Article

A hybrid method of FEM, modified NSGAII and TOPSIS for structural optimization of sandwich panels with corrugated core

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

Low weight and high load capacity are remarkable advantages of sandwich panels which make them more considerable by structure designers. In this paper, multi-objective optimization of sandwich panels with corrugated core is carried out using modified Non-dominated Sorting Genetic Algorithm (NSGAII) considering two objective functions: the structure's weight and deflection. Deflection of the panel as one of the objective functions is calculated using finite element analysis by commercial software ANSYS. To employ this FE model in the multi-objective optimization process, the software products ANSYS and MATLAB have been coupled together during the run time. Finally, nearest to ideal point (NIP) method and technique for ordering preferences by similarity to ideal solution (TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. © The Author(s) 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... In this method, a base design is considered and it is desired to improve the objectives as much as possible compared to the base design. Despite of many conventional MCDM methods such as The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) Khalkhali et al (2014) and Nearest to Ideal Point (NIP) Khalkhali. A, Khakshournia. ...
... This method is widely used in both engineering and non-engineering MCDM problems. The governing equations and the procedure of this method are present in the prior works Khalkhali et al (2014). Table 14. ...
... The first step in both methods is similar. Calculation of the non-dimensional variation for each alternative in SVCB and according to Khalkhali et al (2014), calculation of the normalized rating ̃ for each alternative in TOPSIS. However, this procedure is shorter and simpler in SVCB; because a division (SVCB) takes shorter time compared to a division along with calculation of square root of sum of squares (TOPSIS). ...
Article
Full-text available
The floor pan is an important component that connects the front and rear segments of the automotive underbody structure. Global stiffness and NVH characteristics of BIW are highly dependent to shape, thickness and mass of the body panels and could be evaluated by modal characteristics of these panels. The feeling of solidness and comfort of passengers in an automotive is also dependent to the modal behavior of the underbody components as well as the floor pan. On the other hand, it is desired to reduce the total mass of the floor pan, in order to have a lighter vehicle with better fuel economy and emission standards. In this paper, the effect of geometrical parameters on natural frequency and total mass of the floor pan of a conventional B-Segment automotive body is investigated using finite element simulation. The finite element model is verified using an experimental test on the floor pan. Taguchi L16 orthogonal array is used to design the numerical experiments. Subsequently, S/N ratio analysis is performed to evaluate the effect of each design variable on the output functions. The panel’s thickness is determined to have the most contribution in affecting the natural frequency and weight using Analysis of Variance (ANOVA). The best combination of geometrical variables which leads to the trade-off results is then figured out by a new multi-criteria decision making (MCDM) method developed in this study. Accuracy of this method is verified by comparing the trade-off results with TOPSIS, as a conventional MCDM method. © 2016, Brazilian Association of Computational Mechanics. All rights reserved.
... Theories and approaches of MADM have been widely utilized in many fields, such as engineering, technology, economy, management, military etc. [1][2] .MADM is usually utilized to solve the two kinds of the problems such as evaluation and selection through index ranking and weight calculating in reliability & testability verification test [3] . The main methods to deal with the problem are Elimination et choix traduisant laréalité(ELECTRE) [4] ,Multi-Attribute Value Theory(MAVT) [5] ,and Quality Function deployment(QFD),Analytic Hierarchy Process(AHP),Topsis that combined with Delphi method etc. [6][7][8][9] at present. However, ELECTRE is based on priority between attributes that different from general function model. ...
... QFD often utilize the 1-5 or 1-9 integer numbers in ranking attributes, so that there is a certain subjectivity and randomness. There is a reverse problem in scheduling problems in AHP, so the consistency is still controversial [7] .Topsis usually aim at index ranking, not for weight calculating [8,9] .Therefore, presenting a weight calculating and index ranking method of MADM which is convenient and applicable to engineering test is an urgent problem. ...
