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In this paper, multi-objective optimization of perforated square tubes is performed considering absorbed energy, peak crushing force and weight of the tube as three conflicting objective functions. In the multi-objective optimization problem (MOP), absorbed energy and peak crushing force are defined by polynomial models extracted using the software...
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... The change in thickness and axial force of the plate will affect the stress σ max and σ min at both ends of the wall. According to Equations (38) and (39), it can be seen that in the case of regular tube walls without obvious thickness changes, the influence on the stability coefficient and the constraint coefficient between plates is relatively small. However, for the design of complex cross-sectional tubes, parameters k and l can effectively correct the coefficient of effective width, so that the calculation deviation can be controlled within a reasonable range. ...
... In this study, the critical force ICF and specific energy absorption SEA are used as optimization indicators for the collision resistance performance of multicellular tubes [37]. From the non-dominated sorting genetic algorithm (NSGAII), a set of Pareto solutions with high accuracy can be obtained through non-dominated sorting while maintaining population diversity, which is suitable for nonlinear optimization of SEA and critical forces [38,39]. Given its superiority, NSGAII was selected in this study for multi-objective optimization, so as to determine the objective functions and constraints, which can be detailed as follows: ...
A lattice-filled multicellular square tube features a regular cross-sectional shape, good energy consumption, and good crashworthiness, which is suitable for the design of energy absorbers in various protection fields such as automobiles, aerospace, bridges, etc. Based on the super folding theory, two reference planes are set to refine the energy consumption zone of the super folding element in this study. The energy consumption calculation of convex panel stretching is involved, and the critical crushing force formula is introduced in this study. Meanwhile, the calculation method from a single-cell square tube to a multicellular thin-walled square tube is extended and the structural optimization is investigated, in which the NSGAII algorithm is used to obtain the Pareto front (PF) of the crashworthiness performance index of the square multicellular tubes, the Normal Boundary Intersection (NBI) method is adopted to select knee points, and the influence of different cross-sectional widths on the number, as well as the thickness, of cells are discussed. This study’s results indicate that the theoretical value is consistent with that obtained from the numerical simulation, meaning that the improved theoretical model can be applied to predict the crashworthiness of multicellular square cross-sectional tubes. Also, the optimization method and study results proposed in this study can provide a reference for the design of square lattice multicellular tubes.
... And to avoid the influence of subjective factors, scholars mainly rank the Pareto solutions by integrating the multi-criteria decision-making method, and then select the scheme with better comprehensive. Khalkhali et al. (2016) uses NSGA-II optimization algorithm for multi-objective optimization design of thin-walled beam structures, and sorts Pareto frontier solutions by approaching ideal point method (NIP) and technique for order preference by similarity to an ideal solution (TOPSIS) to obtain the optimal compromise solution. ...
Due to the discreteness of material variables and nonlinearity of material plastic segment, the material-structure matching design efficiency of multiple parts is very low, and it is even difficult to achieve a feasible solution. To solve these problems, a performance-driven lightweight optimization method that combines multi-material selection method and multi-objective optimization is proposed. First, a lightweight multi-material selection method for the cab is proposed, which integrates static stiffness constraint, equivalent crashworthiness, and evaluation method for material selection. Subsequently, the multi-material selection designs for the skeleton beam of cab are carried out. The results show that the material selection scheme achieved a mass reduction of 12.41 kg and material cost reduction of 0.861 yuan. Finally, a multi-objective optimization method incorporating TOPSIS method is used to solve material-structure coupling design. The results show that the mass of cab is reduced by 47.4 kg. The performance of cab are slightly changed, indicating the rationality of the lightweight design method.
... The mechanical properties of thinwalled channels and tubes mainly rely on the cross-sectional geometry. Investigations on straight beams with constant crosssection along the longitudinal axis [4], including circle [5], square [6,7], triangular [8], multi-corner [9], start shape [10], and polygonal tubes [11][12][13] have been conducted in previous studies. Simple geometrical changes along the axis such as tapering and conical tubes were also analysed to exploit further potential in lightweight and stiffness improvement [14][15][16][17][18][19][20][21]. ...
