Effects of loading conditions and objective function on three-dimensional shape optimization of femoral components of hip endoprostheses

A numerical procedure was implemented for the three-dimensional (3D) shape optimization of the femoral component in total hip replacement. An algorithm was developed for defining the component geometry in terms of longitudinal and cross-sectional shape variables. The 3D design model was combined with a 3D finite element analysis and a numerical optimization procedure. An idealized femoral geometry and perfectly bonded interfaces were used for cemented and uncemented implants. The design objective was to smooth some measure of the stresses along the local interface. The effects of two different load conditions and several different objective functions were examined. A common initial implant design was used for all cases. The general trend in all design optimization was to produce a somewhat bulky implant with a rectangular cross-section. The outcome was more strongly affected by loading condition than the choice of objective function. The use of a strain energy density criterion as the objective function proved to be the most effective in reducing all equivalent stress criteria.