... The basis of Topsis is establishing the ideal solution and negative-ideal solution. The distance relation between the target and ideal/negative-ideal solution named S * and Sis taken as the judgment basis C * [8][9] .The ideal solution indicates the nearest value of the distance from the optimal solution of all the attribute index in all of the candidate scheme, and the negative-ideal solution indicates the farthest value of the distance from the optimal solution of all the attribute index in all of the candidate scheme. C * is the function of ideal solution and negative-ideal solution that shown in Eq .1. ...
... It is necessary to employ some methods to choose the trade-off optimal design point through the Pareto front. In this work, nearest to ideal point (NIP) method and technique for order performance by similarity to ideal solution (TOPSIS) method are used [26]. ...
... To find the trade-off optimum design point from non-dominated optimum points obtained in the previous section, NIP and TOPSIS methods are applied. The details of these methods can be found in previous publications [26]. In TOPSIS 1, the weight coefficient for all three objective functions, is considered equal to 1/3. ...
Article
Full-text available
Carbon nanotube (CNT)/polymer nanocomposites have vast application in industry because of their light mass and high strength. In this work, a cylindrical tube which is made up of functionally graded (FG) PmPV/CNT nanocomposite, is optimally designed for the purpose of torque transmission. The main confining parameters of a rotating shaft in torque transmission process are mass of the shaft, critical speed of rotation and critical buckling torque. It is required to solve a multi-objective optimization problem (MOP) to consider these three targets simultaneously in the process of design. The three-objective optimization problem for this case is defined and solved using a hybrid method of FEM and modified non-dominated sorting genetic algorithm (NSGA-II), by coupling two softwares, MATLAB and ABAQUS. Optimization process provides a set of non-dominated optimal design vectors. Then, two methods, nearest to ideal point (NIP) and technique for ordering preferences by similarity to ideal solution (TOPSIS), are employed to choose trade-off optimum design vectors. Optimum parameters that are obtained from this work are compared with the results of previous studies for similar cylindrical tubes made from composite or a hybrid of aluminum and composite that more than 20% improvement is observed in all of the objective functions.
... 夹层称为大支撑。整个结构的高度、宽度分别为 H、 b,面板厚度为 t f ,大支撑面板倾角、厚度、长度和 高度分别为 θ、t、l 和 h,小支撑的倾角、厚度和长 度分别为 θ 1 、t 1 、l 1 。需要指出的是,基于有限元分 析确定失效模式较为困难,通常需要人为判断失效 类型, 并且一般需采用效率较低的显式动力学算法。 近年来,一些学者已经对该结构开展了相关工作。 Kooistra 等 [9] 使用梁模型分析了该结构的失效模式, 在工程应用中具有一定的指导意义,但是仅适用于 厚度较小的结构。方耀楚等 [10] 推广到板模型及无限 宽板模型,并总结了两种模型的适用范围。上述理 论分析为控制结构的失效模式提供了可能。 图 1 二级层级褶皱结构单胞示意图 Fig.1 The unit cell of the hierarchical corrugated structure 优化方法在结构性能设计中发挥越来越重要 的作用 [11][12][13][14][15][16][17] 。 徐龙河等 [13] 提出基于性能的钢框架结 构失效模式识别方法,并以性能指标为目标函数、 构件截面尺寸为变量,建立钢框架结构失效模式多 目标优化方法。 郝鹏等 [14] 针对 T 型截面多级加筋柱 壳,构造了面向低缺陷敏感性的优化模型,可以高 效的得到可靠性更强的优化解。易桂莲等 [15] 类比独 立连续映射方法来改进 SIMP 方法的惩罚函数并用 其求解应力约束下板壳结构的拓扑优化设计问题。 仇翯辰等 [16] 基于区间不确定性优化对平流层飞艇 充气膜结构进行区间可靠性优化设计,降低了结构 的失效概率。王峰等 [17] 对船用人字齿轮面进行了以 齿根动应力疲劳寿命为目标的优化设计。对于二级 层级褶皱结构,轻量化和刚度是工程应用中需要考 虑的两个重要指标。在以往的研究中,已有较多学 者针对三明治夹芯板开展了基于减重、吸能或挠度 指标的优化设计工作 [7,[18][19][20] 。Hou 等 [7] 以变形和承 载力为多目标,分别优化了三角形和四边形夹芯的 三明治板,取得了较好的结果。郑华勇、吴林志 等 [18] [19][20] ...
