Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 8th Sem New 2181911 Finite Elements Method Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2181911 Date:09/05/2019
Subject Name:Finite Elements Method
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) What does discretization mean in the finite element method? 03
(b) Write advantages of the finite element method.
Problems d 27
04
(c) List and describe the general steps of the Finite Element Method.
Finite
Finite Element Method
finite element method.
07
Q.2 (a) Write strain-displacement equations. 03
(b) Derive elemental stiffness matrix for truss element. 04
(c) Explain Rayleigh Ritz method with example. 07
OR
(c) Figure shows the compound section fixed at both ends. With the help of
FEA estimate the reaction forces at the supports and the stresses in each
material when a force of 200 KN is applied at the change of cross
section. Solve using penalty approach.
07
Q.3 (a) What is dynamic analysis? Why is it required? 03
(b) Explain Consistent and Lumped mass matrices. 04
(c) Derive the element stiffness matrix and stress equation for plane truss. 07
OR
Q.3 (a) State properties of stiffness matrix. 03
(b) Define shape function and list its properties. 04
(c) For the spring assemblage shown in Figure, obtain (a) The global
stiffness matrix, (b) The displacements of nodes 2?4, (c) The global
nodal forces, and (d) The local element forces. Node 1 is fixed while
node 5 is given a fixed, known displacement ? = 20:0 mm. The spring
constants are all equal to k = 200 kN/m.
07
Q.4 (a) Discuss the term CST & LST. 03
(b) Explain jacobian matrix of a 3 nodded CST element. 04
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VIII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2181911 Date:09/05/2019
Subject Name:Finite Elements Method
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) What does discretization mean in the finite element method? 03
(b) Write advantages of the finite element method.
Problems d 27
04
(c) List and describe the general steps of the Finite Element Method.
Finite
Finite Element Method
finite element method.
07
Q.2 (a) Write strain-displacement equations. 03
(b) Derive elemental stiffness matrix for truss element. 04
(c) Explain Rayleigh Ritz method with example. 07
OR
(c) Figure shows the compound section fixed at both ends. With the help of
FEA estimate the reaction forces at the supports and the stresses in each
material when a force of 200 KN is applied at the change of cross
section. Solve using penalty approach.
07
Q.3 (a) What is dynamic analysis? Why is it required? 03
(b) Explain Consistent and Lumped mass matrices. 04
(c) Derive the element stiffness matrix and stress equation for plane truss. 07
OR
Q.3 (a) State properties of stiffness matrix. 03
(b) Define shape function and list its properties. 04
(c) For the spring assemblage shown in Figure, obtain (a) The global
stiffness matrix, (b) The displacements of nodes 2?4, (c) The global
nodal forces, and (d) The local element forces. Node 1 is fixed while
node 5 is given a fixed, known displacement ? = 20:0 mm. The spring
constants are all equal to k = 200 kN/m.
07
Q.4 (a) Discuss the term CST & LST. 03
(b) Explain jacobian matrix of a 3 nodded CST element. 04
2
(c) The nodal coordinates of triangular elements are as shown in figure. The
X coordinate of interior point P is 35 and N1 = 0.3. Determine N2, N3
and Y co-ordinate of P.
07
OR
Q.4 (a) Write difference between FEM and classical methods. 03
(b) Explain Wilson's method. 04
(c) Determine the displacement and slope at the load point for the stepped
beam as shown in figure. Each elements has E = 200GPa. The area
moment of inertia are given as I1 = 1.25?10
5
mm
4
and I2 = 4?10
4
mm
4
.
Determine the elemental stiffness matrices of each element, global
stiffness matrix and application of boundary condition.
07
Q.5 (a) Write different types of 2D elements. 03
(b) Define plane stress and plane strain condition. 04
(c) Heat is generated in a large plate (K = 0.8W/m?C) at the rate of 4000
W/m
3
. The plate is 25 cm thick and the outside surfaces of the plate are
exposed to ambient air at 30?C with a convective heat transfer
coefficient of 20 W/m
2
?C. Determine the temperature distribution in the
wall.
07
OR
Q.5 (a) Write application of FEM for fluid flow problems. 03
(b) Define heat transfer, conduction, natural convection and radiation. 04
(c) For the smooth pipe of variable cross section shown in Figure, determine
the potential at the junctions, the velocities in each section of pipe and
the volumetric flow rate. The potential at the left end is p1 = 10 m
2
/s and
that at the right end is p4 = 1 m
2
/s.
07
************
300N
100mm 100mm 150mm
Y
X
1 (10, 20) 2 (50, 30)
3 (40, 60)
P (35, y)
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This post was last modified on 20 February 2020