Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III FINITE ELEMENT TECHNIQUES Previous Question Paper (November/December - 2017 - R13)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
Part A
Explain briefly the basic steps to solve the problems using ANSYS.
Answer
- Preprocessing: Define geometry, material properties, element types, and mesh generation.
- Solution: Apply boundary conditions and loads, then solve the system of algebraic equations.
- Postprocessing: View and analyze results such as displacements, stresses, and strains.
State the minimum potential energy principle and explain different terms of it.
Answer
The principle of minimum potential energy states that for a conservative system, the configuration that satisfies equilibrium is the one that minimizes the total potential energy, Π.
Where U is the internal strain energy stored in the body and Ω is the potential energy of external loads (body forces and surface tractions).
Draw a plane truss element and write equation for q1' and q2'.
Answer
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Derive the element stiffness matrix of a truss element.
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Find Jacobian and [B] matrix of a triangular element which has the following coordinates: (1, 2) (4, 6) and (3, 9).
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The (x, y) co-ordinates of nodes, i, j and k of a triangular element are given by (0, 0), (3, 0) and (1.5, 5) mm respectively. Evaluate the shape functions N1, N2 and N3 at an interior point P (2.2, 2.6) mm for the element.
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List out the characteristics of tetrahedran element.
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Write the strain displacement [B] matrix of a 3 noded axi-symmetric element.
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Find the temperature at =0.4, if Temperature at nodes are given by T=[35 45]T.
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Derive the consistent mass matrix of a two noded bar element.
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Part B
Consider a tapered cylinder subjected to self weight as shown figure 1, determine the nodal solution by using finite element method. Use three equal length bar elements to obtain the nodal solution.
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For the structure shown figure 2, determine the nodal displacements, stress in each element, and support reactions by using FEM procedure.
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Find the nodal solution, stress in each element of a two bar truss shown figure 3.
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For the beam loaded as shown figure 4, determine nodal deflections and slopes using two elements.
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A two dimensional plate is shown in the Figure 5. Determine the equivalent point loads at nodes 7, 8 and 9 for the linearly distributed pressure load acting on the edge 7 – 8 – 9.
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Explain the convergence criterion for h-refinement and p-refinement of 2D problems.
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Derive the stress strain equations using plane stress conditions.
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A four noded quadrilateral element is shown in figure 6. The nodal displacement vector is given as: [q] = [0 0 0.15 0.1 0.1 0.125 0.2 0]T cm. Find the following: a) The x and y co-ordinates of a point ‘p’ whose location in the element is given by = 0.5; = 0.5 and b) the displacements of the point ‘p’.
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For the element of an axisymmetric body rotating with a constant angular velocity of 1500 rpm, determine the body force vector. Include weight of the material, where the specific density is 7850 kg/m3. The co-ordinates of a triangular element are (30, 30), (55, 30), (30,55).
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Draw a tetrahedron element used to solve 3D problems with natural coordinates. And, also write the shape functions of it.
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Determine the temperature distribution in a straight fin of circular c/s. Use three one dimensional linear elements and consider the tip is insulated. Diameter of fin is 1 cm, length is 6 cm, h = 0.6 W/cm2-C, = 250 C and base temperature is 1 = 800C.
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For the triangular element with co-ordinates (1, 2) (5, 4) and (3, 10), find [B] matrix of the element for a 2 D heat conduction heat transfer.
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Consider axial vibrations of the steel stepped bar as shown figure 7. Determine mode shapes of the bar by using finite element method. Take Young’s modulus as 200 GPa density of steel 7850 kg/m3.
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