Finite Element Analysis -Engineering-Nov2019 - Grad Plus

Finite Element Analysis -Engineering-Nov2019

B.E. (Mechanical Engineering )
(2015 Pattern) (End sem) ( Semester-I) (Elective-I)

Time : 2½ Hours Max. Marks : 70
Instructions to the candidates:
1) All questions carry equal marks.
2) Neat diagrams must be drawn wherever necessary.
3) Assume suitable data if required.

Q.1) a) Explain in brief Rayleigh-Ritz method and relation between FEM and Rayleigh-Ritz method.[6M]

b) List different types of analysis and explain thermal analysis.[4M]


Q.2) For truss given in figure 1, determine: [10M]

a) Nodal displacements
b) Stresses in each element and
c) Reaction at support. Take E = 200 x 103 N/mm2 and A = 200 mm2.

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Q.3) a) Explain pascal’s triangle with neat sketch, show that pascal’s triangle satisfies all convergence conditions required for deciding interpolation function formulation.[6M]

b) Write element stiffness matrix for plane stress/strain problems and explain each terms of it.[4M]


Q.4) a) The nodal coordinate of triangular element are as shown in figure 2. The x coordinate of interior point P is 3.3 and shape function N1 = 0.3. Determine N2,N3 and y coordinate of point P. (Use co-factor method).[4M]

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b) Write a short note on: Element stiffness matrix and load vector for Beam element.[6M]

Q.5) a) Write short note on: [8M]

i) Natural coordinates of element and its significance in FEA.

ii) mesh refinements.

b) For the element shown in the figure 3 assemble Jacobin matrix for the Gauss point (0.7,0.5) also Check the element for uniqueness mapping.[8M]

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Q.6) a) Write a short note on Jacobian matrix for ”4-node Quadrilateral element”.[8M]

b) Evaluate Integral: I\;=\;\int_{y=4}^{y=6}\;\int_{x=-2}^{x=2}\;{(1-x)}^2\;{(4-y)}^2dxdy [8M]

Q.7) a) Write a note ”Heat transfer through pin-Fin” Explain with appropriate governing equation.[8M]

b) A metallic fin, with thermal conductivity 70W/m°K, 1 cm radius and 5 cm long extends from a plane wall whose temperature is 413°K. Determine the temperature distribution along the fin if heat is transfer to ambient air at 293 °K with heat transfer coefficient of 5 W/m²K. Take two elements along the fin.[10M]


Q.8) a) Write Element thermal conductivity(stiffness) matrix and Element thermal load sector compare them Element stiffness matrix and element load vector of Bar element respectively.[8M]

b) A composite wall as shown in figure 4 is composed of two homogeneous slabs in contact. Let thermal conductivities be K =1W/m °C for firebrick slab 1 and K=0.3 W/m °C for insulating slab2. The left side is exposed to an ambient temperature of TfL = 1000 °C inside the furnace with heat transfer coefficient of h1 = 10W/m² °C. The right side ambient temperature is TfR=25 °C outside the furnace with heat transfer coefficient of hR = 3 W/m² °C. The thickness of the slabs are L1 = 0.2 m and L2 = 0.1 m. Determine the temperature at the left edge, point between the two slabs and right of the composite wall.[10M]

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Q.9) a) List different between consistent and lumped mass matrix technique for modal analysis of structure.[10M]

b) Find the natural frequency of longitudinal vibrations using consistent and lumped mass matrix method with one element of bar as shown in figure 5. Take E = 2 x1011 N/m2, ρ = 7800 kg/m3, L =1m. [6M]

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Q.10) a) Find the natural frequency of longitudinal vibration of the stepped bar of cross-sectional areas A1 = 2500 mm2 and A2 = 1200 mm2 having equal stepped length L= 1 m as shown in figure 6. (Use consistent mass matrix). [10M]

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b)Write a dynamic equation and explain each term. Convert this into a Eigen value problem and explain its significance.[6M]

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