<p> M.TECH. DEGREE EXAMINATION Branch : Civil Engineering Specialization – Computer Aided Structural Engineering Model Question Paper - I Second Semester MCESE 201 NUMERICAL METHODS IN ENGINEERING (Regular – 2011Admission onwards) Time : 3 Hours Total : 100 marks</p><p>1 (a) Solve the following system of equations using Cholesky method.</p><p>5 2 4 x 1 9</p><p>10 6 4 x 2 = 15</p><p>5 -2 – 4 x 3 -9 ( 12 Marks )</p><p>(b) Explain the different types of storage schemes of matrices stating the advantages and disadvantages of each. ( 8 Marks ) </p><p>(c) Explain the concept of substructure analysis. ( 5 Marks )</p><p>OR</p><p>0.5 0.5 2 (a) Solve x = [ 10 – xy ] ; y = [ ( 57 – y ) / 3x ] using Newton – Raphson method. Assume xo =</p><p>1.5, yo = 3.5. ( 15 Marks )</p><p>( b) Explain the procedure for the solution of non linear solution of equations by alpha -constant method. ( 5 Marks )</p><p>(c) Discuss the advantages of submatrix equation solver. ( 5 Marks )</p><p>3 (a) Determine all the principal stresses using Jacobi method. Illustrate three iterations.</p><p>20 -6 10 [ σ ] = -6 10 8 10 8 7 ( 12 Marks )</p><p>( b) Explain how a matrix is transformed in to a tridiagonal matrix using Given’s method and obtain the expression for the tridiagonal elements. ( 8 Marks )</p><p>(c) Discuss how a generalized eigen value problem is transformed into a standard form. ( 5 Marks ) [P.T.O]</p><p>OR</p><p>4 (a) Calculate λmin using inverse iteration method. ( 15 Marks )</p><p>4.8 -2.4 0 1.2 -2.4 9.6 -2.4 { x } = λ 2.4 { x } 0 -2.4 4.8 1.2</p><p>(b)Explain subspace iteration method for solution of large eigen value problems ( 5 Marks )</p><p>(c) Explain the concept of static condensation used in the solution of equilibrium equations ( 5 Marks )</p><p>5 (a) The bending moments at various sections of a beam are given below. Using Lagrangian interpolation, locate point of contraflexure. ( 12 Marks )</p><p>Distance ‘x ’ (m) 3.2 4.2 6.2 7.2 Bending Moment ‘M’ (kNm) 448 378 -62 -432</p><p>(b)Explain (i) steps involved interpolation by Hermitian polynomials (ii) cubic spline method of interpolation ( 2 x 4 Marks )</p><p>(c) Integrate f(x) = 10 + 20x – (3x2 / 10) +( 4x3/100)– (5x4 /1000 )+ (6x5/10000) between 8 and 12 using Gauss Quadrature. ( 5 Marks )</p><p>OR</p><p>6(a) Find the Hermitian interpolation for the following table of values given below and find value of log (0.6) using Hermitian interpolation formulae. ( 12 Marks ) x Yi = log xi Yi ’ – 1 / xi</p><p>0.4 -0.916291 2.5</p><p>0.5 -0.693147 2 0.7 -0.356675 1.43</p><p>0.8 -0.223144 1.25</p><p>[P.T.O]</p><p>(b)Evaluate the deflection at the free end of a cantilever beam of span l and loaded with a uniformly distributed load of w /m length by Gauss- Quadrature technique. ( 8 Marks )</p><p>(c ) Discuss the isoparametric style of interpolation. ( 5 Marks )</p><p>7.(a)Explain Newton’s forward backward and central difference methods on finite difference technique (10 marks) (b)From the table given below, evaluate f(3.8) using Newton’s backward difference formula.</p><p> x 0 1 2 3 4</p><p>F(x) 1 1.5 2.2 3.1 4.6 (15 marks)</p><p>OR</p><p>8. (a) Discuss the apllication of finite differences equations to the bending of simply suppoted plates (15 marks)</p><p>(b) Determine the critical load for a hinged- hinged column of length l subjected to an axial load ‘P’, using finite differnce technique. (10 marks) </p>