... 夹层称为大支撑。整个结构的高度、宽度分别为 H、 b,面板厚度为 t f ,大支撑面板倾角、厚度、长度和 高度分别为 θ、t、l 和 h,小支撑的倾角、厚度和长 度分别为 θ 1 、t 1 、l 1 。需要指出的是,基于有限元分 析确定失效模式较为困难,通常需要人为判断失效 类型, 并且一般需采用效率较低的显式动力学算法。 近年来,一些学者已经对该结构开展了相关工作。 Kooistra 等 [9] 使用梁模型分析了该结构的失效模式, 在工程应用中具有一定的指导意义,但是仅适用于 厚度较小的结构。方耀楚等 [10] 推广到板模型及无限 宽板模型,并总结了两种模型的适用范围。上述理 论分析为控制结构的失效模式提供了可能。 图 1 二级层级褶皱结构单胞示意图 Fig.1 The unit cell of the hierarchical corrugated structure 优化方法在结构性能设计中发挥越来越重要 的作用 [11][12][13][14][15][16][17] 。 徐龙河等 [13] 提出基于性能的钢框架结 构失效模式识别方法,并以性能指标为目标函数、 构件截面尺寸为变量,建立钢框架结构失效模式多 目标优化方法。 郝鹏等 [14] 针对 T 型截面多级加筋柱 壳,构造了面向低缺陷敏感性的优化模型,可以高 效的得到可靠性更强的优化解。易桂莲等 [15] 类比独 立连续映射方法来改进 SIMP 方法的惩罚函数并用 其求解应力约束下板壳结构的拓扑优化设计问题。 仇翯辰等 [16] 基于区间不确定性优化对平流层飞艇 充气膜结构进行区间可靠性优化设计,降低了结构 的失效概率。王峰等 [17] 对船用人字齿轮面进行了以 齿根动应力疲劳寿命为目标的优化设计。对于二级 层级褶皱结构,轻量化和刚度是工程应用中需要考 虑的两个重要指标。在以往的研究中,已有较多学 者针对三明治夹芯板开展了基于减重、吸能或挠度 指标的优化设计工作 [7,[18][19][20] 。Hou 等 [7] 以变形和承 载力为多目标,分别优化了三角形和四边形夹芯的 三明治板,取得了较好的结果。郑华勇、吴林志 等 [18] [19][20] ...
Article
Six failure modes may occur for hierarchical corrugated structures under compressive or shear loads, and the corresponding nominal stress of plate model were analyzed based on the theories of Euler beams and elastic plates in this study. The failure modes were designed by comparing the nominal stress, and then the multi-objective optimization was performed to minimize both weight and deflection. Two optimization formulations were established, with one controlling a special failure mode occurs first and another classifying the failure modes into two grades considering the loss degree, and then the failure mode occurs as a specific sequence. On this basis, the performance index of several typical design points from the Pareto front of two models was discussed. Finally, the failure modes were verified by FEM. The results show significant improvement of the performance for both models, and the failure modes occur as expected. The second model is safer, in which the difference of nominal stress for each failure mode is considered, in order to avoid sudden occurrence of global failure.
... Structural parameters of the corrugated core and plates strongly govern the main mechanical performance. Therefore, the influencing mechanism of structural parameters received special attention by some researchers to optimize these parameters for better mechanical properties [9]. Hou et al. [10] explored the effect of the corrugated sandwich configuration and layer number on the failure mechanism under quasi-static crushing loading by numerical and experimental methods. ...
