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

Ghais Kharmanda,Antypas Imad,Hasan Mulki,D Rudoy,A Olshevskaya,N Ugrekhelidze

doi:10.1051/e3sconf/202127304009

Abstract

In general, two types of topology optimization models can be found in literature. The first type is called Deterministic Topology Optimization (DTO) leading to a single layout when considering a given design space. The second type is called Reliability-Based Topology Optimization (RBTO) leading to various solutions. In our previous work, two strategies based on the Inverse Optimum Safety Factors (IOSF) were established and applied simply to the normal (Gaussian or linear) distribution law. In this work, linear and nonlinear (normal and lognormal) distribution RBTO cases are compared. A bridge structure is considered a numerical application to perform this comparison where different layouts at the same level of reliability can be found. The numerical results show that regarding the distribution laws, certain output parameters and safety factor values are affected. This change can affect the resulting topology layouts as well as the output parameter such as the compliance. When rising the values of the reliability index, the values of the compliance become larger and the volume values become lesser for the lognormal distribution when comparing to the normal one.

Highlights

Topology optimization is performed at the conceptual design stage where the objective is to obtain the best distribution of material density
The classical Deterministic Topology Optimization (DTO) leads to a single layout, while the Reliability-Based Topology Optimization (RBTO) model leads to several solutions with special advantages
The different RBTO developments can be regrouped in two points of view: The first point of view is 'topology optimization', the original RBTO form have been established with aim of supplying the designer with several reliability-based topology layouts, in the classical topology optimization, the designer gets only a single deterministic one [1]

Summary

Introduction

Topology optimization is performed at the conceptual design stage where the objective is to obtain the best distribution of material density. This layout is essential for all following analysis and optimization measures. The classical Deterministic Topology Optimization (DTO) leads to a single layout, while the Reliability-Based Topology Optimization (RBTO) model leads to several solutions with special advantages. [4] developed a hybrid method of RBTO with the aim of handling epistemic and aleatory uncertainties. This method consists of an efficient single optimization loop method based on Karush–Kuhn–Tucker optimality condition

Methods

Results

Conclusion