The trend in automotive manufacturing towards lower volumes and an increased number of car variants combined with the need for forming higher strength metals to reduce weight has led to the implementation of alternative and flexible manufacturing methods. These have new manufacturing constraints compared to conventional stamping that change the part shapes that can be formed. This requires new methods for part shape optimisation. This study proposes a novel parametrisation for shape design that allows: 1) implementation of a gradient-based optimisation approach; and 2) taking manufacturing constraints into account. Our novel parameterisation can describe most long automotive structural parts using only a small number of design variables. The parts are described using multiple series of straight and curved connected profiles. We have uniquely conducted a detailed sensitivity analysis on the profiles to determine analytical solutions for the first order derivatives of the design variables with respect to the surface area/mass of a generic part. The profiles are also used to determine the final manufacturing strains in a part based on ideal forming. These ideal manufacturing strains can be compared to manufacturing process strain limits to determine the potential manufacturability of the part. The proposed parametrisation is applied to optimise a variable width channel formed by flexible roll forming. The channel is optimised to maximise the stiffness while maintaining both mass and manufacturability. In detail, the effectiveness and the general applicability of the established parametrisation technique and shape optimisation platform are demonstrated using three case studies of a flexible roll formed automotive S-rail channel part subjected to compression and bending loads. Furthermore, the manufacturability of the optimised structure is demonstrated by a forming model of the flexible roll forming process, where the model has been previously validated against experimental data. These examples show that the presented parametrisation and the associated shape optimiser can be successfully applied to increase part stiffness while reducing weight and maintaining manufacturability. The range of problems analysed demonstrates the flexibility and capability of the newly developed optimisation platform.
... When the precise hierarchy of domination of each solution in each setting is concerned, the maximum N non-dominant levels arises (Deb 1999). It is known as the Non-dominated Sorted Genetic Algorithm (NSGA) (Khalkhali et al. 2016;Thompson et al. 2017) we have utilized the NSGA-II so far. ...
... The DA tool employs a multi-objective genetic algorithm (MOGA) for it. The MOGA algorithm uses the Non-dominated Sorted Genetic Algorithm-II (NSGA-II), described by Khalkhali et al. (2016) as "one of the most powerful evolutionary algorithms for solving multi-objective optimization problems." ...
Flare gas recovery is a procedure that reduces the greenhouse gas emissions. Ejectors play a technically efficient and productive role in the recovery of flare gas. The higher the secondary fluid entrainment rate causes better performance of the ejector. The main purpose of the recent study is increasing the flow of gas in the gas recovery ejectors. A two-phase ejector is examined using computational fluid dynamics (CFD) in order to have an optimized performance. The diameter and length of the throat, the nozzle diameter, as well as the converging and diverging angles are the geometrically assigned influence the secondary fluid flux. To achieve the highest entrainment rate, the optimal value of these parameters was determined using the multi-objective genetic algorithm (MOGA) proposed three points as an ejector design candidate. As a result, the rate is improved when a reduction occurred in the length of the throat and the converging angle. It was also increased while reducing the nozzle and throat diameters and the diverging angle. Compared to the basic case, the optimal geometries raised the amount of flow by 25.5, 16.06, and 12.76 times, respectively. Energy efficiency evaluation for the base model and all design points has been made was about 3.5 times higher than the basic case in the second candidate. The first point could also improve the efficiency up to 78%, whereas it was dramatically reduced by the third candidate (47%).
... A number of methods are widely used to address the MCDM problem, such as the analytic hierarchy process (AHP; Bhattacharya and Singla 2016), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS; Khalkhali et al. 2016), GRA (Zhang et al. 2019a), and complex proportional assessment (COPRAS; Zheng et al. 2014), among which the GRA method is employed in this paper due to its comprehensive advantages. It outperforms other MCDM methods in terms of computational time, simplicity, mathematical calculations involved, and stability (Wang et al. 2013). ...