... where E z denotes the equivalent elastic modulus in Z-direction. Equation (9) can be expressed in another form as follows where the volume of the perpendicular corrugations V \ is defined as ...
Article
Full-text available
A novel sandwich panel with double-directional corrugated core is proposed in this paper. This complex-corrugated core makes the conventional detailed finite element analysis of large structures a tough work. Thus, an equivalent homogeneous method is proposed, the key of which is to obtain the equivalent property of this novel structure. The equivalent elastic modulus considering the effect of geometrical parameters is analytically derived and verified by finite element method. Besides, equivalent shear modulus and Poisson’s ratios are obtained by finite element method. Three-dimensional detailed and equivalent models are established for further validation of this equivalent homogeneous method. Results show that elastic modulus predicted by analytical formulas is in good agreement with that by finite element method no matter how geometrical parameters change. It has been proved that stretching deformation is dominating in thickness direction, and only corrugation along loading direction can bear the load. The proposed novel sandwich structure owns better mechanical property than the conventional one with single-corrugated core. The result by equivalent model agrees well with that by detailed model, which means that this equivalent homogeneous method can well predict the macroscopic property of this novel structure.
... A computational model combined topology and stacking sequence optimization of composite laminated structures was presented by using an optimization algorithm Interior Point Algorithm with the finite element code, Abaqus [10]. A modified Non-dominated Sorting Genetic Algorithm NSGAII was used to solve two-objective functions the weight and the deflection of the of sandwich panels with corrugated core and Pareto front for non-dominated design points was obtained [11]. Multi-parameter optimization approach was applied to optimize the lightweight-fiber-reinforced polymer (FRP) composite truss structure subjected to nonlinear structural constraints [12]. ...
... Evolutionary algorithms have been widely used for engineering optimization. As an instance, Khalkhali et al. (2014) optimized sandwich panels with corrugated core using genetic algorithm. In another work, Khalkhali et al. (2016) used particle swarm to optimize perforated square tubes. ...
Article
Full-text available
This paper focuses on the regularization of structural configurations by employing meta-heuristic optimization algorithms such as Particle Swarm Optimization (PSO) and Biogeography-Based Optimization (BBO). The regularization of structural configuration means obtaining a structure whose members have equal or almost equal lengths, or whose member’s lengths are based on a specific pattern; which in this case, by changing the length of these elements and reducing the number of different profiles of needed members, the construction of the considered structure can be made easier. In this article, two different objective functions have been used to minimize the difference between member lengths with a specific pattern. It is found that by using a small number of iterations in these optimization methods, a structure made of equal-length members can be obtained.
... The finite element software applications are often used to numerically solve differential equations during structural analysis [42][43][44]. Khalkhali et al. used a modified genetic algorithm to solve the weight and the deflection functions of sandwich panels with a corrugated core [45]. Corvino et al. introduced a procedure for multi-objective optimization based on genetic algorithms with the ANSYS software [46]. 5. ...
Article
Full-text available
The application of fiber-reinforced plastic (FRP) composites as structural elements of air vehicles provides weight saving, which results in a reduction in fuel consumption, fuel cost, and air pollution, and a higher speed. The goal of this research was to elaborate a new optimization method for a totally FRP composite construction for helicopter floors. During the optimization, 46 different layer combinations of 4 different FRP layers (woven glass fibers with phenolic resin; woven glass fibers with epoxy resin; woven carbon fibers with epoxy resin; hybrid composite) and FRP honeycomb core structural elements were investigated. The face sheets were composed of a different number of layers with cross-ply, angle-ply, and multidirectional fiber orientations. During the optimization, nine design constraints were considered: deflection; face sheet stress (bending load, end loading); stiffness; buckling; core shear stress; skin wrinkling; intracell buckling; and shear crimping. The single-objective weight optimization was solved by applying the Interior Point Algorithm of the Matlab software, the Generalized Reduced Gradient (GRG) Nonlinear Algorithm of the Excel Solver software, and the Laminator software. The Digimat-HC software solved the numerical models for the optimum sandwich plates of helicopter floors. The main contribution is developing a new method for optimizing a totally FRP composite sandwich structure—due to its material constituents and construction—that is more advantageous than traditional helicopter floors. A case study validated this fact.
