STUPIDSID
1 (a)
What is Fem? Sketch the different types of elements used based on geometry in finite element analysis(1D,2D,and 3D).
4 M
1 (b)
Explain with a sketch plane stress and plane strain.
6 M
1 (C)
Derive the equilibrium equation in elasticity subjected to body force and traction force and traction force
10 M
2 (a)
A cantilever beam of span 'L' is subjected to a point load at free end. Derive an equation for the deflection at free end by using RR method. Assume polynomial displacement function.
10 M
2 (b)
Write the properties of stiffness matrix and derive the element stiffness matrix(ESM) for a 1D bar element.
10 M
3 (a)
A modal co-ordinate of the triangular element is shown in Fig Q3(a). at the interior point 'P' the co-ordinate is 3.3 and N1=0.3 Determine 'N2'' and the y co-ordinate at point P.
5 M
3 (b)
What is convergence requirement? Discuss the 3 conditions of convergence requirement.
5 M
3 (c)
Derive the shape function of a 4 noded quadrilateral element.
10 M
4 (a)
Consider the bar shown in FigQ4(a). using elimination method of handling boundary conditions. Determine the following:
i) Nodal displacements
ii)Stress in each element.
iii) Reaction forces
Take E=200GPa.
i) Nodal displacements
ii)Stress in each element.
iii) Reaction forces
Take E=200GPa.
10 M
4 (b)
Consider the bar shown in figQ4(b).An axial load P=60×103N is applied at its midpoint. Using penalty method of handling boundary condition. Determine i) Nodal displacements; ii) Stress in each element; iii) Reaction at supports. Take A=250mm2; E=200GPa.
10 M
5 (a)
Derive the Shape Function for a quadratic bar element using Lagrange's interpolation.
5 M
5 (b)
Evaluate \[I=\int_{-1}^{+1}\left ( 3e^{\xi } +\xi ^{2}+\frac{1}{\xi +2}\right )d\xi \]using 1P and 2P Gaussian quadrature.
6 M
5 (c)
Derive 1 arange quadratic quadrilateral (elements)
9 M
6 (a)
List out the assumptions made in the derivation of truss element.
4 M
6 (b)
For thr truss shown in Fig Q6(b), determine
i) Nodal displacement; ii) Stress in each element iii) Reaction supports.
A=200m2; E-70GPa.
i) Nodal displacement; ii) Stress in each element iii) Reaction supports.
A=200m2; E-70GPa.
16 M
7 (a)
Derive the Hermine shape function of a n beam element
8 M
7 (b)
For the beam and loading shown in fig Q7(b) determine
i) the slopes at 2 and 3 and ii) the vertical deflection at the midpoints of the distributed load. Take E=200 Gpa, I=4×106 mm4.
i) the slopes at 2 and 3 and ii) the vertical deflection at the midpoints of the distributed load. Take E=200 Gpa, I=4×106 mm4.
12 M
8 (a)
Bring out the differences between continuum methods and FEM.
6 M
8 (b)
Solve the temperature distribution in the composite wall using 1D heat elements, use penalty approach of handling boundary conditions. (Fig Q8(b)).
K1=20W/m°C; k2=30W/m°C; k3; h=25W/m2°C;T∞=800°C
K1=20W/m°C; k2=30W/m°C; k3; h=25W/m2°C;T∞=800°C
14 M
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