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Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

The purpose of this paper is to calculate the Hugoniot relations of polyurea; also to investigate the atomic-scale energy change, the related chain conformation evolution and the hydrogen bond dissociation of polyurea under high-speed shock.

The atomic-scale simulations are achieved by molecular dynamics (MD). Both non-equilibrium MD and multi-scale shock technique are used to simulate the high-speed shock. The energy dissipation is theoretically derived by the thermodynamic and the Hugoniot relations. The distributions of bond length, angle and dihedral angle are used to characterize the chain conformation evolution. The hydrogen bonds are determined by a geometrical criterion.

The Hugoniot relations calculated are in good agreement with the experimental data. It is found that under the same impact pressure, polyurea with lower hard segment content has higher energy dissipation during the shock-release process. The primary energy dissipation way is the heat dissipation caused by the increase of kinetic energy. Unlike tensile simulation, the molecular potential increment is mainly divided into the increments of the bond energy, angle energy and dihedral angle energy under shock loading and is mostly stored in the soft segments. The hydrogen bond potential increment only accounts for about 1% of the internal energy increment under high-speed shock.

The simulation results are meaningful for understanding and evaluating the energy dissipation mechanism of polyurea under shock loading, and could provide a reference for material design.