Robust expected violation criterion for constrained robust design problems and its application in automotive lightweight design

Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.     

Equivalent continuum model of rock mass with arbitrary fractures

The constitutive model and equivalent deformation modulus of an arbitrary column in representative elementary volume (REV) of fractured rock mass are derived. The deformation of fractured rock mass is composed of the rock part and the fracture part. The elasto-visco-plastic property is considered in this model. For the convenience in engineering practice, the complex elasto-visco-plastic model and its equivalent modulus are degraded, and the rock is taken as an elastic body. By statistical analysis of the geometric positions of the column and the fracture, the equivalent modulus of rock mass with arbitrary fractures is obtained.