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Finite Element Method (Elective) (October 2010)

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Total No. of Questions : 12] [Total No. of Pages : 4 P1022 [3864]-107 B.E. (Civil) FINITE ELEMENT METHOD (2003 Course) (Elective) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer Q1 or Q2, Q3 or Q4, Q5 or Q6 from Section - I & Q7 or Q8, Q9 or Q10, Q11 or Q12 from Section - II. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of electronic pocket calculator is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) Determine half band width of overall stiffeness matrix of truss shown in fig. 1(a). [4] b) Is it possible to minimise above half band width? If yes, then suggest alternative node numbering scheme & hence half band width. [8] Using direct approach, obtain [k] for bar element with axial deformation as DOF at end nodes. [6] c) OR P.T.O. Q2) a) b) Q3) a) b) A beam element having uniform EI = 4000 kNm2 is of length l = 2m. For unit anticlockwise rotation at left node, obtain nodal forces developed. [6] A prismatic beam ABC is loaded & supported as shown in fig. 2(b). Using member approach, analyse for nodal unknowns & hence draw B.M. diagram. [12] Taking example of plane portal frame, explain member approach & structure approach for analysis. Draw neatly sketches showing the [6] difference in approach. Analyse for nodal unknowns of portal frame shown in fig 3(b). EI is uniform. Determine member end moments & draw B.M. diagram.[10] OR Q4) a) State & explain stiffeness matrix for grid element using its local axes. [8] b) What is Transformation Matrix ? With a neat sketch derive [T] for grid element. [8] [3864]-107 2 Q5) a) Explain with neat sketches requirements of polynomial displacement functions for convergence. [8] b) Using proper polynomial displacement function for two noded beam -1 element, state [A] matrix & obtain [A] . [8] OR Q6) a) Using first principles, establish relation between global & local stiffeness matrices. [6] b) A three noded triangular element is used in plane elasticity problem. Coordinates at nodes are 1(0, 0), 2(4, 0) & 3(2, 2). If u1, u2 & u3 are nodal displacements, find 1, 2 & 3 & hence shape functions. [10] SECTION - II Q7) Write in brief following : a) Serendipity elements & shape functions. [9] b) Jacobian Matrix. [9] OR Q8) Explain concept of isoparametric element taking examples of : a) Four noded quadrilateral. [9] b) Eight noded quadrilateral with four corner nodes and four midside nodes. [9] Q9) Enlist all 2D & 3D elements known to you write polynomial displacement functions for each element. Explain Geometric isotropy of element state which element satisfies the quality of geometric isotropy. [16] OR Q10)What is known as aspect ratio of element. How aspect ratio affects the accuracy of finite element solution. Explain with example. [16] [3864]-107 3 Q11)Explain practical applications in which 3D element plays important role using Tetrahydron element, obtain [A], [B] & [D] matrices. [16] OR Q12) Explain axisymmetric problems. Selecting polynomial displacement functions, obtain [A], [B] & [D] matrices in case of triangular axisymmetric element. [16] vvvv [3864]-107 4

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Additional Info : 2003 Course
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