STUPIDSID
1(a)
What is the difference between shape function and interpolation function?Derive the shape function for cubic bar element in local co-ordinates and sketch the same along the length of the element.
10 M
1(b)
A quadrilateral element is defined by the co-ordinates (1,4),(4,2),(5,6) and (2,7).The temperature at the nodes are 20°C,30°C,40°C, and 25°C respectively.Determine the temperature at apoint P(3,4)
10 M
2(a)
The following differential equation arises in connection neat transfer through a rectangular fig
\[-KA \dfrac{d^{2}T}{dx^{2}} +hp(T-T_{infty})=0; 0 \leq x \leq 1
BCS: T(0) =T(0)\]
\[ KA \dfrac{dT}{dx}+hA(T-T_{infty})]_{x=L}=0\]
Develop an element matrix equation for the same linear element.
After getting element matrix equation use following data to find nodal temperature,K=385 W/m.k, h =25 W/m2-k to =100°C T=20°C,L=100mm,b=5mm and t=1mm
Take 4 elements (linear)
\[-KA \dfrac{d^{2}T}{dx^{2}} +hp(T-T_{infty})=0; 0 \leq x \leq 1
BCS: T(0) =T(0)\]
\[ KA \dfrac{dT}{dx}+hA(T-T_{infty})]_{x=L}=0\]
Develop an element matrix equation for the same linear element.
After getting element matrix equation use following data to find nodal temperature,K=385 W/m.k, h =25 W/m2-k to =100°C T=20°C,L=100mm,b=5mm and t=1mm
Take 4 elements (linear)
15 M
2(b)
Explain different types of nodes with suitable examples.
5 M
3(a)
Determine the displacement at the nodes principle of minimum potential energy and reaction at the supports
Use; K1=100N/mm, K3=150N/mm and K4=200 N/mm.
Use; K1=100N/mm, K3=150N/mm and K4=200 N/mm.
8 M
3(b)
Analyse completely the problem given below; Assume,E =200 Gpa
8 M
3(c)
What do you mean by pre-processing and post-processing related to FEA software?
4 M
4(a)
Analyse the following truss for displacements reaction and stresses
For each element
E=100 Gpa
A=50cm2
For each element
E=100 Gpa
A=50cm2
14 M
4(b)
Explain different types of boundary condition with suitable examples.
6 M
5(a)
Derive shape function for nine noded quadrilateral element in natural co-ordinates.
10 M
5(b)
Find the natural frequencies of axial vibration for a bar as shown in figure below using one linear element by using consistent and lumped mass matrices.
take E = 2 × 1011 N/m2 , ρ = 7800 kg/m3
take E = 2 × 1011 N/m2 , ρ = 7800 kg/m3
10 M
6(a)
Solve the following differential equation by
Galerkin method
Rayleigh-ritz method over entire domain
\[\dfrac{d^{2}u}{dx^{2}}-9u=x^{3}; 0\pm x\pm 1
BCS; U(0)=0 and u(1)=2
Compare the answer with exact solution at x=0.25,0.5 and 0.75.
Galerkin method
Rayleigh-ritz method over entire domain
\[\dfrac{d^{2}u}{dx^{2}}-9u=x^{3}; 0\pm x\pm 1
BCS; U(0)=0 and u(1)=2
Compare the answer with exact solution at x=0.25,0.5 and 0.75.
14 M
6(b)
Explain subparametric, isoparamertric and superparametric elements.
6 M
7(a)
Evaluate for following integral by using 2 × 2 Guass Quadratic rule
\[I= \int_{y=4}^{6} \int_{x=2}^{2} (1-x)^{2}(4-2)^{2}dx dy
Compare your answer with exact solution:
\[I= \int_{y=4}^{6} \int_{x=2}^{2} (1-x)^{2}(4-2)^{2}dx dy
Compare your answer with exact solution:
| No.of Sampling Points | ϵi | Wi |
| 1 | 0 | 2 |
| 2 | \[\pm \dfrac{1}{\sqrt{3}}\\] | 1 |
| 3 |
0 \[\pm \sqrt{0.6} |
8/9 5/9 |
10 M
7(b)
What are the sources of error in FEM.
5 M
7(c)
Compare FEM with classical methods.
5 M
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