Keywords: space structures, reliability-based topology optimisation, eigenvalue, Monte Carlo simulation, third order approximation, ant colony optimisation.

Topology optimisation methods enable designers to find a suitable structural configuration for the required performance of structures [1]. The ground structure method is based on formulations of structural elements that derived from fundamental mechanics. So, design engineers can easily understand the reasons for optimality and the mechanical viewpoints of the structure. But real structural behaviour is subjected to uncertain conditions such as applied loads, material properties, and dimensional variation due to manufacturing factors. Because these uncertainties may affect desired performance negatively, there is a great need for optimisation methods which can effectively work despite their presence. Reliability-based topology optimisation is a useful strategy to consider such uncertainties [1].

This paper presents a reliability-based topology optimisation method (RBTO) for space structures that considers uncertainties in applied loads and non-structural masses. The structural stiffness and the eigenvalue which are two main structural characteristics were simultaneously considered as two failure modes in reliability analysis. The probability of failure in each mode can be evaluated by combining the Monte Carlo simulation method (MCS) and the third order approximation (TOA). The MCS method is a powerful tool that is often employed when an analytical form can not express or approximate the failure function [2]. The proposed methodology makes use of the capability of the TOA [3] to approximate a function for reproducing the structural eigenvalue, allowing the computation of performance measures at a much lower cost. Through a numerical example, reliability-based topology designs of a typical space structure are obtained using the ant colony optimisation (ACO) method with discrete cross-sectional areas. The results show that the main advantage of the RBTO model is that the resulting optimal topologies are more reliable than the deterministic topologies. The topological solution results with the consideration of failure probability under uncertain load and mass conditions are useful. For structural designers, the obtained configurations are reasonable because the structural behaviour for the obtained topologies is extremely clear.

1

S.R. Kim, J.Y. Park, W.G. Lee, J.S. Yu, S.Y. Han, "Reliability-based Topology Optimisation-based on Evolutionary Structural Optimisation", International Journal of Mechanical Systems Science and Engineering, 1(3), 135-139, 2007.

2

J.B. Cardoso, J.R. Almeida, J.M. Dias, P.G. Coelho, "Structural Reliability Analysis using Monte Carlo Simulation and Neural Networks", Advances in Engineering Software, 39(6), 505-513, 2008. doi:10.1016/j.advengsoft.2007.03.015

3

P. Torkzadeh, J. Salajegheh, E. Salajegheh, "Efficient Method for Structural Optimisation with Frequency Constraints using Higher Order Approximations", International Journal of Structural Stability and Dynamics, 8(3), 439-450, 2008. doi:10.1142/S0219455408002739

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