JNTU
JNTU B.Tech III Year FINITE ELEMENT METHODS Previous Question Paper (April - 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.
Part A
What boundary conditions are imposed for 1 Dimensional bar element.
Answer
For a 1D bar element, the boundary conditions are either Dirichlet (essential) boundary conditions, where displacement is specified at a node (u = δ), or Neumann (natural) boundary conditions, where force or stress is specified at a node (F = AE(du/dx)).
Discuss the shape functions of one dimensional quadratic element.
Answer
A 1D quadratic element has three nodes (two end nodes and one mid-side node). The shape functions are quadratic polynomials in the natural coordinate ξ (ranging from -1 to 1):
These functions satisfy the Kronecker delta property, where each function is unity at its respective node and zero at others.
Write the hermitian shape function of a beam element.
Answer
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How local and global coordinates are related in a truss problem.
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What are the properties of a triangular coordinates.
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Write the strain displacement equation of axisymmetric problems using a cylindrical coordinate system.
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List one requirement which is sufficient for convergence for a plate element.
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Write governing differential equation for two dimensional heat transfer problem.
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Describe the features of NISA software.
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Differentiate lumped and consistent mass matrix.
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Part B
Derive the stiffness matrix and consistent load vector in matrix form for one dimensional quadratic element.
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Explore the stress strain relation for 2D and 3D elastic problems.
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Determine the nodal displacement of the following truss as shown in figure 1.
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Determine the slope and vertical deflection at the centre for the following beam figure 2.
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Derive the area and strain displacement matrix for the triangular element and thus calculate the same for the triangle as shown in figure 3.
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Derive the element stiffness matrix for the following figure 4 axisymmetric annular ring element.
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Use galerkin’s approach to find the stiffness matrix of a torsional triangular element.
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Determine the temperature distribution in a fin having rectangular cross section and is 8 cm long, 4 cm wide and 1 cm thick. Assume convection heat loss occurs from the free end of the fin. One end is fixed. Take k=3 W/cm0C, h= 0.1 W/cm2 0C and T∞=200C.
Answer
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Find the natural frequency of the following truss bar figure 5.
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Derive the eigen values and eigen vectors of the stepped bar. Assume the required data.
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