JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III FINITE ELEMENT TECHNIQUES Previous Question Paper (January/February - 2023 - 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
Explain the importance of ANSYS in solving FEM problems.
Answer
ANSYS is a powerful commercial finite element analysis software that automates the complex mathematical computations required in FEM. It allows for the efficient modeling, meshing, and solving of large-scale engineering problems, significantly reducing the time and cost associated with manual calculations or physical prototyping.
Explain the concept of minimum potential energy.
Answer
The principle of minimum potential energy states that for a stable conservative system, the configuration that satisfies the equilibrium conditions is the one that minimizes the total potential energy. Total potential energy is defined as the sum of internal strain energy and the potential energy of external loads.
What are the different types of boundary conditions?
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Explain about plane stress and plane strain.
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State the significance of shape functions.
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Derive the equivalent load vector of beam element for UDL case.
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Specify the various elasticity equations in CST.
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Write the advantages and applications of axisymmetric element.
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Define dynamic analysis.
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Bring out the difference between continuum methods and FEM.
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Part B
Explain the potential energy formulation for obtaining element equations in finite element methods.
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Consider a bar as shown in figure 1 Young’s Modulus E = 2 × 105 N/mm2. A1= 2cm2, A2 = 1cm2 and force of 100N is applied. Determine the nodal displacement.
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Write the advantages, disadvantages, and applications of FEM.
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Explain the terms i) Mesh generation ii) Node number generation iii) Element assembly.
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Derive an expression for stiffness matrix for 2D-truss element.
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Calculate nodal displacement and elemental stresses for the truss shown in the figure 2. E=70GPa and cross-sectional area A=2 cm2 for all truss members.
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Determine the displacement and slopes at the nodes for the beam shown in figure 3. Take k=200KN/m, E=70GPa and I=2×10-4 m4.
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What are essential and natural boundary conditions for a beam element?
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Derive the strain displacement relationship matrix for CST element.
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Discuss the effect of element shape and size on the convergence of the finite element solution.
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Define Iso-parametric, Super Parametric and Sub-Parametric elements.
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Derive strain displacement [B] matrix for a 3 noded Triangular element.
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Derive the shape functions of two dimensional nine eight quadrilateral element.
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Consider a quadrilateral element as shown in figure 4 the local coordinates are ξ =0.5, η = 0.5. Evaluate Jacobian matrix and strain-Displacement matrix.
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Derive the stress-strain relationship matrix (D) for the axisymmetric triangular element.
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Derive shape function for a 4-noded quadrilateral Element using Lagrange’s methods.
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For the composite wall shown in figure 5, determine the interface temperatures considering three elements.
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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 1400C and the free end is open to the atmosphere. Assume Tα = 400C, h = 10 W/cm2/0C, k = 70 W/cm0C.
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Discuss Eigen value and Eigen vector analysis.
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Explain the following: (i) Consistent mass matrix (ii) Lumped mass matrix.
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