, 0< x< 1 Trial Function,

y=a1(x-x4).Boundary condition are y(0)=0, y(1)=0.

Calculate the value of the parameter a1 by the

following methods:

(i)Point collocation (ii) Subdomain collocation

(iii) Least squares

(iv)Galerkin‟s

L4 Analyzing (13)

11.b-2 A beam AB of span „l‟ simply supported at the ends

and carrying a concentrated load „W‟ at the centre „C‟.

Determine the deflection at the mid span by using

Rayleigh-Ritz method and compare with exact

solution.

L4 Analyzing (13)

11.b-3 A simply Supported beam subjected to uniformly

distributed load over entire span it is subjected to a

point load at the centre of the span. Calculate the

deflection using Rayleigh-Ritz method and compare

with exact solutions

L4

Applying (13)

11.b-4 Determine the expression for deflection and bending

moment in a simply supported beam subjected to uniformly

distributed load over entire span. Find the deflection and

moment at mid span and compare with exact solution

Rayleigh-Ritz method. Use

L4 Applying

(13)

UNIT- II

12.a-1 A steel bar of length 800mm is subjected to an axial load of

3kN as shown in fig. Estimate the nodal displacement of

the bar and load vectors.

L4 Applying (13)

12.a-2 For a tapered bar of uniform thickness t=10mm as

shown in figure. Predict the displacements at the

nodes by forming into two element model. The bar

has a mass density ρ = 7800 Kg/m3, the young‟s

modulus E = 2x105

N/mm2. In addition to self-weight,

the bar is subjected to a point load P= 10 KN at its

centre. Also determine the reaction forces at the

support.

L1 Applying (13)

12.a-3 Consider a bar as shown in fig. Young‟s Modulus E= 2 x

105 N/mm

2. A1 = 2cm

2, A2 = 1cm

2 and force of 100N.

Calculate the nodal displacement.

L1 Applying (13)

12.a-4 For the two bar truss shown in the fig, Estimate the

displacements of node 1 and the stress in element 1-3.

L3 Applying (13)

12.b-1 Consider a three bar truss as shown in Fig.It is given that

E=2X105N/mm

2.Calculate the following.

(i) Nodal Displacement

(ii) Stress in each member.

(iii) Reaction at the support.

L3 Applying (13)

Take Area of element(1)=2000mm2

Area of element(2)=2500mm

2

Area of element(3)=2500mm

2

12.b-2 Consider a four bar as shown in Fig.It is given that

E=2X105N/mm

2 and Ae=625 mm

2 for all elements.

(i) Determine the element stiffness matrix for

each element.

(ii) Assemble the structure stiffness matrix K for

the entire truss.

(iii) Solve for the nodal displacement.

L3 Applying (13)

12.b-3 For the plane truss shown in Fig. Determine the

horizontal and vertical displacement of nodel and

stress in each element. All element have E=201GPa

and A=4X10-4

m2

L5

Applying (13)

12.b-4 For the three-bar truss shown in Fig. Determine the

displacement of node 1 and the stress in element 3

L1 Knowledge

(13)

UNIT- III

13.a-1 Calculate the element stiffness matrix and temperature

force vector for the plane stress element shown in fig.

The element experiences a 20ºC increase in

temperature. Assume α= 6x10^-6 C. Take E=2x10^5

N/mm2, v= 0.25, t= 5mm

L4 Analyzing (13)

13.a-2 Determine the shape function N1,N2 and N3 at the

interior point P for the triangular element shown in

Fig.

L4 Analyzing (13)

13.a-2 Determine the stiffness matrix for the constant strain

triangular (CST) element shown in Fig.The Co-

Ordinates are the given in units of mm. Assume plain

stress conditions. Take E=210GPa v=0.25 and

t=10mm.

L1 Knowledge

(13)

13.a-3 For the two dimensionalloaded plate shown in fig.

Determine the nodal displacement and element stress

using plane strain condition considering body force.

Take Young‟s modulus as 200Gpa, r=0.3 and density

as 7800kg/3m3.

