In this study, a dual response surface model-based multi-objective robust optimization method is introduced to deal with the uncertainties in the tube hydroforming process. The objective of this study is to maximize the protrusion height and minimize the thinning ratio; meanwhile, the variations of the objectives should be minimized. A valid finite element model obtained from experimental result and LS-DYNA is employed to simulate the T-shape tube hydroforming process. To improve computation efficiency, radial basis function combined with Latin hypercube and orthogonal design sampling strategies is employed to construct dual response surface model, which are the mean and standard deviation response of the hydroforming process, respectively. The robust Pareto solutions can be obtained using NSGA-II; meanwhile, the ideal point method is used to obtain the most satisfactory solution from the Pareto solutions for the design engineers. As a conclusion, a significant improvement of the robustness can be achieved; however, the mean performance of the protrusion height has to be sacrificed.

The objective of this study is to introduce adaptive support vector regression, whose accuracy and efficiency are illustrated through a numerical example, to determine the Pareto optimal solution set for T-shape tube hydroforming process. A validated finite element model developed by the explicit finite element code LS-DYNA is used to conduct virtual T-shape tube hydroforming experiments. Multiobjective optimization problem considering contact area between the tube and counter punch, maximum thinning ratio, and protrusion height is formulated. Then, the Latin hypercube design is employed to construct the initial support vector regression model, and some extra sampling points are added to reconstruct the support vector regression model to obtain the Pareto optimal solution set during each iteration. Finally, the ideal point is used to obtain a compromise solution from the Pareto optimal solution set for the engineers.

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The objective of this study is to investigate the influence of gyri and sulci on the response of human head under transient loading. To this end, two detailed parasagittal slice models with and without gyri and sulci have been developed. The models comprised not only cerebrum and skull but also cerebellum, brain stem, CSF, and corpus callosum. In addition, white and gray matters were separated. The material properties were adopted from the literature and assigned to different parts of the models. Nahum's and Trosseille's experiments reported in relevant literature were simulated and the simulation results were compared with the test data. The results show that there is no evident difference in terms of intracranial pressure between the models with and without gyri and sulci under simulated conditions. The equivalent stress below gyri and sulci in the model with gyri and sulci is slightly higher than that in the counterpart model without gyri and sulci. The maximum principle strain in brain tissue is lower in the model with gyri and sulci. The stress and strain distributions are changed due to the existence of gyri and sulci. These findings highlight the necessity to include gyri and sulci in the finite element head modeling.

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