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- Finite Element Methods - FEM
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Registration No : Total Number of Pages : 02 B.Tech. PCAE4306 6th Semester Back Examination 2017-18 FINITE ELEMENT METHOD BRANCH : AERO Time : 3 Hours Max Marks : 70 Q.CODE : C205 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right-hand margin indicate marks. Q1 a) b) c) d) e) f) g) h) i) j) Q2 a) b) Q3 a) b) Q4 a) Answer the following questions : What do you mean by traction? Differentiate between essential and natural boundary conditions. State the properties of stiffness matrix. Explain the principle of minimum potential energy. What is LST element? Write the stiffness matrix equation for 2-D CST element. What are the isoparametric elements? State the shape function. How stress will change with the effect of temperature? List some software packages of FEA. (2 x 10) Derive element stiffness matrix and load vector for linear element using potential energy approach. A long rod is subjected to loading and a temperature increase of 30°C The total strain ata point is measured to be 1.2 X 10-5. If E = 200GPa and α = 12 X 10-6/0C; determinethe stress at the point. (5) A bar is subjected to an axial force is divided into a number of quadratic elements. For a particular element the nodes 1, 3, 2 are located at 15mm, 18mm and 21mm respectively from origin. If the axial displacements of the three nodes are given by u1 = 0.00015mm, u2 = 0.00024mm and u3 = 0.0033mm. Determine the shape function. Derive the mass matrix and geometric stiffness matrix for a beam element. (5) Determine the Jacobian of the transformation J for the triangular element shown in Figure. (5) (5) (5)

Q5 b) Derive the Stiffness matrix for a 3D truss Element. (5) a) Derive the thermal gradient vector for a triangular element with six nodes (three nodes at the vertices of the triangle and three mid side nodes). Explain Iso-parametric, sub-parametric and super-parametric elements and explain the advantages of Iso-parametric elements. (5) Explain the various stages involved in solving a problem using a commercial Finite element package. The governing differential equation for the fully developed laminar flow is (5) b) Q6 a) b) (5) (5) 2 given by d v du g cos 0 with the boundary conditions v(L) = 0, Іx= 2 d x dx 0 = 0, find velocity distribution v(x) using weighted residual method. Q7 An axial load P=300x103N is applied at 200C to the rod as shown in figure below. The temperature is the raised to 600C. Calculate the followings: (a) Assemble the K and F matrices. (b) Determine the nodal displacements and stresses. Q8 Write short answer on any TWO : Rayleigh-Ritz method. Characteristic Equation. One-point formula. Serendipity family of elements. a) b) c) d) (10) (5 x 2)

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