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Finite Element Method (Elective I) (October 2009)

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Total No. of Questions : 12] [Total No. of Pages : 3 [3664] - 107 P 1372 B.E. (Civil) FINITE ELEMENT METHOD (2003 Course) (Elective - I) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer Q.1 or Q.2; Q.3 or Q.4; Q.5 or Q.6 from Section I and Q.7 or Q.8; Q.9 or Q.10; Q.11 or Q.12 from Section II. 2) Answers to the two sections should be written in separate answer books. 3) Neat diagrams must be drawn wherever necessary. 4) Use of electronic calculator is allowed. 5) Figures to the right indicate full marks. SECTION - I Q1) a) b) Explain properties of element stiffness matrix & overall matrix. [4] Using any three different schemes of node numbering justify one which is effective. Refer figure no. 1 for truss application. [12] [12] OR Q2) A propped cantilever AB is of uniform EI. It is subjected to point load P at midspan of length AB if A is fixed, using only one element as member AB show that fixing moment at A is 3 Pl/16. [16] Q3) a) Explain member approach & structure approach used for portal frame [4] analysis. P.T.O. b) Develop matrix equation to solve for unknown DOFs for portal frame loaded & supported as shown in figure 2. EI is uniform. Solution is not expected. [12] OR Q4) a) In which circumstances you need transformation of stiffeness matrix from local to global axes. Prove necessary equation. [8] b) Orthogonal grid is in plane XY. It consists of two prismatic members having same EI & GJ as well as length L. Develop stiffness matrix of grid. [8] Q5) Express polynomial displacement function for beam element of length l & EI. Obtain shape functions from first principles. [18] OR Q6) a) Explain plane stress & plane strain problems. State [D] in case of plane stress problem. [8] b) Stating polynomial displacement functions explain CST & LST elements used for plane stress problems. Why LST is preferred? [10] SECTION - II Q7) A two noded bar element is subjected to axial displacement u at each end node. Develop [K] for element using polynomial displacement function.[16] OR Q8) Write step by step procedure in using finite element technique for two dimensional elasticity problem. Explain significance of boundary conditions. Take a suitable 2D example & show mesh using triangular element. [16] [3664] - 107 -2- Q9) Explain concept of isoparametric element consider four noded quadrilateral element. Write only Jacobian matrix. [18] OR Q10)Explain various factors affecting solution of finite element technique. Draw neat sketches wherever required. What do you mean by convergence? [18] Q11)In which circumstances you need 3D finite element technique. Draw different 3D elements. Write step by step procedure in deriving [K] for element of tetrahydron for 3D analysis. Write all necessary matrices. [16] OR Q12)For Hexahydron element derive shape functions for any two nodes using natural coordinate system. Draw a neat sketch of element with node numbers. Write [D] matrix for 3D elasticity problem. [16] [3664] - 107 -3-

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Additional Info : 2003 Course
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