... Huge amount of investigations with PSO were conducted, and the results showed that PSO method was viable and efficient [12][13][14][15]. Apart from PSO based approaches, GA Method was also performed for structural optimization [16][17][18][19][20]. The aforementioned researches demonstrated that GA was able to arrive at an optimal solution. ...
Conference Paper
This paper presented the structural optimization of a positioning pile for VLFS. A method that combined the genetic algorithm with finite element analysis (GA-FEA) was used. Stress constraints issued by the rules were taken into account with the penalty method. The optimized design was achieved using the aforementioned method. To validate the efficiency of GA-FEA method in optimization of the pile structure, comparison was made with two methods native to ANSYS.
... Coefficient values of the polynomials and complexity of network are the main criteria for designing GMDH-type neural networks. To design connections in the network optimally and, also, embody polynomial coefficients effectively, Nariman-zadeh et al. [39,40] employed genetic algorithm and singular value decomposition to develop a software product, called GEvoM [41]. In fact, GEvoM is a lab-developed software that generates polynomials based on GMDH-type neural networks to model the relationship between input-output data pairs. ...
Article
In a real-world loading case (e.g., car crash accidents), energy-absorbing components are subject to oblique loads at various uncertain angles. This paper aims to investigate the behavior of such components under three-dimensional (3D) oblique loads in deterministic and probabilistic loading conditions. In this way, some square tubes are tested experimentally, and results are utilized to validate numerical models. To apply the 3D oblique load, a special test setup is designed, constructed, and installed on a universal tensile testing machine. Hammersley method is employed to design sample points. ABAQUS software is used for the finite element modeling and analysis. GEvoM software is implemented for mapping design variables onto crashworthiness characteristics including energy absorption (EA) and peak crush force (PCF). Both deterministic and reliability-based robust design (RBRD) optimizations are performed, and their results are compared with each other. The primary outcome of this research is the effect of incidence angles on the energy-absorbing characteristics, as well as some remarkable trade-off design points obtained from various multiple-criteria decision-making (MCDM) methods. It was discovered that the obtained design points of probabilistic study, which satisfied the reliability constraint, were roughly 60% more robust than deterministic points.
... The TOPSIS method has been studied to great length in recent years, and the best compromise solution has been determined. [45][46][47][48][49] The literature review presented earlier shows that researchers in various fields used TOPSIS method, but the principal component analysis (PCA) method with TOPSIS approach applied in B-pillar optimization design is not included in the literature. Therefore, in the present work, the PCA method with the TOPSIS is used in ranking the Pareto solutions, and some compromise optimum points compromising objective functions are found in this study. ...
Article
Full-text available
This study presents a hybrid approach to integrate the comprehensive sensitivity analysis method, support vector machine technology, modified non-dominated sorting genetic algorithm-II method and the technique for order preference by similarity to ideal solution, which have been applied to multi-objective lightweight optimization of the B-pillar structure of an automobile. First, numerical models of the static–dynamic stiffness and the crashworthiness performance of automobile are established and validated by experimental testing. Then, the comprehensive sensitivity analysis method is used to define the final optimization variables. Experimental design and support vector machine based surrogate model techniques are introduced to establish the approximate model; subsequently, the modified non-dominated sorting genetic algorithm-II algorithm is applied to the multi-objective lightweight optimization design of the B-pillar structure, and the non-dominated solution set is determined. The principal component analysis method is applied to determine the weight of each objective. Finally, the technique for order preference by similarity to ideal solution method is used to rank Pareto front from best to worst to obtain the optimal solution; furthermore, a comparison between the original model and optimized design denotes that the mass of the B-pillar being reduced by 22.55% under the other impacting indicators is well guaranteed. Therefore, the proposed hybrid approach provided promising prospects in the lightweight and crashworthiness optimization application of the B-pillar.
