Optimal distribution of material properties for an elastic continuum with structure-dependent body force

The simultaneous optimization of material properties and structural layout for an elastic continuum is formulated and analyzed[ The objective is to obtain the maximum structural sti}ness for prescribed surface loads and displacements\ taking into account a body force that depends on the structural layout[ Optimization with an account of self!weight or centrifugal forces are examples of these type of problems[ Arbitrary elasticity tensor _elds are considered as the problem|s variable and necessary conditions satis_ed by the solution are established[ The use of a spectral decomposition of the elasticity tensor is emphasized since it provides a simple geometrical interpretation[ Typical examples which illustrate the e}ects of the structure! dependent body force are analyzed[ It is found that a commonly used isoperimetric restriction "known as the resource constraint# is not necessarily active and that the optimal structure is locally sti}er in areas where the body force and the displacement _eld have opposite directions and locally weaker otherwise[ Thisinterestingly\ leads to a non!symmetrical distribution of material properties even for prismatic bodies under anti!symmetric surface loads