2) Determine the Cartesian coordinates of the point P which has local coordinates ε = 0.8 and η = 0.6 as
Shown in figure
Shown in figure
1) For the constant strain triangular element shown in figure 1) Assemble strain displacement matrix
Take E = 2 x 105 N/mm2 and t = 20 mm
Take E = 2 x 105 N/mm2 and t = 20 mm
4) Find the natural frequencies of longitudinal vibration of the unconstrained stepped bar for shown in the above figure.
B) Integrate the function f(r) = 1 + r + r2 + r3 gu between the limits -1 and +1 using
1. exact method
2. Gauss Integration method and compare the two results.
C) Derive the stiffness matrix for two dimensional CST element and temperature effect in CST element.
A ) Find the eigen values and eigen vectors of { 4 -20 -10
-2 10 4
6 -30 -13 }
What is Isoparametric representation ?
Define Shape function?
Write down the expression for transverse vibration of beam element ?
What do you mean by amplitude of vibration ?
Write about damping effect in vibration ?
What is two dimensional elements explain with some sketches ?
What is CST Element?
What is Geometric isotropy or spatial isotropy or Geometric invariance ?
What do you mean by amplitude of vibration ?
Write about damping effect in vibration ?
. State how the types of vibrations are classified and explain.
. Write natural frequency of vibration or equation of motion for undamped free vibration of an element
What is Plane stress and Plane strain ?
Write Displacement function equation for CST element ?
Write down the expression of longitudinal vibration of bar ement ?
What do you mean by transverse vibrations ?
How the two dimensional elements are defined ?
What is QST element ?
Write down the stiffness matrix equation for two dimentional CST element ?
What is Plane stress and Plane strain ?
Write Displacement function equation for CST element ?
Write down the expression of governing equation for free axial vibration of rod ?
State the difference between direct and iterative method of solving the system of equation.
Show that the matrix A = { cosθ sinθ }
{-sinθ cosθ } is orthogonal.
2. Gauss Integration method and compare the two results.
C) Derive the stiffness matrix for two dimensional CST element and temperature effect in CST element.
D) The (x,y) co-ordinates of nodes i,j and k of an axisymmetric triangular element are given by(3,4),
D) The (x,y) co-ordinates of nodes i,j and k of an axisymmetric triangular element are given by(3,4),
(6,5) and (5,8) cm respectively .The element (in cm) vector is given as q = [0.002, 0.001, 0.004, - 0.004, 0.007 ]t Determine the element strains
(6,5) and (5,8) cm respectively .The element (in cm) vector is given as q = [0.002, 0.001, 0.004, - 0.004, 0.007 ]t Determine the element strains