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

Ghias Kharmanda,Imad R Antypas,Alexey G Dyachenko

doi:10.15507/2658-4123.029.201903.332-344

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.

Highlights

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
In order to demonstrate the effect of reliability index, we generate several topologies considering different reliability levels
The Deterministic Topology Optimization (DTO) algorithm leads to a single topology considering a given initial design space while the Reliability-Based Topology Optimization (RBTO) algorithm leads to several topologies relative to the reliability index values

Summary

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. The problem of topology is to determine the general characteristics of the studied structure, and the purpose of topology optimization is to make this initial choice as automatic as possible [1] Both macroscopic structures and microscopic materials can be found using topology optimization concepts. When using the RBTO model, the obtained layout is more reliable in comparison with the deterministic topology at the same weight values. When using the RBTO model, the obtained layout is more reliable in comparison with the deterministic topology at the same weight values3 To develop this model, two points of view are presented: topology optimization and reliability analysis. To compare the resulting topologies, a shape optimization is considered and shows that for the same boundary conditions, the RBTO configurations reduce the structural weight when increasing the reliability index values

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Conclusion