Reverse optimum safety factor approaches as effective tools for reliability-based topology optimization with application to cementless hollow stems used in total hip replacement

Abstract

During the last two decades, the different developments of Reliability-Based Topology Optimization (RBTO) can be divided into two groups. The first group called developments from a point of view 'topology optimization', leading to different layouts with decreasing rigidity (increasing compliance) levels which is considered as a drawback of these methods. In addition, some researchers consider that there is no physical meaning when representing the limit state function by the prescribed volume constraint. However, the second group, being called developments from a point of view 'reliability analysis', often leads to same layouts with increasing rigidity (or decreasing compliance) levels. The single drawback of these methods is to provide the same layouts with different thickness. Some researchers consider that this finding does not represent any importance since a detailed design stage is required to control the structural rigidity. To overcome both drawbacks, Reverse Optimum Safety Factor (ROSF) approaches are presented here to combine the two points of view to generate several layouts with increasing rigidity levels. These strategies are applied to the total hip replacement at the conceptual design stage. This way several types of hollow stems are generated considering the daily loading cases. The ROSF approaches are compared with the previous Inverse Optimum Safety Factor (IOSF) approaches. The results show that despite both approaches leading to several layouts, the ROSF approaches provide layouts with increasing rigidity (or decreasing compliance) levels. In addition to this advantage, the developed approaches lead to a decrease of material quantity in some cases (higher rigidity and less material quantity). The resulting hip stems can be additively manufactured to guarantee the configuration optimality without performing shape and sizing optimization procedures.