... Stochastic and multi-objective optimization methods, such as particle swarm optimization (PSO) and genetic algorithms (GA), are examples of data-driven techniques which have been successful in previous studies and are well suited for the case of multi-component systems [3,13,18,[24][25][26][27][28]. Chen et al. [18], for example, applied multiobjective genetic algorithms coupled to a neural net model to find optimal configurations for double-ceramic-layer thermal barrier systems. ...
Article
Share link (until March 06 2020): https://authors.elsevier.com/a/1aPhK~2-EzJro Materials selection of multi-component systems is a challenging task, which is usually not properly tackled in furnace linings (FL) design. In an attempt to generate a systematic approach to select FL ceramic materials, an evolutionary screening procedure (ESP) is proposed in this paper, where a multi-objective genetic algorithm coupled with a finite element model aims to transform a list of potentially feasible ceramic candidate materials into an optimized set of multi-component systems simultaneously computing external lining temperatures and costs. An ESP-based selection methodology is proposed and studied in light of a case-study concerning an electric resistance furnace. A customized initial screening was carried out to select potential single candidate materials to be used. Next, the ESP was used to select optimized lining configurations while discarding infeasible combinations, such as those in which one of the materials maximum allowed temperature had been breached. Afterwards, TOPSIS (a multi-criteria decision-making approach) was applied to rank the optimized results according to some furnace preference scenarios. The ESP-based selection diminished a universe of 1.9x10⁵ lining configurations into a few units to be investigated in more details by simulating only 3.8% of them, thus requiring reduced amount of time for completing this task. The adopted quantitative strategy uses commonly used computational techniques and could be applied to metallurgical ladle linings, be adapted to select raw materials or resolve other complex decision-making problems in the ceramic community.
... severe vibration and axial impact [1][2][3][4]. For such applications, it is desirable to construct sandwich-walled cylindrical and conical structures (shells) sandwich structures are known to possess high specific strength, sound absorption performance, high designability, and good heat dissipation capability [5][6][7][8][9][10][11][12][13]. It is thus of great significance to investigate simultaneously the vibration and axial load-bearing capabilities of sandwich-walled cylindrical and conical shells with, for example, corrugated cores. ...
Article
Full-text available
All-metallic sandwich-walled cylindrical and conical structures for aerospace applications often require simultaneous excellent vibration and load-carrying capacities. In the present study, the free vibration and axial compression behaviors of cylindrical and truncated conical sandwich shells with corrugated cores are investigated using a combined experimental and numerical approach. Excellent agreement between experimental measurements and finite element simulations for representative vibration and axial compression characteristics is achieved. Parametric studies based on the response surface model are subsequently performed to quantify the influence of key geometrical parameters on vibration and axial compression performance. A multi-functional collaborative design to meet the requirement of high load-bearing capacity subjected to the constraint of low natural frequency is also carried out, which demonstrates the unique advantages of the novel sandwich-walled shells for aeronautical and astronautical applications.
... The underlying principles of GA are centered on evolution and the survival of the fittest concept. Huge amount of investigations with GA were conducted, and the results showed that GA was viable and efficient (Gauchia et al., 2010, Mohan et al., 2013and Khalkhali et al., 2014. In this connection, GA is used as an optimizer herein. ...
