QBank FEM
QBank FEM
QBank FEM
2 For The 3 stepped bar shown in figure, find the nodal displacements, stress
in the middle portion and left support reaction.
3 Consider the three bar truss shown in figure 3. It is given that E= 200GPa,
determine the nodal displacement and stress in each member.
4 (a) Consider the bar shown in figure 4(a), an axial load P = 60kN is
applied at its mid point. Using the penalty method of handling
boundary condition; determine the nodal displacement and support
reaction.
(OR)
(b) Determine the nodal displacement, stress in each element and
reaction at the fixed support for the thin plate of uniform thickness
of 1 mm as shown in figure 4(b). Take E = 200GPa, weight density
of the plate ρ=76.6×10-6 N/mm3. In addition to its weight it is
subjected to a point load of 100N at its mid point. Model the plate
with two bar element.
5 (a) Obtain the expression for stiffness matrix and stress matrix of a
truss element.
(OR)
(b) For the two bar truss shown in figure 5(b), determine the nodal
displacement and the stress in each member. Also find the support
reaction. Take E= 200GPa.
(c)
1 a) Interpolation functions used to interpolate the value of field variable at any point within element in
terms of nodal values is called
a)degree of polynomial b)geometric boundary c)shape function d)CST
b) CST element finds its application in
a)areas with small strain b)mesh transition area c)preliminary FEA d)all of these.
c) If the heat flux for a system is zero and no heat source then the force vector [F]
a)is zero b)is equal to boundary convection vector c) is 1 d) none
d) Element heat flux vector is given by
𝑝𝑞𝑙 1 𝑝𝑞𝑙 𝑎𝑞𝑙 1 𝑝𝑞𝑙 1
a)( 2 [ ]) b) ( 2 [1 1])c) ( 2 [ ]) d) ( 6 [ ])
1 −1 1
e) Boundary conditions which are imposed on the secondary variable like forces and traction are called
……………… boundary conditions.
a)essential b)geometric c)natural d)none
f) The stiffness matrix is a _______
a)skew-symmetric matrix b)symmetric matrix c)asymmetric d)both a) and b)
g) If there are 4 numbers of nodes then global stiffness matrix is _____, provided element is one
dimensional and one degree of freedom at each node.
a)3X3 b)4X4 c)1X1 d)2X2
h) Relation between shear modulus(G), young’s Modulus(E) and Poisson’s ratio (m)
a)G = E/(2+4m) b)E =G(2+2m) c) E=2GM d) G=2EM
i) Example of 2d elements used in FEA
a)Triangular element b)quadrilateral c)both a) and b) d)none of these.
j) If the nodes are 3 in number for triangle element, it is_______
a)Linear strain triangle b)Constant strain triangle
c)Quadratic strain angle d)3-D triangular element
(OR)
7 For the two bar truss shown in figure, determine the nodal displacements and the stress in each element. Also
find the support reaction. Take E= 200GPa.
(a) Briefly discuss the basic steps involved in Finite Element Method. 06
(b) Using Rayleigh-Ritz approach, find the displacement at the midpoint of a beam as
shown in figure Q2(b) carries a central point load P, having Young’s modulus E 10
and cross sectional area A.
Fig. Q2(b)
(b) Obtain the Jacobian matrix and strain displacement matrix for 3 noded CST 12
element.
(a) Obtain the stiffness matrix of bar element using direct method. 06
(b) Determine the nodal displacement and reaction forces for the given structure by 10
using elimination method.
Fig. Q4(b)
For the two bar truss shown in, determine the nodal displacements and the stress in each
element. Also find the support reaction. Take E= 200GPa.
(b) Consider the three bar truss shown in the fig. It is given that E=2*105MPa, 12
Determine the nodal displacement, stress in each element and support reaction.
(b) A cantilever beam subjected to UDL of 12kN/m and point load of 50kN as shown 08
in figure. Determine deflection at free end and support reaction. Take E= 2*10 11
N/m2, I = 2*10-6 m4.
Consider For the four bar truss shown in figure determine
Define the plane truss and enlist the assumptions usually made in the analysis of trusses.
