Reliability-based Topology Optimization Design Under Random Field Model

Traditional structural analysis and optimization design are mostly based on deterministic assumptions,ignoring the inherent uncertainties such as the loading conditions,material properties,manufacturing errors and so on,which have a negative effect on the structural performance.Therefore,in the process of structural analysis and design,these uncertainties need to be analyzed quantitatively,so as to reduce the influence of uncertain variations on structural performance and improve the reliability of structural design.The random uncertainty information is mainly represented by random variables,processes and fields,in which as an extension of stochastic processes in the spatial domain,the random field is used to describe the spatial variability with the spatial location,such as the material properties fluctuating over the spatial domain,geometric imperfections arising from manufacturing errors.This paper develops a new reliability-based topology optimization framework based on random field model.The elastic modulus is modeled as a Gaussian random field correlated with the whole domain to represent material properties uncertainty.The geometric uncertainties are modeled with a random threshold model,which the projection threshold is represented by a uniform random field.The Expansion Optimal Linear Estimation(EOLE)is adopted to the discretization of random fields for the purpose of dimensionality reduction.The polynomial chaos expansion(PCE)based on sparse grid scheme is developed to evaluate the structural response and their sensitivities.The reliability-based topology optimization problem consists of two parts: reliability analysis and topology optimization design.The reliability index approach(RIA)and performance measure approach(PMA)are adopted to establish a reliability-based topology optimization framework based on random field model in this paper.The proposed method is applied to 2D and 3D uncertainty problems,and realized the reliability-based structural design considering material properties and geometric uncertainties.In addition,a topology optimization problem considering multiple random field models is solved,the generality and efficiency of the proposed method are verified.Finally,the Sequence Optimization and Reliability Assessment model(SORA)is applied to integrate the reliability algorithm based on random field model into the commercial software ABAQUS,which realizes the reliability design of the practical structures.