Article
Full-text available
A conceptual design of using novel telescopic piles to position a multi-modular very large floating structure (VLFS), which is supposed to be severed as a movable floating airport, is proposed. The telescopic piles can automatically plug in the soil to resist the environmental loads and pull out from the soil to evacuate or move on to the next operational sea. The feasibility demonstration of the conceptual design includes two parts: function verification and structure design. In the latter part of the conceptual design, a time-domain structural analysis is firstly conducted by using Abaqus software. The simulation results suggest that the preliminary structure scheme is not optimum due to the insufficient structure utilization, although both structure safety of the piles and positioning accuracy are guaranteed. To realize a cost reduction of construction and installation, a Genetic Algorithm-Finite Element Analysis (GA-FEA) method is employed to perform structural optimization. After optimization, 31 percent of the weight of each pile is reduced and higher structure utilization is maintained. The difference of the self-weight and allowable buoyancy of a single module (SMOD) of a semisubmersible-type VLFS is much larger than the weight of the piles. Combing with function verification in our previous work (Ji et al., 2020), the conceptual design of using the novel telescopic pile to position VLFS is demonstrated to be feasible.
... Mass optimization of composite-faced foam-core sandwich beams subjected to bending loads was performed by Steeves [13]. The non-dominated sorting GA was used for weight and deflection optimization of corrugated-core sandwich panels via ANSYS by Khalkhali et al. [14]. Gholami et al. [15] minimized the weight of a composite sandwich panel with honeycomb core using PSO. ...
Article
The main purpose of this paper is multi-objective optimization of soft-core composite sandwich plates using a known accurate high-order sandwich plate theory. In this three-layer theory, high-order kinematic assumptions are dedicated to each face sheet and the core layer. This theory considers the transverse flexibility of the soft core and satisfies transverse shear stresses continuity conditions and zero transverse shear stresses conditions at the upper and lower surfaces of the plate. The governing equations for bending and buckling analyses are derived using Hamilton’s principle, and their analytical solutions are presented for cross-ply plates. Two multi-objective optimization problems consist of weight/deflection optimization and weight/buckling load optimization of the unidirectional and cross-ply sandwich plates being studied. The thicknesses of the core and the face sheet layers are set as problems variables. The genetic algorithm is employed to find the optimal solutions for the problems, and the results are presented in form of the Pareto front. The accuracy of the present modeling and optimization method is evaluated for special case of buckling load maximization of laminated composite plates. For each problem, the optimization process is continued for more than 200 generations, but the results don’t change after 100 generations and the optimized results are obtained. The results confirm that there is no significant difference between the optimal solutions of unidirectional and cross-ply sandwich plates in both optimization problems. The process statistics show that cross-ply layup optimization takes about 25% more time than the unidirectional layup.
... Vehicle collision is a typical nonlinear problem. Since traditional optimization algorithms perform poorly on such nonlinear, complex problems, researchers often rely on intelligent optimization algorithms to tackle vehicle collision optimization problems (Perez and Behdinan 2007;Gu et al. 2013;Khalkhali et al. 2014). One of the most popular global optimization methods is particle swarm optimization (PSO) (Kennedy and Eberhart 1995). ...
Article
Full-text available
When designing a sport utility vehicle (SUV), designers strive to improve the vehicle’s rollover crashworthiness while avoiding a significant increase in its weight. To aid in optimizing such a trade-off, this paper proposes a multi-disciplinary and multi-objective hybrid optimization algorithm that combines particle swarm optimization and the artificial immune method. First, the SUV structure’s influence on body mass and rollover crashworthiness is studied using contribution analysis, and structural improvements are discussed according to Federal Motor Vehicle Safety Standard 216. Building on the analysis results, the SUV’s rollover crashworthiness and weight optimization model are proposed. Radial basis function neural network and a genetic algorithm are used to build and optimize surrogate models of total weight, maximum contact force, and torsion frequency. The proposed algorithm then utilizes particle swarm and artificial immune to seek Pareto solutions that optimize SUV structure. Finally, the technique for order preference by similarity to ideal solution method determines a final solution from Pareto-optimal solutions. Compared to previous studies, the results show that the proposed hybrid optimization algorithm improves the Pareto solution sets’ diversity and distribution uniformity, enhances SUV rollover crashworthiness, and reduces SUV structure components’ weight.
