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Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (2012 Batch) (Sem.-6)
FINITE ELEMENT METHODS
Subject Code : ASPE-313
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M.Code: 72458
Time: 3 Hrs.
Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.
- Assume suitably missing data if any.
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SECTION-A
- Answer briefly :
- Write the expression of six strain components in terms of displacements.
- Differentiate between natural and Cartesian coordinate systems.
- Explain the kinematically admissible displacement field term as being used in FEM.
- Explain plain stress condition with one example.
- Draw eight noded quadrilateral element in Cartesian and natural coordinate systems.
- Explain Lagrange's shape functions/elements.
- What is carried out in the processing module of FEM software?
- What is super-parametric type of Finite Element formulation?
- Write the equation of 2-D heat conduction problem in terms of temperature (T), thermal conductivity (k) and heat source/sink (Q).
- Differentiate between complex and multiplex elements with examples.
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SECTION-B
- Explain the principle of minimum potential energy and virtual work with their relevant equations.
- Derive the transformation matrix for a 2-D truss element which transforms elemental local displacement to elemental global displacement.
- Explain convergence in reference to Finite Element Method. Also explain the different conditions to achieve the same.
- Derive the stress-strain matrix for plane stress conditions from the basic concept.
- For 1-D bar element, transformation is given as ?= 2/X2-X1(x-x1)-1 which is used to relate x and ?. Let the displacement field is interpolated as u(? ) = N1q1 + N2q2 where N1 = cos(p(1+?)/4) and N2 = cos(p(1-?)/4). Plot the shape functions and develop the strain-displacement matrix. Also develop elemental matrix (you need not to evaluate the integrals).
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SECTION-C
- Explain the Finite Element modeling and shape function for linear interpolation of temperature field (1-D heat transfer element).
- For the two-bar truss as shown in Fig. 1. determine the displacement of node 1. Assume for both members E = 70 GPa and Area = 200 mm². Assume k = AE/L
where I and m have usual meanings.l² lm -l² -lm lm m² -lm -m² -l² -lm l² lm -lm -m² lm m²
Fig. 1
- A Constant Strain Triangle (CST) element is shown in Fig. 2. The element is subjected to a body force fx = x² N/cm³. Determine the nodal force vector due to the body force. Assume element thickness as 1 cm. The coordinates in the Fig. 2 are given in cm.
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Fig. 2
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