The Effect of Reliability Index Values on Resulting Reliability-Based Topology Optimization Configurations: Numerical Validation by Shape Optimization

Abstract

Introduction. The classical topology optimization leads to structural type and general layout prediction and gives a rough description of the shape of both the external and internal structure boundaries. However, Reliability-Based Topology Optimization (RBTO) model produces multiple reliability-based topologies with high levels of performance. The aim of this work is to study the effect of reliability changes on the obtained topologies. Materials and Methods. The developed Gradient-Based Method (GBM) has been used efficiently as a general method for several applications (statics and dynamics). When considering several reliability levels, several topologies can be obtained. In order to compare the resulting topologies, a shape optimization is considered as a detailed design aspect. Results. Numerical applications are carried out on an MBB (Messerschmitt-Bölkow-Blohm) beam subjected to a distributed load. The DTO model is carried out without consideration of reliability concept. However, for the RBTO model, an interval of reliability is considered that produces several topologies. Here, the randomness is applied on geometry and material parameters. The application of the shape optimization algorithm leads to reduced structural volumes when increasing the reliability levels. Discussion and Conclusion. In addition to its simplified implementation, the developed GBM strategy can be considered as a generative tool to provide the designer with several solutions. The shape optimization is considered as a numerical validation of the importance of the different resulting RBTO layouts.

Linear versus nonlinear reliability-based topology optimization with application to bridge structures

“…Considering the Performance-Based Approaches, the RBTO problem consists of minimizing the structural volume taking into account the compliance constraint and the reliability one. The problem is mathematically formulated as: (8) The optimum value of the normalized vector can be expressed by: (9) taking into account the sign of the objective function derivative with respect to random variables , we have for the performance-based iosf approach: and (10)…”

“…It leads to several configurations, but the developments from a point of view 'reliability analysis' provides same configurations with different densities that doesn't represent importance sense for the following optimization stages. Newly, two different approaches based on the IOSF (Inverse Optimum Safety Factor) are elaborated and applied to linear distribution law [7][8][9]. In this paper, an extension of these approaches is carried out considering nonlinear distribution laws such as lognormal distribution law.…”

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

“…The reliability index values affect the conceptual design stage. The validation of this effect is studied by [28]. In general, the nuclear and spatial applications require very small values of failure probability, the failure probability has to be: P f ϵ [10 -6 -10 -8 ] which corresponds to a reliability index interval β ϵ [4.75 -5.6], while in civil engineering, the failure probability has to be: P f ϵ [10 -6 -10 -5 ] which corresponds to a reliability index interval β ϵ [3 -4.25].…”

Comparison of two points of view when developing reliability-based topology optimization model: Validation on fatigue damage analysis

“…Recently, Kharmanda et al (2019a) and (2019b) developed an efficient tool, called Inverse Optimum Safety (IOSF) method, which is applied to modal analysis cases. The effect of the reliability index values on the resulting reliability-based topology configurations is also studied by Kharmanda et al (2019c).…”