The structural optimal design, as an effective way to improve the crashing performance of energy-absorbing structures (EASs), still faces some challenges, e.g., multiple conflicting objectives and the non-uniqueness of Pareto solutions. To address these problems, this study proposes a hybrid optimization approach that combines the theories of multi-objective optimization and multiple-criteria decision-making to select the most preferred solution from the Pareto set with the consideration of engineering practitioners’ preferences. Specifically, this approach integrates the modified non-dominated sorting genetic algorithm (g-NSGA-II), fuzzy DEMATEL method, and GRA to handle the structural optimization problem in the field of passive safety protection for trains. First of all, a coupled thermal–structural finite element model of a cutting-type EAS is established and verified by experimental results. Next, a sensitivity analysis is conducted to explore the effects of knife count on the crashing performance of the structure and select the best alternative. After that, multi-objective optimization of this structure is performed using the proposed hybrid optimization method. Analysis and discussion are conducted to verify the effectiveness and practicability of this proposed approach. The optimization results show that the proposed conjoint method can be effectively employed to solve the multi-objective optimization problem of EASs.
... The movable block was applied artificial ramping velocity of 0.3 m/s, which it reduces the time step of the process. In FE simulation the AMPLITUDE and SMOOTHSTEP sub option was utilized to control the velocity of the striking end [26]. ...
The use of gradiently grooved tubes has reaped emphasis in designing of crashworthiness systems for safeguard of commuters in passenger bus collisions. Also it is very essential to improve the performances of energy absorption systems of gradiently grooved profiles. The tubular structures exhibit superior energy absorption characteristics when subjected to uni-axial loading, on contrary it is highly susceptible to global bending mode when subjected to oblique loading pattern. This work proposes a novel design to enhance the crashworthiness metrics of circular tubular structures subjected to both direct and oblique loading by the engraving of grooves in circumferential direction with varying depths. The structure with varying groove configurations has undergone quasi-static and finite element simulations. The effect of friction contact interaction between the striker and the structure and critical loading angle (θ = 0˚ to 30˚) between them on energy absorption had been explored. The outcome reveals the merits of utilizing gradiently grooved tubes with varying groove depths which may be decreased from the striker end to the stationary end over the original, uniform and gradiently grooved structures subjected to direct and oblique loading patterns. The outcome of the work facilitates designer to enhance the energy absorbing performances for different loading conditions. Lastly, the designed tubular structure as crash buffer befitted in commercial automotive bus application is considered and demonstrated successfully.
... Among them, meta-heuristic methods have gained popularity for black-box type optimization as they can capture discontinuity or convex or concave type Pareto front. Non-dominated sorting genetic algorithm-II (NSGA-II) [66,67], multi-objective particle swarm optimization (MOPSO) [68], multi-objective ant lion optimization (MOALO) [69], multi-objective dragonfly algorithm [70] are one of the meta-heuristic methods. The use of meta-heuristic methods for multi-objective optimization for efficient vibration control of structures may be found in Refs. ...
This study proposes a shape memory alloy (SMA)-based damped outrigger system for vibration control of tall timber buildings. In this study, the core of the structure is idealized as a cantilever beam, and each floor mass is considered as a discrete mass that acts at the junction between the floor and the core of the structure. The governing equations of motion of the combined system of shear core and outrigger are derived using the Lagrange formulation. The SMA spring is installed between the outrigger beam and the column to dissipate earthquake-induced energy and reduce excessive load demand on the column. Optimal performance of the proposed system requires optimizing the outriggers’ location and tuning the SMA properties in an uncertain environment. Two conflicting objective functions, minimization of acceleration and inter-storey drift ratio, are solved through a multi-objective optimization. Four different multi-objective meta-heuristic optimization algorithms (ant-lion, dragonfly, particle swarm optimization, and non-dominated sorting genetic algorithm II) are considered. Three different tall timber buildings (10-, 15-, and 20-storey) and up to two outrigger beams are considered for optimization. The seismicity of Vancouver, BC is used for the numerical simulation and vulnerability assessment. The optimum outrigger location for a one-outrigger system is found to be approximately 60%, while for a two-outrigger system, the same is obtained as 33% and 68%, respectively. Finally, the fragility analysis is carried out, which shows the superiority of this passive device in terms of minimizing the probability of failure exceeding a given threshold limit, which yields an improvement in the reliability of the structure.