L1 Knowledge (13)

13.a-4 Determine the nodal displacement of nodes 1 and 2

and element stress for the two dimentional loaded

plate as shown in Fig.Assume plane stress

L4 Analyzing (13)

condition.Take v=0.25,E= E=2x10^5 N/mm2, t=15mm

13.b-1 Find the temperature distribution in a square region

with uniform energy generation as shown in

Fig.Assume that there is no temperature variations in

thez-direction.Takek=30w/cmoc,l=10cm,

q=100w/cm3.

L3 Knowledge

(13)

13.b-2 A thin plate subjected to surface traction as shown in

Fig. Calculate the global stiffness matrix.Take

t=25mm, E=2x10^5 N/mm2,v=0.30,Assume the plain

stress condition.

L1 Knowledge (13)

13.b-3 Derive the shape functions for a constant strain

triangular (CST) element in terms of natural Co-

ordinate system.

L1 Knowledge (13)

UNIT- IV

14.a-1 The nodal coordinates for an axisymmetric triangular

element shown in fig are given below. Evaluate the strain-

displacement matrix for that element.

L1 Knowledge

(13)

14.a-2 Calculate the stiffness matrix for the axisymmetric element

shown in fig E= 2.1 x 106 N/mm

2 and Poisson‟s ratio as

0.3.

L4 Analyzing (13)

14.a-3 For the element shown in Fig,determine the sfiffness

matrix.Take E=200Gpa and v=0.25

L3 Apply

(13)

14.b-1 For the axisymmetric element shown in Fig.determine

the element streses.Take E= 2.1 x 106

N/mm2

and

v=0.25.The co-ordinates shown in Fig(i) are in

mm.The nodel displacement are,

u 1=0.05,u2=0.02,u3=0,w1=0.03,w2=0.02,w3=0

L4 Analyzing (13)

14.b-2 Calculate the element stiffness matrix and the thermal

force vector for the axisymmetric triangular element

shown in Fig. The experience a 15oc increase in

temperature.

L4 Analyzing (13)

14.b-3 For the axisymmetric element shown in Fig.

Determine the element stresses.Let E=210Gpa and

v=0.25.The co-ordinates in mm are shown in Fig.

u 1=0.05,u2=0.02,u3=0,w1=0.03,w2=0.02,w3=0

L3 Apply (13)

UNIT- V

15.a-1 Calculate the Cartesian coordinates of the point P which

has local coordinates ε = 0.8 and η = 0.6 as shown in figure

L4 Analyzing (13)

15.a-2 For the isoparametric four noded quadrilateral element

shown in Fig.Determine the Cartesian co-ordinates of

point P which has local co-ordinates ε = 0.5 and η =

0.5

L4 Analyzing (13)

15.a-3 For the isoparametric quadrilateral element shown in

Fig.determine the co=ordinate of the point P which

has Cartesian Co-ordinates (7,4)

L3 Apply (13)

15.b-1 Evaluate [J]= η=1/2 for the linear quadrilateral

element shown in Fig.

L4 Analyzing (13)

15.b-2 For four noded rectangular element is shown in Fig.

Determine the following:

1.Jacobian Matrix 2.Strain-Displacement matrix

3.Element Stresses .

L1 Knowledge (13)

15.b-3 Evaluate the Jacobian matrix for the isoparametric

quadrilateral element shown in Fig

L4 Analyzing (13)

15.b-4 For the isoparametric quadrilateral element shown in

Fig. The Cartesian co-ordinates of point P are

(6,4).The loads 10Kn and 12kN are acting in x and y

direction on that point P. Evaluate the nodal

equivalent forces.

L3 Apply (13)

Part – C ( 1 x 15 = 15 Marks)

UNIT-I

16 .a-1 What are the steps involved in FEA . L5 Evaluation (15)

16 .a-2 Explain the discretization process. L5 Evaluation (15)

(OR)

16.b-1 Explain the Following:

(i) Variational approach

(ii) Weighed residual methods.

