This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second-level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second-level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.
A practical modeling method for conducting thermal analysis of a microsatellite with multilayer insulation (MLI) was proposed by introducing a new concept for the fitted conductivities of MLI blankets. A finite element (FE) model was first established, in which the MLI blankets are simplified as homogeneous materials with the thermal conductivities initially given. Subsequently, the conductivities were adjusted and determined using an optimization problem that minimized the root mean square (RMS) of temperature residuals between the test data and analysis results based on the current FE model. The FE model with the determined conductivities (i.e., fitted conductivities) was used for thermal analysis. By making comparisons between thermal balance test data and steady-state analysis results of a microsatellite, the rationality and validity of the proposed modeling method were evaluated. Based on the proposed method, the analysis model was further utilized for microsatellite on-orbit temperature prediction. The results revealed that the thermal control scheme with MLI meets the mission requirements.
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