Optimum design of elastic moduli for the multiple load problems

Authors:

• Tomasz Denis Lewiński

Abstract

The paper deals with minimization of the weighted averageof compliancesof structures, made of an elastic material of spatially varying elasticity moduli, sub-jected tonload variants acting non-simultaneously. The trace of the Hooke tensoris assumed as the unit cost of the design. Three versions of thefree material de-signare discussed: designing the moduli of arbitrary anisotropy (AMD), designingthe moduli of an isotropic material (IMD), designing of Young’s modulus for a fixedPoisson ratio (YMD). The problem is in all cases reduced to the Linear ConstrainedProblem (LCP) of Bouchitté and Fragalà consisting of two mutually dual problems:stress based and strain based, the former one being characterized by the integrand oflinear growth depending on the trial statically admissible stresses. The paper showsequivalence of the stress fields solving the (LCP) problem and those appearing in theoptimal body subjected to subsequent load cases.