Extended optimality in topology design
Most existing studies of 2D problems in structural topology optimization are based on a given (limit on the) volume fraction or some equivalent formulation. The present note looks at simultaneous optimization with respect to both topology and volume fraction, termed here "extended optimality". It is shown that the optimal volume fraction in such problems - in extreme cases - may be unity or may also tend to zero. The proposed concept is used for explaining certain "quasi-2D" solutions and an extension to 3D systems is also suggested. Finally, the relevance of Voigt's bound to extended optimality is discussed.
extended optimality topology optimization volume fraction voigt's bound compliance quasi-2d topologies