A bionics approach for stiffness design of continuums with displacement constraints

A new bionics approach called floating interval of reference strain energy density (FLIRSED) approach is presented to solve continuum structural topology optimization with displacement constraints. The major idea of the present method is to consider the structural topology optimization process as the bone remodelling process, which is controlled by a strain energy density (SED) dead zone (a reference interval), i.e., the update of each material point in design domain is determined by its current SED and the reference interval. For instance, the density of a material point in design domain increases when the local SED exceeds the supremum of the reference interval and the density decreases when the local SED is less than the infimum of the reference interval. To make the final results to satisfy the active constraint in optimization problem, the reference interval needs updated during iteration process. Particularly, the update of the reference interval is given to solve the optimization with displacement constraint. Several typical numerical examples are given to show the validity of the present approach.