Introduction to the Finite Element Method
ME 464/564
Homework 7
Due: 4/24/2020
Problems from Logan, 6th Edition (see scans on Canvas). Note: Problems from the 5th
Edition are different, so you must use the scanned problems to complete this
assignment if you have the 5th Edition.
This homework is strongly encouraged but optional and will count for 100 extra
credit points on your homework grade. While you are not required to complete
this assignment you are responsible for understanding the material it covers for
the Final Exam. Homework submissions will be considered on time until solutions
are posted (most likely on 4/25/2020 so you can have them to study for the Final).
Once solutions are posted no late homework will be accepted since this is an
extra credit assignment.
Problems:
8.5 (a), 8.7, 9.1 (c), 9.7 (a), 10.2 (b), 10.10
Required Problems:
9.1
For the elements shown in Figure P9-1, evaluate the stiffness matrices using Eq. (9.2.2).
The coordinates are shown in the figures. Let E = 15 x 106 psi and v = 0.25 for each
element.
9.7
For the axisymmetric elements shown in Figure P9-7, determine the element stresses.
Let E = 105 GPa and v = 0.25. The coordinates (in millimeters) are shown in the figures,
and the nodal displacements for each element are
10.2 (b) For the two-noded one-dimensional isoparametric element shown in Figure P10-2 (b),
with shape functions given by Eq. (10.1.5), determine (a) intrinsic coordinate s at point A
and (b) shape functions N1 and N2 at point A. In the displacements at nodes one and two
are respectively, u1 = 0.005 in. and u2 = -0.005 in., determine (c) the value of the
displacement at point A and (d) the strain in the element.
Figure P10-2