Computational Solid Mechanics Homework #2 Liu Yazhuo
Computational Report of Tapered Bar Problem
Yazhuo LIU
(SID:11710612)
1. Problem description
Solving the 1D elongation of cantilever beam with linear variate cross-sectional area during
axial tension. The bar is fixed at one end and applied with a force P at the other end. Define the
axial direction as x direction. The cross-sectional area A(x) is changing linearly along the x direction.
The Young’s modulus is E.
Parameter List
symbol
Physical Meaning [units]
L
length of the bar [m]
A
0
Original cross-sectional area [m
2
]
A
1
Final cross-sectional area [m
2
]
P
Applied force [N]
E
Young's modulus [Pa]
m
Number of elements
2. Theoretical analysis
cross-sectional area:
From mechanics of materials, stress:
If
L = 10 m, P = 1 N, E = 1 Pa, A
0
= 0.1 m
2
, and A
1
= 0.05 m
2
Easy to get the theoretical results:
