Metoda FMD

The presentation deals with minimization of the weighted average of
compliances of structures, made of an elastic  material of spatially
varying elasticity moduli, subjected to n load variants acting
non-simultaneously. The trace of the Hooke tensor is assumed as the unit
cost of the design. Three versions of the free material design are
discussed: designing the moduli of arbitrary anisotropy (AMD), designing
the moduli of an isotropic material (IMD), designing of Young’s modulus
for a fixed Poisson ratio (YMD). The problem is in all cases reduced to
the Linear Constrained Problem (LCP) of Bouchitté and Fragalà consisting
of two mutually dual problems: stress based and strain based, the former
one being characterized by the integrand of linear growth depending on
the trial statically admissible stresses. The equivalence of the stress
fields solving the (LCP) problem and those appearing in the optimal body
subjected to subsequent load cases  is shown.

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