JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III Year FINITE ELEMENT TECHNIQUES Previous Question Paper (May - 2018 - R15)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
Part A
Answer
The shape functions satisfy the Kronecker delta property, where the function value is unity at its own node and zero at all other nodes. Additionally, the sum of all shape functions at any point within the element is equal to unity, ensuring partition of unity.
Answer
Potential energy is the total energy stored in a system due to its configuration or deformation. For an elastic body, it is defined as the sum of the internal strain energy and the potential energy of the external loads (body forces, surface tractions, and point loads). The principle of minimum potential energy states that among all kinematically admissible displacement fields, the one that satisfies equilibrium minimizes the total potential energy.
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Part B
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A stepped bar fixed at both ends rigidly. Starting from left first step of the bar is of 300 mm length, cross sectional area of 2400 mm^2 and young’s modulus is 70 GPa. Second step immediately follows first step and is of length 400 mm, cross sectional area is 600 mm^2 and young’s modulus is 200 GPa. Determine nodal displacement.
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For the pin jointed truss as shown in the figure. Determine: a) Element stiffness matrices b) Global stiffness matrix c) Stresses in the elements 1 and 2 d) Displacements at all nodes e) Support reactions. Assume E = 200 GPa, L1 = 750 mm, L2 = 900 mm, A1 = 100mm^2, A2 = 1250mm^2
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Derive shear force and bending moment relations for beam element.
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A triangular element is specified with the nodal coordinates 1 (1, 1), 2(5, 2), 3(3, 6), for a point ‘P’ located inside the triangle. The shape functions N1 and N3 are 0.2 and 0.45, respectively. Determine: a) The x, y coordinates of the point P. b) Determine the shape function N1, N2, N3 at a point Q(3, 3) c) Determine the Jacobian matrix.
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Derive shape functions and element stiffness matrix for 4 noded isoparametric quadrilateral elements.
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Derive the shape functions for an axisymmetric triangular element.
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Find the temperatures of circular fin made of pure copper (k= 350 W/m °C). The base of the fin is held at 75° and atmospheric temperature is 27°. The fin length is 5 cm and the diameter is 0.5 cm. the convective heat transfer coefficient h is 200 W/m^2 °C. The tip at the end of the fin is insulated.
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How can you find eigen values and eigen vectors for bar element? Explain with simple example.
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