Nonlinearity investigation of reliability-based topology optimization strategies with application to total hip replacement

¹ INSA Rouen, 685 Avenue de l’Université, 76800 Saint-Étienne-du-Rouvray, France
² College of Engineering and Technology, American University of the Middle East, Kuwait
³ Don State Technical University, 1, Gagarin Sq., 344003 Rostov-on-Don, Russia

^* Corresponding author: imad.antypas@mail.ru

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.