Code No: RT41033 R13 Set No. 1 IV B.Tech I Semester Regular Examinations, November - 2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering) Time: 3 hours Max. Marks: 70 Question paper consists of Part-A and Part-B Answer ALL sub questions from Part-A Answer any THREE questions from Part-B ***** PART A (22 Marks) 1. a) Define Weighted- Residual method? [3] b) What is meant by discretization? [4] c) What is meant by boundary condition? [4] d) Specify the various elasticity equations in CST? [4] e) Evaluate the integral I= [4] f) Define dynamic analysis? [3] PART B (3x16 = 48 Marks) 2. a) Derive the strain displacement relation for a 2 dimensional element? b) For the differential equation for 0 < X< 1and with boundary conditions y(0)=0 and y(1)=0, find the solution of this problem using any two weighted residual methods. 3. a) Briefly discuss elimination approach to handle boundary conditions for solution of system of equations? b) Define shape function? Derive shape function in terms of Cartesian coordinates? 4. a) For the two-bar truss shown in figure, determine the displacements and stress. A 1 =500mm 2, A 2 =1200mm 2, E=2x10 5 N/mm 2. [10] b) What is a beam? Write the hermite shape functions for beam element? [6] 1 of 2

R13 Set No. 1 Code No: RT41033 5. Derive the strain displacement relationship matrix for CST element. [16] 6. a) Define Iso-parametric, Super Parametric and Sub-Parametric elements? [6] b) Consider a quadrilateral element as shown in fig the local coordinates are ξ =0.5, η = 0.5. Evaluate Jacobian matrix and strain- Displacement matrix. [10] 7. a) Determine the temperature distribution through the composite wall shown in figure when convective heat loss occurs on the left surface. Assume unit area. Thickness t1 = 4cm, t2 = 2cm, K1 = 0.5W/cm K, K2 = 0.05W/cm K, Tα = -50C, h = 0.1 W/cm2 K b) Define lumped mass and consistent mass? [6] [10] 2 of 2

Code No: RT41033 R13 Set No. 2 IV B.Tech I Semester Regular Examinations, November - 2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering) Time: 3 hours Max. Marks: 70 Question paper consists of Part-A and Part-B Answer ALL sub questions from Part-A Answer any THREE questions from Part-B ***** PART A (22 Marks) 1. a) What is meant by plane stress analysis? Give examples. [4] b) Differentiate between local and global coordinates? [4] c) What types of problems are treated as one-dimensional problems? [3] d) What is a Jacobian transformation? [3] e) Write short notes on 1 point technique and 2 point technique? [4] f) Define heat transfer? Write the finite element equation for 1-D heat conduction with free end convection? [4] PART B (3x16 = 48 Marks) 2. a) Derive the stress strain relations for a three-dimensional element? b) Explain the following: i) variational approach ii) weighted residual methods. 3. a) Briefly discuss penalty approach to handle boundary conditions for solution of system of equations? b) Explain natural coordinate system? Derive expression for relation between natural & cartesian coordinate systems? 4. a) Derive the stiffness matrix for truss element? b) For the beam shown in figure calculate the deflection under the load for the beam 1 of 2

R13 Set No. 2 Code No: RT41033 5. a) Derive the stiffness matrix for CST element. [6] b) Nodal coordinates for an Axi-Symmetric element are given below. Evaluate Stiffness Matrix. E=2x10 5 N/mm 2, ʋ = 0.25. [10] 6. Derive Strain displacement relation matrix for four noded quadrilateral element? [16] 7. Determine the Eigen values and Eigen Vectors for the stepped bar as shown in figure? [16] 2 of 2

Code No: RT41033 R13 Set No. 3 IV B.Tech I Semester Regular Examinations, November - 2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering) Time: 3 hours Max. Marks: 70 Question paper consists of Part-A and Part-B Answer ALL sub questions from Part-A Answer any THREE questions from Part-B ***** PART A (22 Marks) 1. a) What is meant by plane strain analysis? Give examples. [4] b) Why polynomial type of interpolation functions is mostly used in FEM? [3] c) Derive the load vector for UDL in beam. [4] d) What is axisymmetric element? What are the conditions for a problem to be axisymmetric? [4] e) What is a higher order element? What are the ways in which a 3-D problem is reduced to 2-D problem? [4] f) What do you mean by steady state heat transfer analysis? [3] PART B (3x16 = 48 Marks) 2. a) Describe the procedure involved in finite element method? b) Write the advantages, disadvantages and applications of FEM? 3. a) State & explain the minimum potential energy principle? b) Explain the significance of node numbering and element numbering during the discretization Process. 4. a) What is a truss? State the assumptions made while analyzing the truss? b) Derive the hermite shape functions in a beam element? 1 of 2

R13 Set No. 3 Code No: RT41033 5. a) Calculate the stiffness matrix for the element shown in figure? Co-ordinates are given in mm. Assume plane stress conditions. Take E=2.1X10 5 N/mm 2, ʋ=0.25, t=10mm. b) Derive the constitutive matrix for an axisymmetric element? 6. A 4 noded rectangular element is shown in figure. Determine a) Jacobian Matrix b) Strain Displacement Matrix c) Element Stresses Take E = 2 x 10 5 N/mm 2, ʋ = 0.25, ξ = η = 0, U= [0, 0, 0.003, 0.004, 0.006, 0.004, 0, 0] T. Assume Plane Stress conditions. [16] 7. Determine all natural frequencies of the simply supported beam as shown in figure? [16] 2 of 2

Code No: RT41033 R13 Set No. 4 IV B.Tech I Semester Regular Examinations, November - 2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering) Time: 3 hours Max. Marks: 70 Question paper consists of Part-A and Part-B Answer ALL sub questions from Part-A Answer any THREE questions from Part-B ***** PART A (22 Marks) 1. a) Briefly explain the concept of potential energy? [3] b) What are the locations at which nodes can be positioned during discretization? [4] c) Obtain the transformation matrix from local coordinates to global coordinates for a truss element? [4] d) Write the constitutive matrix, stiffness matrix and strain displacement matrix for axisymmetric element? [4] e) What are the advantages of Gauss quadrature numerical integration for isoparametric element? [3] f) Define Eigen value and Eigen vector? [4] PART B (3x16 = 48 Marks) 2. a) Derive Stress-equilibrium conditions for structural element. b) Briefly explain the concept of plane stress and plane strain with examples. 3. a) Discuss the convergence requirements and mesh generation? b) Briefly discuss the discretization process and types of elements used for discretization? 4. Estimate the displacement vector, stresses for the truss structure as shown below Figure. Take E=2x10 5 N/mm 2. [16] 1 of 2

Powered by TCPDF (www.tcpdf.org) R13 Set No. 4 Code No: RT41033 5. a) Derive the stiffness matrix for axisymmetric element? b) Calculate displacements and stress in a triangular plate, fixed along one edge and subjected to concentrated load at its free end. Assume E = 70,000 MPa, t = 10 mm and ʋ = 0.3. 6. a) Evaluate jacobian matrix at ξ = η = 0.5 for the linear quadrilateral element shown in figure b) Evaluate the following 7. a) Determine the temperature distribution in 1D rectangular cross section fin with 8cm long, 4cm wide, 1cm thick. Assume that convective heat loss occurs from the end of the fin. Take K = 3W/cm K, h = 0.1W/cm 2 k and Tα = 20 0 C. tip temperature is 100 0 C. [10] b) Derive mass matrices for 1D Bar Element and Truss Element? [6] 2 of 2