JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III FINITE ELEMENT METHODS Previous Question Paper (February - 2023 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
Define plane stress conditions.
Answer
Plane stress is a state of stress in which the normal stress and shear stresses directed perpendicular to the plane of the body are assumed to be zero. Specifically, for a thin plate lying in the xy-plane, the stress components σz, τxz, and τyz are negligible. This condition is typically applicable to thin structural members subjected to in-plane loading.
State potential energy principle.
Answer
The Principle of Minimum Potential Energy states that among all kinematically admissible displacement fields that satisfy the boundary conditions of a stable elastic system, the actual displacement field that satisfies the equilibrium equations is the one that minimizes the total potential energy of the system.
The total potential energy Π is defined as the sum of the internal strain energy U and the potential energy of the external loads V:
At the state of equilibrium, the first variation of the total potential energy with respect to the displacement field is equal to zero:
Express the element temperature load in local coordinate system.
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Express the Hermite shape functions of the beam element.
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Express the body force vector of CST element.
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Express the Gauss quadrature for two dimensional integrals.
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What boundary conditions are imposed on the wall of a tank containing hot liquid?
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What is the importance of fin?
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Express the lumped mass matrix for the truss element.
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State the Hamilton’s principle.
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Part B
Determine the nodal displacements of the rod, which is subjected to an axial load of P=400 kN applied at 300C to the rod. The temperature is raised to 700C (figure 1).
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Express the strain displacement and stress strain relations for 2D and 3D elastic problems.
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What is the discretization procedure and why it is required?
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Calculate the nodal displacements and axial forces for the following truss as shown in Figure 2. Take E=200 GPa. The cross sectional area of each member in cm2 is underlined in the figure 2.
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Derive the element stiffness matrix for the beam element.
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Give the isoparametric representation of the constant strain triangle.
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Describe the procedure to find the traction force on the surface of the body.
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For the element of an axisymmetric body rotating with a constant angular velocity ω = 100 rev/min as shown in figure 3. Evaluate the approximate body force matrix. Include the weight of the material, where the weight density ρw is 0.283 lb/in3. The coordinates of the element are as shown in the figure 3.
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Calculate the temperature distribution of one dimensional rectangular fin. Use three element model (figure 4).
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Calculate the surface temperature for the wall. Use 1 element model (figure 5).
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Determine the natural frequency and the mode shape of the following stepped bar element (figure 6).
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What are the convergence requirements in the finite element method.
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Discuss about the following softwares: i) NISA ii) NASTRAN iii) ANSYS iv) HYPERMESH
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