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The Bisection Method and the Accelerated Dynamical Mean Value Optimization Method in Comparison of Different Topology Optimization Approaches

Document Type : Original Article

Authors

1 Mechanical Engineering Department, University of Zabol, Zabol, Iran

2 Civil Engineering Department, University of Zabol, Zabol, Iran

Abstract

Since deterministic topology optimization (TO) does not consider the uncertainties in the structure, including materials, loading and geometric dimensions, it may provide the optimal designs with the lowest state of reliability and safety. To 
solve this problem, reliability-based topology optimization (RBTO) is used, which is actually a combination of TO methods with reliability-based design methods (RBDO) based on a mathematical framework and process. In this article, by considering four TO methods including moving iso-surface threshold (MIST), SIMP, evolutionary structural optimization-extended finite element (XFEM-ESO) and level-set (LS), and considering a constraint or objective function, an optimal volume fraction (Vf) is obtained for TO by the bisection method. Then, with the aid of mean volume fraction, TO is performed and its optimized results are applied by an advanced reliability analysis method, i.e. accelerated dynamical mean value (ADMV), taking into account the uncertainties and their standard deviations to extract the most probable probability point (MPP). Having the MPP and the constraint, the bisection algorithm is used again and the optimized volume fraction for the RBTO model, and thereby the optimal layout for the RBTO solution, is achieved. Several examples are presented to validate and highlight the optimization capability of the RBTO method using a structural model and the mentioned TO methods, and the results are compared together. Based on the results, it is shown that the combination of RBDO and TO approach is able to result in powerful, stable, safe, and reliable structures completely different from the TO results.


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Journal of Computational Methods in Engineering
Volume 43, Issue 1 - Serial Number 27
August 2024
Pages 41-67
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