Reverse Versus Inverse Optimum Safety Factor Approaches for Reliability-based Topology Optimization

Abstract

Objective:The purpose of this study is to develop new reliability-based topology optimization (RBTO) approaches in order to develop new topology layouts, which will improve the structure rigidity and improve reliability levels as compared to previous RBTO layouts (or approaches).Methods: There are two ways in which deterministic topology optimization problems can be categorized: objective-based approach (OBA) and performance-based approach (PBA). The RBTO problems consist of performing the OBA and PBA under reliability constraints. In addition, the different developments of RBTO in literature can be divided into two groups. Developments from a topology optimization standpoint are considered to be the first group, while developments from a reliability analysis standpoint are considered to be the second group. Considering these two topology optimization methods (OBA and PBA) and both RBTO perspectives, reverse optimal safety factor (ROSF) approaches are established in this study with the objective of producing several layouts with increasing rigidity levels. Additionally, these developed approaches combine the advantages of both perspectives. As part of the development of ROSF approaches, optimality conditions are used to demonstrate the robustness of expanded formulations in obtaining local optima. Results:In this paper, the proposed RBTO approaches are applied to a 2D bicycle frame structure. Despite both ROSF and inverse optimum safety factor (IOSF) methodologies leading to several layouts, ROSF approaches always yield layouts with higher rigidity (or lower compliance) levels. In other words, the proposed approaches result in more rigid structures than previous approaches. A sensitivity study demonstrates that geometrical parameters have a significant impact on structural compliance (rigidity). Lastly, it should be noted that ignoring the geometry variability has no significant effect on the layouts. Conclusion:With the proposed methods, the designer is able to produce more layouts with increasing rigidity levels as the reliability level increases. By doing so, it is possible to collect the advantages of the different existing methods described in the literature.

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

“…The developed RBTO approaches in this work allow to control the resulting topologies considering the different used functions (objective and constraints). When comparing the different findings in this work with to our previous one [32], the resulting reliabilitybased topologies here have higher rigidity and less material quantity in certain cases, which can be considered as a new advantage of the use of RBTO approaches. In addition, a sensitivity study in [32] showed a big influence of the geometrical parameters on the structural compliance (rigidity) for the used 2D bicycle frame structure.…”

“…When comparing the different findings in this work with to our previous one [32], the resulting reliabilitybased topologies here have higher rigidity and less material quantity in certain cases, which can be considered as a new advantage of the use of RBTO approaches. In addition, a sensitivity study in [32] showed a big influence of the geometrical parameters on the structural compliance (rigidity) for the used 2D bicycle frame structure. So, the geometry uncertainty of hip stems should be included to study the possibility of providing different layouts with a significant difference.…”