Abstract
In literature, the topology optimization can be divided into two main models. The first model is called Deterministic Topology Optimization (DTO) producing a single configuration for a given design space. The second one is called Reliability-Based Topology Optimization (RBTO) generating several layouts. In our previous work, two approaches considering the concept of Inverse Optimum Safety Factors (IOSF) were elaborated and only applied to the normal distribution being linear distribution. In this work, a nonlinearity investigation is presented to compare between the linear and nonlinear distribution. The RBTO developments are applied to the total hip replacement to provide suitable hollow stems at the conceptual design stage. The nonlinearity presented here, is related to the types of the random variable distributions. The most common distributions such as normal, lognormal, uniform and Weibull are considered here to perform the investigation. The results show the nonlinearity effect on the output parameter values, but lead to almost similar layouts of the resulting hollow stems in several cases. In certain types of distributions such as Weibull, the changes on the input parameters are very variant. At certain values of the reliability index, some input parameters of material properties exceeded their limits and the algorithm stopped.
Highlights
In the Deterministic Design Optimization, the solutions are obtained without taking uncertainty into account, that may lead to unreliable designs. the Reliability-Based Design Optimization (RBDO) seeks to find the structures that should be reliable and economic by considering the uncertainty during the detailed design stage
Before 2000, one of the main challenges in the different topology optimization studies was to obtain the unique solution for a given design space
Two points of view are presented for the Reliability-Based Topology Optimization (RBTO) developments: topology optimization and reliability analysis (For detailed comparison, the interested reader can refer to [3,4,5])
Summary
In the Deterministic Design Optimization, the solutions are obtained without taking uncertainty into account, that may lead to unreliable designs. the Reliability-Based Design Optimization (RBDO) seeks to find the structures that should be reliable and economic by considering the uncertainty during the detailed design stage. When the RBTO model leads to more reliable structures compared to the DTO model for the same weight levels (The interested reader can refer to [2] to see several kinds of applications). Considering the previous works, it has been shown that the point of view 'topology optimization' seems to be interesting for structural designers since it provides several reliability-based structures relative the reliability index changes. It leads to different layout structures while the developments from a point of view 'reliability analysis' leads to same configurations with different densities that have no sense for integrating the reliability concept
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