L5 Evaluation (15)

16.b-2 What are the steps involved in Analysis Process. L5 Evaluation (15)

UNIT-II

16 .a-1 The composite structure shown in Fig., is subjected to

a bar element. Determine the displacement, stresses

and support reaction. Assume the following data:

L5 Evaluation (15)

16 .a-2 An aluminum alloy fin of 7 mm thick and 50mm long

protrudes from a wall, which is maintained at 120o

c.

The air temperature is 220

c. The heat transfer

coefficient and thermal conductivity of the fin

material ARE 140W/m2K and 55W/m

2K respectively.

Determine the temperature distribution of Fin.

L5 Evaluation (15)

(OR)

16.b-1 Consider the bar shown in figure axial force P =

100KN is applied as shown. Determine the nodal

displacement, stresses in each element and reaction

forces.Young‟sModulus. E=2x10^5 N/mm2.

A1=2cm2A2=1cm

2

L5 Evaluation (15)

16.b-2 Define Finite element modelling. L5 Evaluation (15)

UNIT-III

16 .a-1 A composite wall consists of three material as shown

in Fig. The outer temperature is T0=200C.convective

heat transfer takes place on the inner surface of wall

with Tα=8000C and h=75W/m

2 0c.Determine the

temperature distribution in the wall.

L5 Evaluation (15)

16.a-2 Assemble the Stain-Displacement matrix for the CST

element shown in Fig.Take t=25mm and E210Gpa.

L5 Evaluation (15)

(OR)

16.b-1 Evaluate the stiffness matrix for the CST shown in

Fig. Assume plane stress condition.Take t=20mm,

E=2x10^5 N/mm2,t=0.25.

L5 Evaluation (15)

16.b-2 What is CST and LST element? L5 Evaluation (15)

UNIT-IV

16 .a-1 The nodal co-ordinates for an axisymmetric triangular

element are given below:

r 1= 5mm,z1=15mm,r2=25mm,z2=15,r3=35mm,z3=50

mm, Determine [B] matrix for that element.

L5 Evaluation (15)

16.a-2 What are the ways in which a three dimensional

problem can be reduced to a two dimensional

approach?

L5 Evaluation (15)

(OR)

16.b-1 What is the assumption for thin shell theory? L5 Evaluation (15)

16.b-2 What is the assumption used in thick plate element?

And advantages of shell elements?

L5 Evaluation (15)

UNIT-V L5 Evaluation

16 .a-1 Define FEA software packages? L5 Evaluation (15)

16.a-2 Define the following terms with suitable exambles

(i) Isoparametric element

(ii) Axisymmetric analysis

(iii)Node, Element and shape functions

(iv) Plane stress and plane strain

L5 Evaluation (15)

(OR) L5 Evaluation

16.b-1 Define Natural Co-Ordinates? L5 Evaluation (15)

16.b-2 Define Solution Technique to Dynamic Problems. L5 Evaluation (15)

L1: Knowledge, L2: Comprehension, L3: Application, L4: Analysis, L5: Evaluation, L6: Synthesis

QUESTION BANK SUMMARY

S.NO UNIT DETAILS L1 L2 L3 L4 L5 L6 TOTAL

1 Unit-1

PART-A 6 4 2 5 2 1 20

PART-B 01 0 01 05 0 0 07

PART-C 0 0 0 0 03 0 03

2 Unit-2

PART-A 01 02 02 05 02 02 14

PART-B 02 0 03 01 01 0 07

PART-C 0 0 0 0 04 0 04

3 Unit-3

PART-A 05 01 01 07 01 0 15

PART-B 03 0 01 03 0 0 07

PART-C 0 0 0 0 04 0 04

4 Unit-4

PART-A 04 04 02 04 0 0 14

PART-B 01 0 02 03 0 0 06

PART-C 0 0 0 0 04 0 04

5 Unit-5

PART-A 04 05 04 03 01 0 17

PART-B 01 0 02 04 0 0 07

PART-C 0 0 0 0 04 0 04

Total No of Questions

PART-A PART-B PART-C TOTAL

80 34 19 133

Prepared By:

Staff Name1: Mr.V.Thirumalai raj Staff Name2:Mr.P.Surulimani