1.050: Energy Bounds in Elasticity (HW#10)
Due: Friday, November 30, 2007
MIT – 1.050 (Engineering Mechanics I)
Fall 2007
Instructor: Markus J. BUEHLER
Team Building and Team Work:
We strongly encourage you to form Homework teams of three
students. Each team only submits one solution for correction. We expect true team work, i.e. one where
everybody contributes equally to the result. This is testified by the team members signing at the end of the
team copy a written declaration that "the undersigned have equally contributed to the homework". Ideally,
each student will work first individually through the homework set. The team then meets and discusses
questions, difficulties and solutions, and eventually, meets with the TA or the instructor. Important:
Specify all resources you use for your solution.
The following set of exercises is designed to familiarize you with the use of energy bounds in
linear elasticity. This problem set is focused on 1D methods, and you will be able to apply the
techniques you have learned in Lectures 27, 28 and 29.
Please review the lecture notes and
handouts carefully.
For some of the solutions it is recommended to use
Maple
or
Mathematica
software to solve the
resulting system of linear equations.
1. Truss structure
: The sketch below shows a truss structure constructed with 6 vertical
members and a horizontal rigid bar. The structure of subjected to two loads at points A and B
(thus, this is a
forcedriven
experiment). The top of the truss structure is connected to a fixed
boundary. The goal of this problem is to solve for all displacements and axial forces using
the structure’s energy content.
L
L
L
L
L
P
Fixed boundary
Rigid bar
A
B
2P
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Due: Friday – November 30, 2007 (in class)
Page 2 of 7
r
a.
Proposed, approximate solution 1
: Use the displacement field
ξ
'
=
ξ
0
'
e
r
z
, which is
displayed in the following sketch:
P
L
L
L
L
L
z
e
r
r
'
'
0
ξ
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 Fall '08
 MarkusBuehler
 Potential Energy, Truss

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