Optimal design of mesostructured materials under uncertainty

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Patel, Jiten
Choi, Seung-Kyum
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The main objective of the topology optimization is to fulfill the objective function with the minimum amount of material. This reduces the overall cost of the structure and at the same time reduces the assembly, manufacturing and maintenance costs because of the reduced number of parts in the final structure. The concept of reliability analysis can be incorporated into the deterministic topology optimization method; this incorporated scheme is referred to as Reliability-based Topology Optimization (RBTO). In RBTO, the statistical nature of constraints and design problems are defined in the objective function and probabilistic constraint. The probabilistic constraint can specify the required reliability level of the system. In practical applications, however, finding global optimum in the presence of uncertainty is a difficult and computationally intensive task, since for every possible design a full stochastic analysis has to be performed for estimating various statistical parameters. Efficient methodologies are therefore required for the solution of the stochastic part and the optimization part of the design process. This research will explore a reliability-based synthesis method which estimates all the statistical parameters and finds the optimum while being less computationally intensive. The efficiency of the proposed method is achieved with the combination of topology optimization and stochastic approximation which utilizes a sampling technique such as Latin Hypercube Sampling (LHS) and surrogate modeling techniques such as Local Regression and Classification using Artificial Neural Networks (ANN). Local regression is comparatively less computationally intensive and produces good results in case of low probability of failures whereas Classification is particularly useful in cases where the reliability of failure has to be estimated with disjoint failure domains. Because classification using ANN is comparatively more computationally demanding than Local regression, classification is only used when local regression fails to give the desired level of goodness of fit. Nevertheless, classification is an indispensible tool in estimating the probability of failure when the failure domain is discontinuous. Representative examples will be demonstrated where the method is used to design customized meso-scale truss structures and a macro-scale hydrogen storage tank. The final deliverable from this research will be a less computationally intensive and robust RBTO procedure that can be used for design of truss structures with variable design parameters and force and boundary conditions.
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