Two decades review of reliability-based topology optimization developments

This review seeks to classify the different developments of the Reliability-Based Topology Optimization (RBTO) according to their formulations and methods. According to the RBTO formulations, two standpoints (topology and reliability standpoints) are generally treated, while according to methods, they are divided into loop and mixed methods. The different trends and gaps are discussed later. The selected publications over the last two decades (from December 2001 to December 2021) contain the term RBTO in their title and restricted to English language. There are several other publications, which have been written in other languages and some others containing the integration of the reliability analysis into topology optimization, but the RBTO was not included in their titles. These two types of publications are unfortunately not included in this review since it is the objective to provide the readers (especially the new researchers) a good guide (map) to the different RBTO developments and applications. Some additional publications considering other objective and constraint functions and dealing the RBTO with microstructural levels are also included since they were realized under the same period and containing the term of RBTO in their title. The first publication of the Reliability-Based Topology Optimization model was a technical report at Aalborg University in Denmark, published in December 2001. It was a new model where many critical discussions appeared between the topology optimization community and the reliability one during 2002 and 2003 (in several meetings and conferences). That led to delay the appearance of the first journal articles until 2004. According to the author’s knowledge, more than 70 journal papers and more than 25 other publications (conference papers, chapters, reports... etc.) have been found during the last two decades. Almost 50% of journal papers have been published during the last four years which means that there is a strong interest to implement this model.

This review seeks to classify the different developments of the Reliability-Based Topology Optimization (RBTO) according to their formulations and methods. According to the RBTO formulations, two standpoints (topology and reliability standpoints) are generally treated, while according to methods, they are divided into loop and mixed methods. The different trends and gaps are discussed later. The selected publications over the last two decades (from December 2001 to December 2021) contain the term RBTO in their title and restricted to English language. There are several other publications, which have been written in other languages and some others containing the integration of the reliability analysis into topology optimization, but the RBTO was not included in their titles. These two types of publications are unfortunately not included in this review since it is the objective to provide the readers (especially the new researchers) a good guide (map) to the different RBTO developments and applications. Some additional publications considering other objective and constraint functions and dealing the RBTO with microstructural levels are also included since they were realized under the same period and containing the term of RBTO in their title. The first publication of the Reliability-Based Topology Optimization model was a technical report at Aalborg University in Denmark, published in December 2001. It was a new model where many critical discussions appeared between the topology optimization community and the reliability one during 2002 and 2003 (in several meetings and conferences). That led to delay the appearance of the first journal articles until 2004. According to the author’s knowledge, more than 70 journal papers and more than 25 other publications (conference papers, chapters, reports... etc.) have been found during the last two decades. Almost 50% of journal papers have been published during the last four years which means that there is a strong interest to implement this model.

Reliability Analysis Topology Optimization Reliability-Based Topology Optimization uncertainty Optimization Methods

Reliability Analysis Topology Optimization Reliability-Based Topology Optimization uncertainty Optimization Methods