MECHANICS PART – A

5.1) Write down the one dimensional heat conduction equation. [AU, April / May – 2011] 5.2) Distinguish between homogenous and non – homogenous boundary conditions.

[AU, Nov / Dec – 2013]

5.3) Write down the expression of shape function and temperature function for one

dimensional heat conduction. [AU, May / June – 2011]

5.4) Write down the governing differential equation for the steady state one dimensional

conduction heat transfer. [AU, Nov / Dec – 2010, 2012]

5.5) Write down the governing differential equation for a two dimensional steady-state

heat transfer problem. [AU, Nov / Dec – 2009]

5.6) Write down the stiffness matrix equation for one dimensional heat conduction

element. [AU, Nov / Dec – 2011]

5.7) Sketch a two dimensional differential control element for heat transfer and obtain the

heat diffusion equation. [AU, Nov / Dec – 2012]

5.8) Define element capacitance matrix for unsteady state heat transfer problems.

[AU, May / June – 2013]

5.9) Name a few boundary conditions involved in any heat transfer analysis.

[AU, April / May – 2010]

5.10) Mention two natural boundary conditions as applied to thermal problems.

[AU, April / May – 2011]

5.11) Consider a wall of a tank containing a hot liquid at a temperature T0 with an air

stream of temperature Tx passed on the outside, maintaining a wall temperature of TL

at the boundary. Specify the boundary conditions. [AU, April / May – 2009]

5.12) Define static condensation. [AU, Nov / Dec – 2010]

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₇₈ 5.14) Write the step by step procedure of solving a torsion problem by finite element

method. [AU, April / May – 2011]

5.15) Outline the step by step procedure of handling torsion problem using the finite

element method. [AU, May / June – 2012]

5.16) Define streamline. [AU, May / June – 2012]

5.17) Define the stream function for a one-dimensional incompressible flow.

[AU, April / May – 2011]

5.18) List the applications of the potential flow. [AU, Nov / Dec – 2011]

5.19) List the method of describing the motion of fluid. [AU, May / June – 2012] 5.20) State the relation between the velocity of fluid flow and the hydraulic gradient

according to Darcy's law, explaining the terms involved. [AU, Nov / Dec – 2012]

5.21) Define the stream function for a one dimensional incompressible flow.

[AU, Nov / Dec – 2013]

5.22) Define the stream function for a two dimensional incompressible flow.

[AU, May / June – 2013]

Part – B

5.23) Write the mathematical formulation for a steady state heat transfer conduction

problem and derive the stiffness and force matrices for the same.

[AU, Nov / Dec – 2008]

5.24) Consider a plane wall with uniformly distributed heat source. Obtain the finite

element formulation for the above case based on the stationarity of a functional.

[AU, Nov / Dec – 2013]

5.25) Derive a finite element equation for one dimensional heat conduction with free end

convection. [AU, May / June – 2013]

5.26) The temperature at the four corners of a four – noded rectangle are T1, T2 T3 and T4.

Determine the consistent load vector for a 2-D analysis, aimed to determine the thermal stresses. [AU, Nov / Dec – 2007, April / May – 2009]

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₇₉ 5.27) Derive the stiffness matrix and load vectors for fluid mechanics in two dimensional

finite element. [AU, May / June – 2012]

5.28) Give the one-dimensional formulation for one-dimensional flow and derive the

element stiffness matrix for the flow through a porous medium.

[AU, Nov / Dec – 2012]

5.29) In the finite element analysis of a two dimensional flow using triangular elements, the

velocity components u and v are assumed to vary linearly within an element (e) as

u(x ,y) = a

1

U

i(e)

+ a

2

U

j(e)

+ a

3

U

k(e)

v(x ,y) = a

1

V

i(e)

+ a

2

V

j(e)

+ a

3

V

k(e)

where (

U

_i(e)

, V

_i(e)) denote the values of (u, v) at node i. Find the relationship between (

U

i(e)

, V

i(e)

... V

k(e))which is to be satisfied for the flow to be incompressible.

[AU, May / June – 2013]

5.30) Develop stiffness coefficients due to torsion for a three dimensional beam element.