... In this study, optimizations of CO1D and CSIN2D tubes are studied using four different multi-objective optimization methods to discuss the effect of the optimization method on the results. Two of these methods are non-dominated sorting genetic algorithm II (NSGA-II) [54][55][56] and multi-objective particle swarm optimization (MOPSO) [57][58][59], which are frequently used in crashworthiness problems. The other two methods are paired offspring generation for constrained large-scale multiobjective optimization (POCEA) [60] and an evolutionary algorithm for large-scale many-objective optimization (LMEA) [61], which have been recently introduced in the literature. ...
Twenty-six nested structures with a circumferentially corrugated circular outer wall and inner ribs are investigated under quasi-static axial compression using the finite element method. The finite element model is validated by literature. Also, theoretical predictions for the nested structures are derived and compared with finite element analyses. Among the structures whose crashworthiness performances are examined, CO1D and CSIN2D are selected as the best ones. The comparisons have shown that the ribs attached to the closest points of the corrugated outer wall provide stable collapse modes and better crash performance. Also, the crashworthiness performance of the nested structures with octagon inner structures is higher than other alternative structures because the number of corner members and the cross-section lengths are more efficient. Finally, the objective functions developed by the surrogate modeling method are optimized by non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO), paired offspring generation for constrained large-scale multiobjective optimization (POCEA) and an evolutionary algorithm for large-scale many-objective optimization (LMEA). Optimum CO1D and CSIN2D designs obtained by the NSGAII method have 37.00% and 26.68% higher SEA values, respectively than ‘Cribs’ structure at the same PCF value.
... Ding et al. (Ding et al. 2018) found an optimal distribution of lateral thickness for a square multi-cell tube with lateral variable thickness by comparing the accuracy of four different approximate models. Khalkhali et al. (Khalkhali et al. 2016) weighed three conflicting objectives of EA, peak crushing force, and weight for perforated square tubes. Xu et al. ) optimized the thicknesses of adjacent tube walls and the diaphragm thickness. ...
Deterministic optimization has been successfully applied to a series of design problems of square thin-walled energy absorption tubes and to a certain extent has fulfilled great expectations for the application of such structures in subway vehicles. However, most studies have not considered the uncertainty of parameters or the correlation of uncertainty parameters, leaving little or no tolerance and resulting in over-conservative structural design. This research proposes a multi-objective uncertain method with an ellipsoid-based model to address the effects of parametric uncertainties of a centrally symmetrical square tube with diaphragms (CSSTD) on design optimization, in which the ellipsoid model is adopted to describe the related uncertainty parameters. The nonlinear interval number programming method coupled with a reliability-based possibility degree of interval (RPDI) model is introduced to handle the transformation of uncertain optimization problems. Simultaneously, local-densifying technology is adopted to enhance the local accuracy of the approximate model. Finally, the outer layer of the micro multi-objective genetic algorithm (μMOGA) combined with the inner layer of the intergeneration projection genetic algorithm (IP-GA) is applied to solve the Pareto optimal solution set of the transformed deterministic optimization. The optimization results indicate that the proposed multi-objective uncertain optimization with an ellipsoid-based model not only guarantees the crashworthiness of the CSSTD, but also improves the design robustness, which means that the proposed method can provide insightful information for crashworthiness design of subways.
... (5) The 2 N number of solutions are ranked based on non-domination rank and crowding distance and N number of them are selected and the algorithm goes to step 3. Fig. 7 depicts the algorithm steps. Since 2002 many researches have used NSGAII in their studies and many have tried to improve or modify this algorithm (Golrang, Golrang, Yayilgan, & Elezaj, 2020;Khalkhali, Mostafapour, Tabatabaie, & Ansari, 2016). NSGAII is still among the best and most useful multi-objective meta-heuristic algorithm in science and could outperform the other algorithms in many types of problems. ...
Process-based plants, including chemical complex units, due to having considerable complexity and interdependencies between the units carrying different types of hazardous materials, have a high potential to face disastrous domino effects. Thus, preventing dominoes and mitigating the domino effects are a vital and challenging task for onsite decision-makers. In this regard, decision-makers need to have a reliable tool to make feasible and optimum decisions to prevent and mitigate the occurrence and consequences of domino effects, respectively. This chapter reviews the advanced decision-making tools that complex chemical plants can effectively use to deal with domino effects.
