JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III FINITE ELEMENT METHODS Previous Question Paper (May - 2019 - R16)
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 and may have a, b, c as sub questions.
Part A
Write the temperature load vector in the matrix form of a one dimensional bar element.
Answer
The temperature load vector {f}t for a one-dimensional bar element of length L, cross-sectional area A, and modulus of elasticity E, subjected to a temperature change ΔT is given by:
where α is the coefficient of thermal expansion.
How the order of the assembled global stiffness matrix is decided?
Answer
The order of the assembled global stiffness matrix is determined by the total number of degrees of freedom (DOF) in the entire finite element model. It is equal to the product of the number of nodes and the number of degrees of freedom per node.
What is force transformation matrix in a truss element?
Answer
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What assumptions are made in classical beam theory?
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Differentiate LST and CST Element.
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What are non zero stress components of axisymmetric element.
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Write the governing equation and the functions used into determine the shearing stresses.
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What are the various boundary conditions of heat convection to take place?
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Describe the features of NASTRAN software.
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What are the convergence requirements of a finite element model?
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Part B
Derive finite element equation using galerkins method for one dimensional bar element.
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Derive the element stiffness matrix for a one dimensional quadratic element.
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Determine the nodal displacement of the following figure 1.
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Determine the shear forces and bending moments for the cantilever beam having length ‘l’.
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Derive the element stiffness matrix for triangular element and thus find the matrix element for the triangular element as shown in figure 2.
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Derive the element stiffness matrix for the following axisymmetric ring of triangular cross section (figure 3).
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Derive the element stiffness matrix of a thin plate.
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Derive the stiffness matrix for heat flow in a rectangular fin, where k, h and P denotes thermal conductivity, convective heat coefficient and perimeter of fin and A is area of cross section of fin.
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Find the natural frequency of the following truss bar (figure 4).
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Draw the mode shapes of the following stepped bar. Take E= 200 GPa, specific weight 7850 kg/m3. Take A1 = 400 mm2, and A2=200 mm2 (figure 5).
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