[AU, April / May – 2009]

5.31) Establish the finite element equations including force matrices for the analysis of two

dimensional steady – state fluid flows through a porous medium using triangular element. [AU, Nov / Dec – 2013]

5.32) Explain the potential function formulation of finite element equations for ideal flow

problems. [AU, May / June – 2013]

5.33) Find the temperature at a point P(1,1.5) inside the triangular element shown with the

nodal temperatures given as T1 = 400C, TJ = 340C, and TK = 460C. Also determine the

location of the 420C contour line for the triangular element shown in figure below.

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₀ 5.34) Obtain the finite element equations for the following element. The thermal

conductivity (k) of the material of the element is 2 W/ mK. The convective heat transfer coefficient (h) is 3 W/m2K. The ambient temperature (Tf) is 25˚ C. The

thickness (t) of the material is 1mm. Assume convection along the edge ‘jk’ alone.

[AU, April / May - 2011]

5.35) Compute the elemental stress vectors for the following element, assuming plane stress

conditions. The nodal displacements in ‘mm’ [q] = [0 1 1 0 1 1]T. The temperature increase in the element is 5˚C. Take E = 200 GPa and µ = 0.3. The thermal coefficient of expansion is 11 * 10-6 /˚C. The thickness of the material is 1 mm. [AU, April / May - 2011]

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₁ 5.36) Calculate the element stiffness matrix and the thermal force vector for the

axisymmetric triangular element as shown below. The element experiences a 150 C increase in temperature. Take  = 10 x 10-6 / 0C, E = 2 x 105 N/mm2 and = 0.25

5.37) Determine the temperature and heat fluxes at a location (2, 1) in a square plate as

shown in figure. Draw the isothermal for 125°C. T1 = 100°C, T2 = 150°C, T3 =

200°C, T4 = 50°C [AU, Nov / Dec – 2010]

5.38) Consider a brick wall of thickness 0.3 m, k = 0.7 W/m˚C. The inner surface is at 28˚C

and the outer surface is exposed to cold air at -15˚C. The heat transfer coefficient associated with the outside surface is 40 W/m2˚C. Determine the steady state

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₂

temperature distribution within the wall and also the heat flux through the wall. Use two 1D elements and obtain the solution. [AU, Nov / Dec – 2013]

5.39) Consider a brick wall as shown in figure of thickness L = 30cm, K = 0.7 W/m˚C. The

inner surface is at 28˚C and the outer surface is exposed to cold air at -15˚C. The heat transfer coefficient associated with the outside surface is h = 40 W/m2˚C. Determine the steady state temperature distribution within the wall and also the heat flux through the wall. Use a two element model. Assume one dimensional flow.

[AU, April / May – 2011]

5.40) A composite wall consists of three materials as shown in figure. The outer

temperature is T0 = 20˚C. Convection heat transfer takes place on the inner surface of

the wall with T∞ = 800˚C and h = 25W/m2˚C. Determine the temperature distribution

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₃ 5.41) A composite wall is made of three different materials. The thermal conductivity of the

various sections are k1 = 2 W/cm ˚C, k2 = 1 W/cm ˚ C, k3 = 0.2 = W/cm ˚C. The

thickness of the wall for the section is 1cm, 5cm and 4cm respectively. Determine the temperature values of nodal points within the wall. Assume the surface area to unity. The left edge of the wall is subjected to a temperature of 30˚C and the right side of the wall is at 10˚C. [AU, Nov / Dec – 2011]

5.42) Figure shows a sandwiched composite wall. Convection heat loss occurs on the left

surface and the temperature on the right surface is constant. Considering a unit area and with the parameters given, use three linear elements (one for each layer) and

(i) Determine the temperature distribution through the composite wall and (ii) Calculate the flux on the right surface of the wall. [AU, Nov / Dec – 2012]

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₄ 5.43) A wall of 0.6m thickness having thermal conductivity of 1.2 W/m-K the wall is to be

insulated with a material of thickness 0.06 m having an average thermal conductivity of 0.3 W/m-K. The inner surface temp is 1000˚C and outside of the insulation is exposed to atmospheric air at 30˚C with heat transfer co-efficient of 35 N/m2 K. Calculate the nodal temperature using FEA. [AU, Nov / Dec – 2011]

5.44) A long bar of rectangular cross section having thermal conductivity of 1.5 W/m˚C is

subjected to the boundary condition as shown below. Two opposite sides are maintained at uniform temperature of 180 0C. One side is insulated and the remaining side is subjected to a convection process with T = 85˚C and h = 50 W/m2˚C.

