scholarly journals Robust Design Optimization of Car-Door Structures with Spatially Varied Material Uncertainties

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Yuee Zhao ◽  
Hai Dong ◽  
Haibin Liang
Keyword(s):  
Design Optimization ◽  
Natural Frequency ◽  
Robust Design ◽  
Random Variables ◽  
Robust Design Optimization ◽  
Structural Safety ◽  
Surface Model ◽  
Lateral Stiffness ◽  
Stiffness Coefficient ◽  
Material Uncertainties

This paper presents an effective approach for robust design optimization of car-door structures with spatially varied material properties. This spatially varied material property causes structural response quantities; for example, the natural frequency and the lateral stiffness coefficient become random variables. In this regard, the Karhunen-Loève expansion is first used to represent the elastic modulus and the mass density random fields as a series of random variables. Then, a stochastic finite-element model is formulated for uncertainty quantification of the car-door structure. Combined with a polynomial-based response surface model to mimic the true performance indicator, this allows one to efficiently evaluate probability constraints for the robust design optimization of the uncertain car-door structure. In numerical simulations, design variables of the uncertain car-door structure are defined as thickness values of the tailor rolled blank structure at various regions, whereas multiple design objectives are formulated via the structural weight, the first-order natural frequency, and the lateral stiffness coefficient. Results have shown that the mean value of performance indicators can be generally improved, whereas the response variance is further minimized to archive the robust design objective. The probability-based constraint is significant to relate the Pareto optimum set to the targeted structural safety level. The proposed approach is simple, suggesting an attractive tool for the robust design optimization of car-door structures with spatially varied material uncertainties.

General Robust Design by Semi-Second-Order Taylor Expansion

2008 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Taylor Expansion ◽  
Random Variables ◽  
Second Order ◽  
Robust Design Optimization ◽  
Integration Strategy ◽  
Interval Variables ◽  
Standard Deviations ◽  
Robustness Assessment

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

scholarly journals An effective approach for robust design optimization of wind turbine airfoils with random aerodynamic variables

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987926 ◽  
Author(s):  
Xufang Zhang ◽  
Zhenguang Wu ◽  
Wei He
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Performance Indicator ◽  
Mean Value ◽  
Robust Design Optimization ◽  
Surface Model ◽  
Optimization Constraints ◽  
Numerical Iteration ◽  
Potential Applications ◽  
The Mean

The robust design optimization of an airfoil needs to continuously realize the probability-based aerodynamic simulation for various combinations of geometry and wind climate parameters. The simulation time is lengthy when a full aerodynamic model is embedded for the numerical iteration. To this end, a second-order polynomial-based response surface model is first presented to relate the airfoil performance indicator with geometry and random aerodynamic variables. This allows to quickly evaluate the response moments and optimization constraints. Then, the robust design optimization is formulated to simultaneously maximize the mean aerodynamic performance and minimize the variance of design results due to the variation of geometry and aerodynamic parameters. The robust design optimization based on the NACA63418 and the DU93-W-210 airfoils with random Mach and Reynolds numbers is presented to demonstrate potential applications of this proposed model. Results have shown that the mean-value aerodynamic indicator is generally improved, whereas the variance is minimized to archive the robust design objective. The proposed approach is simple and accurate, suggesting an attractive tool for robust design optimization of airfoils with random aerodynamic variables.

Robust Design Optimization for Crashworthiness of Vehicle Side Impact

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Souvik Chakraborty ◽  
Tanmoy Chatterjee ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Design Optimization ◽  
New Product Development ◽  
Robust Design ◽  
Automobile Industry ◽  
Human Error ◽  
Differential Evolution Algorithm ◽  
Side Impact ◽  
Robust Design Optimization ◽  
Parameter Uncertainties ◽  
Design Engineers

Optimization for crashworthiness is of vast importance in automobile industry. Recent advancement in computational prowess has enabled researchers and design engineers to address vehicle crashworthiness, resulting in reduction of cost and time for new product development. However, a deterministic optimum design often resides at the boundary of failure domain, leaving little or no room for modeling imperfections, parameter uncertainties, and/or human error. In this study, an operational model-based robust design optimization (RDO) scheme has been developed for designing crashworthiness of vehicle against side impact. Within this framework, differential evolution algorithm (DEA) has been coupled with polynomial correlated function expansion (PCFE). An adaptive framework for determining the optimum basis order in PCFE has also been presented. It is argued that the coupled DEA–PCFE is more efficient and accurate, as compared to conventional techniques. For RDO of vehicle against side impact, minimization of the weight and lower rib deflection of the vehicle are considered to be the primary design objectives. Case studies by providing various emphases on the two objectives have also been performed. For all the cases, DEA–PCFE is found to yield highly accurate results.

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