686701 BE Automobile Finite Element Analysis Sathyaba University May 2014

Register Number

                               

SATHYABAMA UNIVERSITY

(Established under section 3 of UGC Act,1956)

Course & Branch :B.E - AUTO

Title of the Paper :Finite Element Analysis          Max. Marks:80

Sub. Code :686701(2008/2009)                             Time : 3 Hours

Date :02/05/2014                                                    Session :AN

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                                       PART - A                    (10 x 2 = 20)

                        Answer ALL the Questions

1.     What do you mean by constitutive law?         

2.     Define the principle of minimum potential energy.

3.     Write down the expression for the stiffness matrix for a truss         element.

4.     Differentiate one dimensional spar element with one dimensional         quadrilateral element.   

5.     What is meant by plane stress analysis?

6.     Evaluate the shape functions N1,N2,N3 at the interior point P for         the triangular element shown in fig.

7.     Give the stiffness matrix equation for an axisymmetric triangular element.

8.     How the temperature effects are considered in solving         axisymmetrical problems. Specify any one method adopted.

9.     What is the purpose of Isoparametric element?

10.   Specify the need of numerical integration for solving two   dimensional problems.

PART – B                       (5 x 12 = 60)

Answer All the Questions

11.   Briefly describe about general procedure of the finite element analysis.

(or)

12.   Use the weighted residual method to find the displacement of the         rod shown in fig.

       

13.   Using two finite element, find the stress distribution in a uniformly tapering bar of circular cross sectional area 3 cm² and         2 cm² at their ends, length 10 cm subjected to an axial tensile load of 50N at the smaller end and fixed at larger end. Take E = 2 x 10⁵ N/mm².

(or)

14.   For the three-bar truss shown in fig. Determine the displacements      of node 2 and stress in element 3.

15.   Derive the shape function for the constant strain triangular element.

(or)

16.   For the two dimensional loaded plate shown in fig determine the displacements of the nodes 1 and 2 and element stress using plane stress conditions. Neglect the body forces. E = 30 GPa, Poisson’s ratio is 0.3 and thickness of the plate is 5 mm.

17.   For the axisymmetric element shown is fig B, determine the element stresses. Take E = 2.1 x 105 N/mm2 and Poisson’s      ratio = 0.25. The co-ordinates are in millimeters and the nodal displacements are

                        u₁     =      0.05 mm          w₁    =      0.03 mm

                u₂     =      0.02 mm          w₂    =      0.02 mm

                u₃     =      0 mm               w₃    =      0 mm      

Fig.B

(or)

18.   A long cylinder of inside diameter 80 mm and outside diameter 120 mm snugly fits in a hole over its full length. The cylinder is then subjected to an internal pressure of 2 Mpa. Using two elements on the 10 mm length shown, find the displacements at the inner radius.

19.   Derive the element stiffness matrix equation for 4 noded Isoparametric quadrilateral element:

(or)

20.   Solve the plane stress problem shown in fig using four – node         quadrilateral element. Compare your deformation and stress       results with values obtained from elementary beam theory.

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