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₅ 5.45) The plane wall shown below is 0.5 m thick. The left surface of the wall is maintained

at a constant temperature of 2000C and the right surface is insulated. The thermal conductivity K = 25 W/Mo_{C and there is a uniform heat generation inside the wall}

of Q = 400 W/m3. Determine the temperature distribution through the wall thickness using linear elements.

5.46) Determine three points on the 50o C contour line for the rectangular element shown in

the figure. The nodal values are i= 42o C, j=54o C, k= 56o C and m= 46o C.

5.47) Compute the steady state temperature distribution for the plate shown in the figure

below. A constant temperature of T0 = 1500 C is maintained along the edge y = w and

all other edges have zero temperature. The thermal conductivities are Kx = Ky = 1.

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₆ 5.48) A steel rod of diameter d = 2 cm, length l =5 cm and thermal conductivity K = 50

W/m˚C is exposed at one end to a constant temperature of 320˚C. The other end is in ambient air of temperature 20˚C with a convection co-efficient of h = 100 W/m2˚C. Determine the temperature at the midpoint of the rod using FEA.

[AU, Nov / Dec – 2011]

5.49) Determine the temperature distribution in one dimensional rectangular cross-section

as shown in Figure. The fin has rectangular cross-section and is 8cm long 4cm wide and 1cm thick. Assume that convection heat loss occurs from the end of the fin. Take h = 3W / cm˚C, h = 0.1 W / cm2˚ C,T ∞ = 20˚C. [AU, April / May – 2011]

5.50) Calculate the temperature distribution in stainless steel fin shown in figure. The

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₇ 5.51) Calculate the element stiffness matrix and thermal force vector for the plane stress

element shown in figure below. The element experiences a rise of 100C.

[AU, April / May - 2008]

5.52) Calculate the temperature at the point for a three noded triangular element as shown

in figure. The nodal values are T1 = 40˚C, T2 = 34˚C and T3 = 46˚C. Point A is located at (2, 1.5). Assume the temperature is linearly varying in the element. Also determine the location of 42˚C contour line. [AU, May / June – 2011]

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₈ 5.53) Determine the element stiffness matrix and the thermal load vector for the plane stress

element shown in figure. The element experiences 20oC increase in temperature. Take

E = 15e6 N/cm2,  = 0.25, t = 0.5 cm and a = 6e - 6/o C. [AU, April / May - 2010]

5.54) The triangular element shown in figure is subjected to a constant pressure 10 N/mm2

along the edge ij. Assume E = 200 Gpa, Poisson’s ratio  = 0.3 and thickness of the element = 2 mm. The coefficient of thermal expansion of the material  = 2 x10-6/ oC and T = 50o C. Determine the constitutive matrix (stress-strain relationship matrix D) and the nodal force vector for the element. [AU, Nov / Dec - 2009]

5.55) Compute the element stiffness matrix and vectors for the element shown in figure

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₈₉ 5.56) Compute the element matrices and vectors for the element shown below, when the

edges jk and ik experience convection heat loss.

5.57) Compute element matrices and vectors for the elements shown in figure when the

FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) ₉₀ 5.58) For the smooth pipe of variable cross-section as shown in Figure. Determine the

potentials at the junctions, the velocities in each pipe. The potentials at the left end is 10 m and that at the right end is 2m.The permeability coefficient is 1 m/sec.

[AU, April / May – 2011]

5.59) For the two dimensional sandy soil region as shown in figure. Determine the potential

distribution. The potential (fluid head) on the left side is 10m and on right hand side is 0. The upper and lower edges are impermeable Kxx = 25*10-5 m/s and Kyy = 25*10-5

0 -. . . . KC*) = 0 . .

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2

2

2

3

4

0

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In document FEA QUESTION WITH CLASS NOTES AND FORMULA BOOK (Page 78-200)