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MNE 490/591- FEM for Additive Manufacturing Fall 2020 Homework 2 (60 Points) Due: Oct

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MNE 490/591- FEM for Additive Manufacturing Fall 2020
Homework 2
(60 Points) Due: Oct. 13 at 3:30pm
For stresses and reactions in all problems, please specify compressive/tensile (stresses) and
reaction force directions.
Problem 1 (25 Points)
Consider the truss structure given in Figure 2.18. Nodes A and B are fixed. A force equal to 10 N acts in the
positive x-direction at node C. Coordinates of joints are given in meters. Young’s modulus is E = 10!'Pa
and the cross-sectional area for all bars are A = 2 - 1077”.
a. Number the elements and nodes.
b. Assemble the global suffness and force matrix.
c. Partition the system and solve for the nodal displacements.
d. Compute the stresses and reactions.
Ci.)
D(0.1) ——+» 10
A(0.0) B(1.0)
Figure 2.18
Problem 2 (20 Points)
Given the three-bar structure subjected to the prescribed load at point B equal to 10° N as shown in
Figure 2.19. The Young’s modulusis E = 10!! Pa. the cross-sectional area of the bar BC is2 x 1077 m* and
that of BD and BF is 10>? m2. Note that point D is free to move in the x-direction. Coordinates of joints are
given in meters.
a. Construct the global stiffness matrix and load matrix.
b. Partition the matrices and solve for the unknown displacements at point B.
c. Find the stresses in the three bars.
d. Find the reactions at nodes C, D and F.
yt
Kies Milligle
Fed.) CO.) DUD
A= 2-107
A= 107 A=10~
P= 10°
Xx
B (0, QO >
Figure 2.19

MNE 490/591- FEM for Additive Manufacturing Fall 2020
Problem 3 (15 Points)
Show that the equivalent suffness of a spring aligned in the x direction for the bar of thickness f with a
centered square hole shown in Figure 2.17 1s:
ke SEtab
(a+b
where Fis the Young’s modulus and fis the width of the bar (Hint: subdivide the bar with a square hole into 3
elements).
——Y x
| | .
a
~ 2b
/10
<9) , ra .
|)_—__ SM
Figure 2.17