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Unformatted text preview: itions of the masses 2, . . . , n−1 using convex optimization.
Be sure to justify convexity of any functions that arise in your formulation (if it is not obvious).
The problem data are mi , ki , li , g , x1 , y1 , xn , and yn .
(b) Carry out your method to ﬁnd the equilibrium positions for a problem with n = 10, mi = 1,
ki = 10, li = 1, x1 = y1 = 0, xn = yn = 10, with g varying from g = 0 (no gravity) to g = 10
(say). Verify that the results look reasonable. Plot the equilibrium conﬁguration for several
values of g .
14.3 Elastic truss design. In this problem we consider a truss structure with m bars connecting a set
of nodes. Various external forces are applied at each node, which cause a (small) displacement in
the node positions. f ∈ Rn will denote the vector of (components of) external forces, and d ∈ Rn
will denote the vector of corresponding node displacements. (By ‘corresponding’ we mean if fi is,
say, the z -coordinate of the external force applied at node k , then di is the z -coordinate of the
displacement of node k .) The vector f is called a loading o...
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