09A51401 Finite Element Techniques B.Tech Question Paper : sphoorthyengg.com

Name of the College : Sphoorthy Engineering College
University : JNTUH
Department : MECHANICAL ENGINEERING
Subject Code/Name : 09A51401/FINITE ELEMENT TECHNIQUES
Year : December 2011
Degree : B.Tech
Year/Sem : III/I
Website : sphoorthyengg.com
Document Type : Model Question Paper

Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/sphoorthyengg.com/4829-09A51401%20-%20FINITE%20ELEMENT%20TECHNIQUES.pdf

Sphoorthy Finite Element Techniques Question

B. Tech III Year I Semester Examinations, December-2011
(MECHANICAL ENGINEERING (MECHATRONICS)
Time: 3 hours

Related : Sphoorthy Engineering College 09A51403 Principles of Machine Design B.Tech Question Paper : www.pdfquestion.in/4828.html

Max. Marks: 75
Answer any five questions :
All questions carry equal marks :

SET-1

1.a) What is meant by the descritization? Explain the important points to be considered during descritization.
b) What is interpolation function? Explain its importance in evaluation of the displacements values in finite element method. [7+8]

2. Calculate displacement vector, strains, stresses, strain energy and reactions for the following figure 1? Take E = 2 X 105 N/mm2. [15]
3. Estimate the displacement vector, strains, stresses and reactions in the truss structure shown below in figure 2.Take A = 1000 mm2 and E = 200 GPa. [15]

4. A beam is fixed at one end an supported by a roller at the other end, has a 20 kN concentrated load applied at the centre of the span of 10 m. Calculate the deflection and slope and also construct the shear force and bending moment diagrams. Take I = 2500 cm4 and E = 20 x 106 N/cm2. [15]

5.a) Evaluate the load vector for the triangular element subjected to a body force and a variable traction force on the side 1-2.
b) Estimate the shape function values at the point P(x, y) in terms of x and y of a triangular element with the coordinates 1(0.0), 2(20,25) and 3(10,35). [7+8]

6.a) Derive the shape functions of four nodded quadrilateral element.
b) Differentiate between Axi symmetric elements and symmetric elements with suitable examples. [7+8]

7.a) Derive the conductivity matrix for 3 noded triangular element with convection boundary condition at one of the faces of the element.

b) Estimate the temperature profile in a pin fin of diameter 30 mm, whose length is 750 mm. The thermal conductivity of the fin material is 50 W/m K and heat transfer coefficient over the surface of the fin is 40 W/m2 K at 300C. The tip is also exposed to convection and the base temperature of the fin is 8000C. [7+8]

8. Determine the Eigen values and Eigen vectors for the stepped bar shown in figure 3. E=30×106 N/m2 ,specific weight = 0.283 Kg/m3 A1= 1 m2 A2= 0.5 m2 L1=10 m.

R09Code No: 09A51401

SET-2

1.a) Derive the stress strain relation matrix for solving 3-D problems based on Generalised Hooke’s law.
b) What do you understand from the terms boundary conditions and initial conditions? Explain them. [7+8]

2. A stepped bar is subjected to an axial load of 300 kN as shown in figure 1. Find the nodal displacements, element stresses and strains and reactions. Take E = 2 X 105 N/mm2. The lengths of the bars are 300 mm and the load is acting at the centre from the one end of the bar. [15]

3.a) The coordinates of the plane truss element is given as 1(10,30) and 2(25,40) mm has the displacement values {0.1 0.2 0.1 -0.3}T with the material properties 200 GPa Youngs Modulus. Calculate the stiffness matrix, load vector and strain energy if the cross sectional area of the truss is 100 mm2.

b) Derive the stiffness matrix for the space truss element. [7+8]
4. Calculate the maximum deflection and slope by using finite element method for the simply supported beam of length L, Young’s modulus E and the moment of Inertia I, subjected to a point load of P at the centre. Compare the results with theoretical equations. [15]

5.a) For the point P located inside the triangular element with the coordinates
1(2,1), 2(4,2) and 3(3,5) if the shape functions N1 and N2 are 0.3 and 0.5. Find the coordinates of x and y at that point P.

b) Calculate the equivalent point loads for the triangular element subjected to a variable pressure on the side 2-3. [7+8]
6.a) Derive the Jacobian matrix for the 2-D quadrilateral element in terms of natural coordinates.

b) Derive the strain displacement relation matrix for axi-symmetric triangular element using Galerkin method. [7+8]
7. Calculate the temperature values at the junction points of the composite slab made of two different materials with 25 W/m K of 0.25 m thick and 40 W/m K of 0.2 5m thick.

The inner wall is exposed to a convective heat transfer coefficient of 50 W/m2K, 500C and other wall is exposed to a heat flux of 50 kW/m2. There is an internal heat generation of 500 kW/m3 in the second layer of the composite slab. [15]

8. Find the natural frequencies of longitudinal vibration for a constrained and unconstrained stepped bar as shown in the fig 2. Where A = area of cross section. [15]
E = young’s modulus