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

Abstract

Introduction. The Deterministic Topology Optimization model provides a single solution for a given design space, while the Reliability-Based Topology Optimization model provides several reliability-based topology layouts with high-performance levels. The objective of this work is to develop two strategies that can provide the designer with two categories of resulting topologies. Materials and Methods. Two alternative approaches based on the Inverse Optimum Safety Factor are developed: the first one is called the Objective-Based IOSF Approach and the second one is called Performance-Based IOSF Approach. When dealing with bridge structures, the uncertainty on the input parameters (boundary conditions, material properties, geometry, etc.) and also output parameters (compliance, etc.) should not be ignored. The sensitivity analysis is the fundamental idea of both developed approaches, identifies the role of each parameter on the structural performance. In addition, the optimization domain choice is important when eliminating material that should not affect the structure functioning. Results. Two numerical examples on a 2D bridge structure are presented to demonstrate the efficiency of the developed approaches. When considering a certain reliability level, the Reliability-Based Topology Optimization leads to two different configurations relative to the Deterministic Topology Optimization one. When increasing the reliability levels, the quantity of materials decreases that leads to an increase in the number of holes in the structures. Discussion and Conclusion. In addition to their simplified implementation, the developed alternative approaches can be considered as two generative tools to produce two different categories (families) of solutions where an alternative choice between two functions (objective/performance) is presented.

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

“…It is almost similar. This is because the sensitivity of the compliance with respect to Young's modulus and the applied force is very small as shown before in [9].…”

“…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)…”

“…However, when considering the RBTO by PBA-IOSF, the optimization problem seeks to minimize the volume subject to the compliance constraint. A sensitivity study of the compliance being the performance function, is carried out in [9], considering four random variables. It is found that the biggest value corresponds the Poisson's ratio, however the smallest value corresponds to the applied force.…”

“…Fig. 4a represents the resulting DTO layout using PBA [9]. Figs 4b and c illustrate the resulting RBTO layouts using PBA-IOSF at , for normal and lognormal distribution, respectively.…”

“…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.…”