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The structure is linearly elastic, i.e., we have a linear relation f = Kd between the vector of
external forces f and the node displacements d. The matrix K = K T ≻ 0 is called the stiﬀness
matrix of the truss. Roughly speaking, the ‘larger’ K is (i.e., the stiﬀer the truss) the smaller the
node displacement will be for a given loading.
We assume that the geometry (unloaded bar lengths and node positions) of the truss is ﬁxed; we
are to design the crosssectional areas of the bars. These crosssectional areas will be the design
variables xi , i = 1, . . . , m. The stiﬀness matrix K is a linear function of x:
K (x) = x1 K1 + · · · + xm Km ,
where Ki = KiT
0 depend on the truss geometry. You can assume these matrices are given or
known. The total weight Wtot of the truss also depends on the bar crosssectional areas:
Wtot (x) = w1 x1 + · · · + wm xm ,
117 where wi > 0 are known, given constants (density of the material times the length of bar i). Roughly
speaking, the truss becomes stiﬀer, but...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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