JNTU
JNTU B.Tech III FINITE ELEMENT METHODS Previous Question Paper (March - 2024 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
What is meant by discretization?
Answer
Discretization is the process of dividing a complex continuous domain into a finite number of smaller, simple sub-regions called finite elements, which are connected at discrete points known as nodes.
What is meant by stiffness matrix?
Answer
A stiffness matrix is a square matrix that represents the relationship between the nodal displacements and the nodal forces of an element or a system. It characterizes the structural resistance to deformation, where
Sketch a typical truss element showing local, global transformation.
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Write down the expressions for the element stiffness matrix and force vector of a beam element.
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How axisymmetric element can be equalized to the CST element?
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Write down the stiffness matrix equation for four noded iso-parametric quadrilateral elements.
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What is the thermal conductivity matrix for 2D heat transfer problems?
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Write down the governing differential equation for the steady-state one-dimensional conduction heat transfer.
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What is transient dynamic analysis?
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Define Eigen value and Eigen vector.
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Part B
For the spring system shown in the figure 1. Find the displacements at the nodes and the reactions. Given K1=100 N/mm, K2=200 N/mm, K3= 100 N/mm, P=500 N.
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Consider a simple one-dimension structure with three elements, explain the process of stiffness matrix and load vector assembly.
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Explain the steps of FEM with the help of an example.
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For the two-bar Truss shown in the figure 2. Determine: (a) Nodal displacements (b) Element stresses (c) Reaction forces. Take E=200Gpa, A=200mm^2.
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For the beam having box loading on it end shown in the figure 3 determine: (a) slope at 2 and 3 (b) vertical deflection at the midpoint of the load Take E = 200GPa, I=4000000 mm^4.
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Briefly discuss elimination approach to handle boundary conditions for solution of system of equations.
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Evaluate the integral by two- and three-point gauss quadrature rule.
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Nodal coordinates for an Axi-Symmetric element are given below figure 4. Evaluate Stiffness Matrix. E=2*10^5 N/mm^2, v=0.25.
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Determine the temperature distribution along a circular fin of length 5 cm and radius 1 cm. The fin is attached to boiler whose wall temperature 140°C and the free end is open to the atmosphere. Assume Tα = 40°C, h = 10 W/cm^2/°C, k = 70 W/cm°C.
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Derive the consistence mass matrix of a two-node bar element.
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A wall of 0.6m thickness having thermal conductivity of 1.2 W/mK. The wall is to be insulated with a material of thickness 0.06 m having an average thermal conductivity of 0.3 W/mK. The inner surface temperature is 1000 and outside of the insulated is exposed to atmospheric air at 30°C with heat transfer coefficient of 35 W/m^2K. Calculate the nodal temperatures.
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Explain the following (i) Consistent mass matrix (ii) Lumped mass matrix.
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Determine the Eigen values and Eigen Vectors for the stepped bar as shown in figure 5.
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Derive mass matrices for 1D Bar Element and Truss Element.
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