JNTU
JNTU B.Tech III FINITE ELEMENT TECHNIQUES Previous Question Paper (November/December - 2018 - R13)
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.
PART - A
What do you understand by quadratic shape function?
Answer
A quadratic shape function is a polynomial of second degree used to interpolate the field variable within an element. It requires three nodes to define the variation, allowing for a parabolic distribution of the variable across the element.
State the properties of stiffness matrix.
Answer
The stiffness matrix is symmetric, positive semi-definite, and singular. Its size is determined by the number of degrees of freedom per element, and it represents the relationship between nodal forces and nodal displacements.
What do you understand by element stiffness matrix?
Answer
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Explain the significance of load vector in analysis of beams.
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What is a CST element?
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Describe the isoparametric element representation.
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What is axisymmetric loading?
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Explain the role of shape function in 3-D problems.
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What is consistent mass matrix?
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What is the role of eigen values and vectors in dynamic analysis?
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PART - B
Explain the method of solving stiffness equations for an axial bar element in local coordinates using potential energy approach.
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What is the importance of stress-strain relations in finite element methods? Explain with an example.
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Consider the structure shown in Figure 1. A rigid bar of negligible mass, pinned at one end, is supported by a steel rod and an aluminum rod. A load P = 30 × 103 N is applied as shown. (a) Model the structure using two finite elements. What are the boundary conditions for your model? (b) Develop the modified stiffness matrix and modified load vector. Solve the equations. Then determine element stresses.
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A three-span beam is shown in Figure 2. Determine the deflection curve of the beam and evaluate the reactions at the supports.
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For the three-bar truss shown in Figure 3, determine the displacements of node 1 and the stress in element 3.
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Assemble the load vectors F6×1 at the three nodes on the inner boundary, which is subjected to a pressure p = 0.9 MPa. (figure 4).
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For the two-dimensional loaded plate shown in Figure 5, determine the displacements of nodes 1 and 2 and the element stresses using plane stress conditions. Body force may be neglected in comparison with the external forces.
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An axisymmetric body with a linearly distributed load on the conical surface is shown in Figure 6. Determine the equivalent point loads at nodes 2, 4 and 6.
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An S-shaped block used in force measurement is subjected to a load as shown in Figure 7. Determine the amount by which the block is compressed. Take E = 70,000 N/mm2 and 1/m = 0.3.
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A long bar of rectangular cross section, having thermal conductivity of 1.5 W/m 0C is subjected to the boundary conditions shown in Figure 8. Two opposite sides are maintained at a uniform temperature of 1800C, one side is insulated and the remaining side is subjected to a convection process with T∞ = 250C and h = 50 W/m2 0C. determine the temperature distribution in the bar.
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Determine the eigen values and eigenvectors for the stepped bar shown in Figure 9.
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