STUPIDSID
1 (a)
Differentiate between plane stress and plain strain problem with examples. Write the stress strain relation for both .
8 M
1 (b)
Explain the node numbering scheme and its effect on the half band-width
6 M
1 (c)
List down the basic steps involved in FEM for stress analysis of elastic solid bodies.
6 M
2 (a)
State the principle of minimum potential energy. Determine the displacement at nodes for the spring system shown in fig Q2(a)
8 M
2 (b)
Determine the deflection of a cantilever beam of length 'L' subjected to uniformly distributed load (UDL) of P unit length, using the trail function \[y=a \sin \left (\dfrac{\pi x}{21} \right )\]. compare the result with analytical solution and comment on occupancy.
12 M
3 (a)
Derive an expression for Jacobian matrix for a four-noded quadrilateral element.
10 M
3 (b)
For the triangular element shown in Fig Q3(b). Obtain the strain-displacement matrix 'B' and determine the strains εx; εy; and γxy.
Nodal displacement {q}={2 1 1 -4 -3 7} × 10-2mm.
Nodal displacement {q}={2 1 1 -4 -3 7} × 10-2mm.
10 M
4 (a)
An axial load P=300× 103 N is applied at 20°C to the rod as shown in the FigQ4(a) the temperature is then raised to 60°C.
i) Assemble the global stiffness matrix(K) and global load vector(F)
ii)Determine the nodal displacement and element stresses.
E1=70×109 N/m2, E2=200×109N/m2
A1=900mm2, A2=1200mm2
α1=23×10-6/°C, α2=11.7×10-6/°C
i) Assemble the global stiffness matrix(K) and global load vector(F)
ii)Determine the nodal displacement and element stresses.
E1=70×109 N/m2, E2=200×109N/m2
A1=900mm2, A2=1200mm2
α1=23×10-6/°C, α2=11.7×10-6/°C
12 M
4 (b)
Solve the following system of equation of Gaussian-Elimination method
x1-2x2+6x3=0
2x1+2x2+3x3=3
-x1+3x2=2
x1-2x2+6x3=0
2x1+2x2+3x3=3
-x1+3x2=2
8 M
5 (a)
Using Lagrangian method, derive the shape function of three-noded one-dimension (1D) element [quadratic element]
6 M
5 (b)
Evaluate \[I=\int_{-1}^{+1}\left ( 3e^{x } +x ^{2}+\frac{1}{x +2}\right )dx\] using one-point and two-point Gaussian quadrature.
6 M
5 (c)
Write short notes on higher order element used in FEM.
8 M
6 (a)
For the two bar truss shown in the figQ6(a). determine the nodal displacement and element stresses. A force of P=1000kN is applied at node 1. take E=210 Gpa and A=600mm2 for each element.
12 M
6 (b)
Derive an expression for stiffness matrix for a 2-D truss element
8 M
7 (a)
Derive the Hermine shape function of a n beam element
8 M
7 (b)
A simply supported beam of span 6m and uniform flexural rigidity EI=40000 kN-m2 is subjected to clockwise couple of 300 kN-m at a distance of 4m from the left end as shown in the Fig Q7(b). find the deflection at the point of application of the couple and internal loads.
12 M
8 (a)
Find the temperature distribution and heat transfer through an iron fin of thickness 5mm. Height 50mm and width 100mm. The heat transfer coefficient around the fin is 10 W/m2. K and ambient temperature is 28°C. The base of fin is at 108°C. Take k=50 W/mK. Use two element.
10 M
8 (b)
Derive element matrices for heat conduction in one-dimension element using Galerkin's approach.
10 M
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