JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III FINITE ELEMENT TECHNIQUES Previous Question Paper (October - 2020 - R13)
Answer any five questions. All questions carry equal marks.
Main
Consider the following figure 1. An axial load P=200 KN is applied as shown. Using FEM approach for handling boundary conditions, find the following:
Answer
To determine the nodal displacements, the bar is discretized into two elements. Element 1 (length L1=0.5m, area A1=500mm², modulus E1=200GPa) and Element 2 (length L2=0.5m, area A2=250mm², modulus E2=70GPa). The stiffness matrices are calculated using k = (AE/L). For element 1, k1 = (500 * 200,000) / 500 = 200,000 N/mm. For element 2, k2 = (250 * 70,000) / 500 = 35,000 N/mm. The global stiffness matrix K is assembled as:
Applying boundary conditions at node 1 (u1=0), the reduced system is:
Solving this system yields nodal displacements u2 = 1.0526 mm and u3 = 1.0526 mm.
Answer
Stress in each element is calculated using the formula σ = E * (Δu / L). For element 1, the displacement difference is u2 - u1 = 1.0526 - 0 = 1.0526 mm. The stress is σ1 = 200,000 * (1.0526 / 500) = 421.04 MPa. For element 2, the displacement difference is u3 - u2 = 1.0526 - 1.0526 = 0 mm. The stress is σ2 = 70,000 * (0 / 500) = 0 MPa.
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Derive the element stiffness matrix and load vector for 1 – D bar element by using the principle of minimum potential energy approach.
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Obtain the forces in the plane Truss shown in Figure 2 below and determine the support reactions also. Take E=200GPa and A= 2000mm2.
Answer
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For the beam shown in Figure 3 below, determine the following: Consider all the elements have E=200GPa, I=5 × 106 mm4.
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Compute the strain displacement matrix [B] for the element shown in Figure 4. Take units in mm. Also determine the stress in the element if the nodal displacements are q = [0.02 0.01 0.01 -0.04 -0.03 0.07]T mm. Take E=210GPa, poision ratio: 0.25.
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For the point P located inside the triangle, the shape functions N1 and N2 are 0.15 and 0.25, respectively. Determine the x and y coordinates of P (figure 5).
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For the Isoparametric quadrilateral element shown in figure 6, determine the local co-ordinates of the point P whose Cartesian co-ordinates as (6,4).
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Determine the temperature distribution in one dimensional fin shown in figure 7, consider heat flux at the tip of the fin, fin diameter = 1 cm, h = 25 w / cm2°C, Tα = 40°C, K = 50 W/cm°C.
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