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Finite Element Method (Elective I) (April 2010)

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Total No. of Questions : 12] P1464 [Total No. of Pages : 2 [3764]-107 B.E. (Civil) FINITE ELEMENT METHOD (Elective - I) (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) Solve Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6 from Section I and solve Q.7 or Q.8, Q.9 or Q.10, Q.11 or Q.12 from Section II. 2) Answers to the two sections must be written in separate books. 3) Figures to the right indicate full marks. 4) Use of pocket calculator is allowed. SECTION - I Q1) A pin jointed truss ABCD, AB = 3m, BC = 2m, consists of five members AB, BC, CD, DA & AC. The truss is hinged at A & D and roller supported at B such that UB is allowed. A load of 100 kN acts vertically downward at C . If AE is same for all members, develop overall matrix equation. [16] OR Q2) State the principle of minimum Potential Energy & hence derive any two equations of matrix equations for a truss member of length l of extensibility AE. Member makes an angle with x axis. [16] Q3) a) Explain direct & variational approach in deriving matrix equation in finite element method use suitable example. [8] b) A propped cantilever of length l & uniform flexural rigidity EI is subjected to moment M at propped end. Using single element analyse the beam & draw B.M. diagram. [10] OR Q4) A continuous beam ABCD is fixed at A & D and roller supported at B & C such that AB = 6m, BC = 4m & CD = 6m. EI is uniform. It is subjected to udl of 30 kN/m on entire length ABCD. Find unknown DOFs. Use structure approach. [18] P.T.O. Q5) a) b) What do you know by transformation? Explain taking suitable example. [8] Explain procedure for finite element analysis of single bay, single storey portal frame. [8] OR Q6) Explain following: a) Effective node numbering. b) Assembly process. c) Characteristics of matrix [K]. [6] [4] [6] SECTION - II Q7) Taking two dimensional triangular element for constant strain, explain procedure to obtain its stiffness matrix. Use polynomial for displacement function. [16] OR Q8) Explain & derive shape functions for three noded triangular element using area coordinates. [16] Q9) For four noded isoparametric quadrilateral element derive shape functions in natural coordinates & obtain Jacobian matrix. The element is used for plane stress condition. [16] OR Q10)What are the advantages of isoparametric element? Derive shape functions for 8 noded serendipity quadrilateral for one corner & one midside node. Use natural coordinates. [16] Q11)Write short notes on: a) Axisymmetric element & its use. b) Elasticity matrix in various problems. OR Q12)Write short notes on: a) Three dimensional element & its use. b) Shape functions for Hexahydron element. Y [3764]-107 2 [9] [9] [9] [9]

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Additional Info : April 2010 Examination - Finite Element Method (Elective I) (2003 Course)
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