JNTU
JNTU B.Tech III FINITE ELEMENT TECHNIQUES Previous Question Paper (May/June - 2019 - R15)
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
Write the basic steps of finite element method.
Answer
The finite element method involves the following fundamental steps:
- Discretization of the domain into finite elements connected by nodes.
- Selection of appropriate displacement or shape functions to represent the variation of the field variable within each element.
- Derivation of element stiffness matrices and load vectors using variational principles or weighted residual methods.
- Assembly of the global stiffness matrix and global load vector by applying inter-element continuity and boundary conditions.
- Solution of the resulting system of algebraic equations for the unknown nodal values.
- Computation of secondary quantities such as strains and stresses from the nodal displacements.
Derive the shape functions of a 2 noded bar element.
Answer
For a 2-noded bar element of length L with nodes at x = 0 and x = L, the displacement field u(x) is assumed to be linear: u(x) = a1 + a2x. At the nodes, the displacements are u(0) = u1 and u(L) = u2.
Substituting these boundary conditions:
Solving for the constants, we get a1 = u1 and a2 = (u2 - u1) / L. Substituting these back into the displacement equation:
The shape functions N1 and N2 are defined by u(x) = N1u1 + N2u2. Therefore, the shape functions are:
Write the basic difference between plane truss and space truss elements.
Answer
Sign in to view the complete answer paper.
A truss element with local node numbers is shown in Figure 1. Find the local displacements [q1', q2'] at nodes along the element coordinate system, if q = [0, 0.01, -0.025, -0.05]T mm.
Answer
Sign in to view the complete answer paper.
Write plane stress and plane strain conditions and also write the property matrices.
Answer
Sign in to view the complete answer paper.
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, 4) mm respectively. Evaluate the shape functions N1, N2 and N3 at an interior point P (2, 2.5) mm for the element.
Answer
Sign in to view the complete answer paper.
Show a 4 noded quadrilateral element along with degrees of freedom on it. And also write the shape functions of a 4 noded quadrilateral element.
Answer
Sign in to view the complete answer paper.
What are the conditions of a problem to be axi-symmetric?
Answer
Sign in to view the complete answer paper.
Find the temperature at ξ=0.44, if Temperature at nodes are given by T=[37 45]T.
Answer
Sign in to view the complete answer paper.
Derive the consistent mass matrix of a two noded bar element.
Answer
Sign in to view the complete answer paper.
PART - B
Explain, how you solve a static structural 1 D problem using ANSYS software.
Answer
Sign in to view the complete answer paper.
Write the properties of global stiffness matrix [K].
Answer
Sign in to view the complete answer paper.
Consider the bar shown in Figure 2. An axial load P = 200 × 10^3 N is applied, Determine the nodal displacements, stress in each element and support reactions by FEM.
Answer
Sign in to view the complete answer paper.
For the structure shown in figure 3 subjected to an increase in temperature, ΔT= 800 C, determine the nodal displacements, stress in each element, and support reactions by using FEM procedure.
Answer
Sign in to view the complete answer paper.
Consider a three bar truss shown in figure 4, determine the nodal solution for the given truss. Take E = 200 GPa and cross section area of 100 mm^2 for all the members. Coordinates of nodes 1 (0, 0) and 2 (3000, 0), length of member 2-3 is 9000 mm. Hinged boundary conditions are used at nodes 1 and 2. Also find the stress in the member 2-3.
Answer
Sign in to view the complete answer paper.
For the fixed-fixed beam as shown in figure 5. Take E = 200 GPa; I1= 20 × 10^-4 m^4; I2= 10 × 10^-4 m^4. Determine the deflection and slope at x=1 m using 2 finite elements.
Answer
Sign in to view the complete answer paper.
Find the stiffness matrix of a triangular plate element shown in figure 6.
Answer
Sign in to view the complete answer paper.
Explain the convergence criterion for h-refinement and p-refinement of 2D problems.
Answer
Sign in to view the complete answer paper.
Derive the element traction load vector of a CST element.
Answer
Sign in to view the complete answer paper.
For the isoparametric quadrilateral elements shown in figure 7, determine: a) Cartesian coordinates of the point P which has local coordinates ξ = 0.57735; and η = 0.57735 b) Local coordinates of the point Q which has Cartesian coordinates (7, 4).
Answer
Sign in to view the complete answer paper.
For the element of an axisymmetric body rotating with a constant angular velocity of 1000 rpm, determine the body force vector. Include weight of the material, where the specific density is 7850 kg/m^3.
Answer
Sign in to view the complete answer paper.
Draw a tetrahedron element used to solve 3D problems with natural coordinates. And, also write the shape functions of it.
Answer
Sign in to view the complete answer paper.
Consider a brick wall of thickness L=30cm, k = 7 W/m 0C shown in figure 8. Determine the steady state temperature distribution within the wall using two bar elements.
Answer
Sign in to view the complete answer paper.
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.
Answer
Sign in to view the complete answer paper.
For the given lumped mass system shown in figure 9, derive the finite element equilibrium equation by Hamilton’s principle.
Answer
Sign in to view the complete answer paper.
Consider axial vibrations of the steel stepped bar as shown in figure 10. Develop global stiffness matrix and mass matrix, natural frequencies.
Answer
Sign in to view the complete answer paper.