MECH4450 Homework #4 Solution
Use ABAQUS to solve the following problems. Please give (1) the discretized domain
with imposed boundary conditions, (2) the deformation/temperature of the structure, (3)
stress/heat flux field, and (4) the maximum stress/heat flux and their locations.
Problem 1: Consider a brick wall (Fig.1) of thickness L= 30 cm, k=0.7 W/m·ºC. The
inner surface is at 28ºC and the outer surface is exposed to the cold air at -15ºC. The
heat-transfer coefficient associated with the outside surface is h=40 W/m2·ºC.
Fig. 1.1 Domain and boundary conditions
The discretized domain with imposed boundary conditions is indicated in Fig. 1.1. The
inner surface is subject to fixed temperature of 28ºC, and the outer surface is exposed to
convection with cold air.
Fig. 1.2 temperature of the brick wall
Fig. 1.3 Heat flux in the brick wall
The temperature of the brick wall and the heat flux field are indicated in Fig. 1.2 and Fig.
1.3 respectively.
Fig. 1.4 Node labels in the structure
Results output from Abaqus: (Node list is shown in Fig. 1.4 above)
Node
Label
1
2
3
4
NT11
@Loc 1
260.370
273.913
287.457
301.
HFL.Magnitude
@Loc 1
94.8031
94.8031
94.8031
94.8031
HFL.HFL1
@Loc 1
94.8031
94.8031
94.8031
94.8031
Minimum
At Node
260.37
1
94.8031
1
94.8031
1
Maximum
At Node
301.
88
94.8031
88
94.8031
88
8.34268E+03
8.34268E+03
Total
24.7003E+03
From the simulation results, it is shown that temperature at outer surface is 260.37 K (12.63 ºC). For this steady – state problem, the heat flux is with the same value of
94.8031 𝑊/𝑚2
Problem 2:
Fig. 2
Note: The second moment of inertia of a circular beam is 𝜋𝑅 4 ⁄4, R is the radius of the
cross section.
Solution:
Fig. 2.1 Domain and boundary conditions
Fig. 2.2 Deformation of beam
Fig. 2.3 Stress field of the beam
The domain with imposed boundary conditions is shown in Fig. 2.1, with node 2 in the
middle of beam. Applied concentrated load, distributed load and moment are all indicated
in the graph.
Results output:
The term UR3 above represents the rotation angle of node. From the results, the
maximum stress is determined to be 6.1 GPa at node 3, which is the right end of the
beam.