STUPIDSID
1 (a)
Explain Pre and post processing in FEM.
5 M
1 (b)
Derive shape function for ID quadratic element in natural co-ordinates.
5 M
1 (c)
Explain the significance of Jacobian matrix.
5 M
1 (d)
Explain Convergence results.
5 M
2 (a)
Solve the following differential Equating using Galerkin Method. \[ \dfrac {d^2y}{dx^2} + 3x \dfrac {dy}{dx}- G_y=0 \ \ \ \ 0 Find y(0.2) and compare with exact solution.
10 M
2 (b)
For the given, steel blocks supporting rigid plates shown in figure, determine displacement matrix and stresses in each element.
| Properties | Steel | Aluminium | Brass |
| C/S Area (mm2) | 200 | 370 | 370 |
| E (N/mm2) | 2×103 | 7×104 | 8.8×104 |
10 M
3 (a)
What do you mean by consistent and jumped mass matrices? Driven the same for linear bar element.
10 M
3 (b)
Consider the truss shown in figure. Given E=210 GPa and cross section area A=1 cm2 for each element. Determine
i) Displacement at each node.
ii) Stresses induced in each element
iii) Reaction at supports
i) Displacement at each node.
ii) Stresses induced in each element
iii) Reaction at supports
10 M
4 (a)
It is required to carry out one dimensional structural analysis of a circular bar of length 'L', fixed at one and carries a point load 'P' at other end. Find the suitable differential equation with required boundary condition (justify) and solve it by using Rayleigh-Ritz method for two linear element.
10 M
4 (b)
A composite wall consists of three materials, as shown in figure. The outer temperature T0=20°C. Convection heat transfer takes place on the inner surface of the wall with T?=800°C and h=30 W/m2°C. Determine temperature distribution in the wall.
K1=25 W/m-°C
K2=30 W/m-°C
K3=70 W/m-°C
K1=25 W/m-°C
K2=30 W/m-°C
K3=70 W/m-°C
10 M
5 (a)
The nodal coordinate of the triangular element are as shown in figure. At the interior point P, the x-coordinate is (4,5) and N1=0.3. Determine N2, N3 and y-coordinate of point P.
10 M
5 (b)
For a CST element the nodal displacement vector QT=[0,0,0,0,2,-0,1] mm. Find the element stress. Take E=200GPa, plate thickness t=5mm and Poisson's ratio=0.3.
10 M
6 (a)
What are serendipity elements? Derive and graphically represent interpolation functions for 8 nodded Quadrilateral elements.
10 M
6 (b)
Find the natural frequency of axial vibration of a bar of uniform cross section of 20mm2 and length 1m. Take E=2×105 N/mm2 and ρ=8000 kg/m3. Take two linear elements.
10 M
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