(a) Obtain the finite equation for the analysis of heat transfer through composite wall. 08
(b) Heat is generated in a large plate at a rate of 4000 W/m3. The plate is 25cm thick;
the outside surface of the plate is exposed to ambient air at 30 0C with the 08
convective heat transfer coefficient of 20W/m2 oC. Determine the temperature
distribution in the wall using two element model, given the thermal conduction of
plate is 0.8W/m 0C.
1 21) Boundary conditions which are imposed on the secondary 1x10 CO1 L1 1
variable like forces and traction are called ………………
boundary conditions.
a)essential b)geometric c)natural d)none
2 Elemental stiffness matrix for a bar element is________ 10 CO2 L3 PO1
1 −1 0 −1 −1 1
a)AE/L [ ] b)AE[ ] c)L/AE[ ] d)none
−1 1 −1 0 1 −1
Explain the Discretization process. Sketch and explain the different 10 CO1 L2 PO1
types of elements used in the finite element analysis.
5 Obtain the finite element equation for the analysis of heat transfer 10 CO5 L4 PO3
through composite wall.
Use Galerkin’s method to find displacement of a cantilever beam shown 10 CO5 L4 PO3
in the figure below.
23) Relation between shear modulus(G), young’s Modulus(E) and Poisson’s ratio (m)
a)G = E/(2+4m) b)E = G(2+2m) c) E=2GM d) G=2EM
a) Boundary conditions which are imposed on the primary variable like displacements are called
……………… boundary conditions.
a)geometric b)natural c)force d)none
b) Boundary conditions which are imposed on the secondary variable like forces and traction are
called ……………… boundary conditions.
a)essential b)geometric c)natural d)none
c) The stiffness matrix is a _______
a)skew-symmetric matrix b)symmetric matrix c)asymmetric d)both a) and b)
d) If there are 4 numbers of nodes then global stiffness matrix is _____, provided element is one
dimensional and one degree of freedom at each node.
a)3X3 b)4X4 c)1X1 d)2X2
e) The main diagonal elements in the Global stiffness Matrix are always _______.
a)same b)negative c)positive d)1
f) Elemental stiffness matrix for a bar element is________
1 −1 0 −1 −1 1
a)AE/L [ ] b)AE[ ] c)L/AE[ ] d)none
−1 1 −1 0 1 −1
g) In a penalty method of handling boundary conditions if node 1 and 2 are fixed then C is added to
______
a)k11 b)k22 c)k12 d)both a) and b)
h) In penalty method C is equal to _________
1 −1
a)AE/L [ ] b) min[kij] x104 c) max[kij] x104 d) all of these
−1 1
i) The stiffness matrix is used to represent the matrix relation between _________and _______
a)force, displacement b)force, velocity c), displacements, velocity d)none of these
j) Stress in each element is given by
𝐸 𝐸 𝐸
a)( 𝐿 [−1 −1] (𝑄𝑄𝑖 )) b)( 𝐿 [−1 1] (𝑄𝑄𝑖 )) c)E/L d) (𝐿 [−1 −1] (𝑄𝑄𝑖 ))
𝑖+1 𝑖+1 𝑖+1
(OR)
Using penalty method of handling boundary condition determine the nodal displacement, stress in each
element and support reaction for the following structure.
Marks CO BL PO
Note: Answer all Questions
1 If the body has no discontinuity then the spacing of nodes is … 1x10 CO1 L1 PO
a)uniform b)non uniform c)nill d)all of these 3,4
5 Discuss the derivation of one dimensional heat transfer in thin film. 10 CO5 L3 PO
1
6 A composite wall consists of 3 materials shown in the figure. The outer 10 CO6 L4 PO
temperature is To = 200C, determine the temperature distribution in the wall. 3
Convection heat transfer takes place at inner surface with T∞= 800 0C take h =
25w/m2 0C, A= 1 m2.
(OR)
7 Explain Simplex, Complex and Multiplex elements and Sketch and explain 10 CO3 L2 PO
Pascal triangle for 2D polynomials. 1
a For the spring shown in the; determine the nodal displacements using principle of
minimum potential energy.