1.
For the triangular element as shown in the Fig, determine the strain –
displacement matrix [B] and constitutive matrix [D]. Assume plane stress
conditions. Take µ = 0.1m. Also calculate the element stiffness matrix for the
triangular element.
11.
A long cylinder of outer diameter 100 mm and inner diameter 70 mm fits
snugly in a hole over its full length as shown in Figure below. The cylinder is
then subjected to an internal pressure of 1.8 MPa. Find the horizontal
displacements of two points lying on inner radius which are vertically apart by a
distance of 10 mm
2.
Determine the stiffness matrix for the CST Element shown in Fig. The coordinates are given in mm. Assume plane stress conditions E = 210GPa, v=0.25 and
t=10mm.
12.
Calculate the strain-displacement matrix and the load vector for the CST elements 1 and 2, and the global
load vector for the domain shown below.
3.
Triangular elements are used for the stress analysis of plate subjected to inplane loads. The (x,y) coordinates
of nodes i,j and k of an element are given by (2,3), (4,1), and (4,5) mm respectively. The nodal displacements
are given as:
u1=2.0 mm; u2=0.5 mm; u3=3.0 mm
v1=2.0 mm; v2=0.5 mm; v3=3.0 mm; Determine the element stresses. Let E= 160 GPa, Poisson’s ratio = 0.25
and the thickness of the element t= 10 mm.
For an axi-symmetric element, determine stiffness matrix. Take E=210GPa and µ=0.25 the coordinates are in
mm the nodel displacements are u1=0.05mm, w1=0.03mm, u2=0.02mm, w2= 0.02mm, u3= 0, w3=0. the nodal
coordinates are (0,0),(50,0), (0,50) for the node 1,2,3 respectively.
Derive the element stiffness matrix for axisymmetric triangular element.
Establish the shape functions and derive the strain displacement matrix for an axisymmetric triangular
element.
13.
……….
4.
5.
6.
7.
Derive the element stiffness matrix for the triangular element shown
in the fig with E=200GPa, Poisson’s ratio=0.3, t=10mm.
8.
The nodal coordinates for an axisymmetric triangular element are given in Fig.
Evaluate the strain – displacement matrix.
9.
10.
A thin plate of thickness 5mm is subjected to an axial loading as shown in the
Figure. It is divided into two triangular elements by diving it diagonally.
Determine the straiin displacement matrix [B], load vector and the constitutive
matrix. How will you derive the stiffness matrix?(Need not be determined).
What will be the size of the assembled stiffness matrix?. What are the
boundary conditions? E = 2 x 107 N/cm2 , μ=0.3
Determine the element strains for an axisymmetric triangular element shown in
figure. The nodal displacements are u1= 0.001, u2= 0.002, u3= 0.003, w1= 0.002,
w2=0.001, w3=0.004. All dimensions are in cm. Assume suitable missing data.