model fea qp

8/11/2019 Model Fea Qp

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K. S. K COLLEGE OF ENGINEERING & TECHNOLOGY

Department of Mechanical Engineering

Model Examinatiion

ME2353, FINITE ELEMENT ANALYSIS

Year/ Sem : III/VI Max. Marks : 100

Date : 16.04.2014 Duration : 3 hours

PART A

Answer all the questions: 10X2=20

1. List the types of nodes.

2. What is an interpolation function?

3. Evaluate the area integrals for the three node triangular element 4. List out the properties of stiffness matrix

5.

What are the types of non-linearity?

6. What are the four basic steps of elasticity equations?

7. What are the types of Eigen value problems?

8. List the types of dynamic analysis problems.

9. Define stream line.

10.List the method of describing the motion of fluid

PART-B

Answer all the questions: 5X16=80

11.

A simply supported beam subjected to uniformly distributed load over entire span and

it is subjected to a point load at the centre of the span. Calculate the deflection using

Rayleigh-Ritz method and compare with the exact solutions. (Fig 11.)

Fig 11.

(OR)

12.The following differential equation is available for a physical phenomenon

By using the trail function, y = a1 (x-x

3) + a2 (x-x5),

Find the value of the parameter a1and a2by the following methods.

a.

Point collocation method

b. Sub domain method

c.

Least square methodd. Galerkins method


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13.

Consider a taper steel plate of uniform thickness, t = 25mm as shown in fig 13. the

Youngs modulus of the plate, E=2 x 105N/mm2 and weight density = 0.82 x 10-4

N/mm3. In addition to its self-weight the plate is subjected to a point load P=100 N at

its mid point . Calculate the following by modeling the plate with two finite elements:

a.

Global force vector{F}b. Global stiffness matrix [K]

c. Displacements in each element

d. Stress in each element

e. Reaction force at the support

Fig 13.

(OR)

14.Consider a four bar truss as shown in fig 14 it is given that E= 2x105N/mm2 and

Ae=625 mm2 for all elements

a. Determine the element stiffness matrix for each element

b.

Assemble the structural stiffness matrix K for the entire stress

c. Solve for the nodal displacement

Fig 14.

15.A four noded rectangular element is shown in fig 15. Determine the following


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a. Jacobian matrix

b.

strain displacement matrix

c. element stressestake E=2x105N/mm2; = 0.25 ; u=[0, 0, 0.003, 0.004, 0.006, 0.004, 0, 0]T

==0; Assume plane stress condition.

Fig 15.

(OR)

16.A long hollow cylinder of inside diameter 100 mm and outside diameter 140 mm is

subjected to an internal pressure of 4 N/mm2 as shown in fig 16. By using two

elements on the 15mm length. Calculate the displacement at the inner radius. Take

E=2.1x 105N/mm2 and =0.3.

Fig 16.

17.Consider the simply supported beam shown in fig 17. Let the length (L) = 1m,

E=2x1011N/m2, area of cross-section ,A=30 cm2, moment of inertia I=100 mm4,

density = 7800 kg/m3. Determine the natural frequency using the two types of mass

matrix i.e., lumped mass matrix and consistent mass matrix.

Fig 17.

(OR)

18.

Determine the Eigen values and natural frequencies of a system whose stiffness andmass matrices are given below.


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model fea qp

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