... Nentwich and Fuchs [43] presented STL of the sandwich structures interlayered with honeycomb core. However, two cost functions including the weight and deflection of the structure were investigated by Khalkhali et al. [44] to multi objective optimize of the sandwich structures. Zhou et al. [45] determined acoustic power of the structure interlayered with porous material in the external flow. ...
Article
Multi-objective vibroacoustic optimization of the double-walled doubly curved composite shells having poroelastic lining in its core in a diffuse field is performed based on Non-dominated sorting Genetic Algorithm-II. To present an analytical model on the basis of multi-objective optimization, the summation of sound transmission loss and transverse displacement along with weight of the structure are considered as two cost functions, which should be optimized in a diffuse field. In fact, the significant achievement of this work is to design an optimization algorithm to improve vibroacoustic fitness and weight of the sandwich doubly curved shells. In the first part of the paper, a general formulation is prepared to analyze the dynamic of the poroelastic composite sandwich structures. Likewise, some validation configurations are presented to confirm the accuracy of the current formulation. Consequently, an optimization algorithm is provided on the basis of considering some appropriate design variables including material and porous types as well as stacking sequences. In this regard, a batch of 19 benchmarks of porous core is investigated. Furthermore, a configuration of optimized points in the Pareto front is plotted in which the simultaneous effects of optimizing the weight and vibroacoustic fitness can be observed. As a result, a new approach is made through optimization of the transverse displacement of the structure as a function of various incidence and azimuth angles in three dimensional configurations with respect to different frequencies.
Article
For sandwich beams with second-order hierarchical corrugated truss core under three-point bending, a correction factor of shear deflection was firstly proposed to improve the prediction accuracy of the bending analysis, which was verified by finite element analysis and compared with the original formula. Then, the failure modes of the sandwich beam under bending were analyzed, including four competing modes of the large struts (i.e. plastic yielding, buckling, wrinkling of facesheet, shear buckling) and two competing modes of the small struts (i.e. plastic yielding, buckling). Subsequently, the analytical expressions of critical load for each failure mode were derived. On this basis, the failure mechanism maps were constructed. Finally, several typical points from the map were selected and verified by finite element analysis, and a good agreement of predicted failure modes was observed.
Article
Corrugated-core sandwich panels are prevalent for many applications in industries. The researches performed with the aim of optimization of such structures in the literature have considered a deterministic approach. However, it is believed that deterministic optimum points may lead to high-risk designs instead of optimum ones. In this paper, an effort has been made to provide a reliable and robust design of corrugated-core sandwich structures through stochastic and probabilistic multi-objective optimization approach. The optimization is performed using a coupling between genetic algorithm (GA), Monte Carlo simulation (MCS) and finite element method (FEM). To this aim, Prob. Design module in ANSYS is employed and using a coupling between optimization codes in MATLAB and ANSYS, a connection has been made between numerical results and optimization process. Results in both cases of deterministic and probabilistic multi-objective optimizations are illustrated and compared together to gain a better understanding of the best sandwich panel design by taking into account reliability and robustness. Comparison of results with a similar deterministic optimization study demonstrated better reliability and robustness of optimum point of this study.
Article
The main purpose of this study is to find a special set of filling and emptying parameters of a three-cylinder engine, including geometrical design of intake manifold, intake and exhaust valve timing as design variables of the multi-objective optimization problem, which lead to the best values of BSFC (Brake Specific Fuel Consumption), and torque of the engine at all working speeds as four separate objective functions. The modified Non-dominated Sorting Genetic Algorithm (NSGA-II), which is an evolutionary Pareto-based method, is used as the optimization algorithm, and the technique for order of preference by similarity to ideal solution is used as a Multi-Criteria Decision Making Method to select the trade-off design based on different design strategies through the design vectors which are proposed. Group Method of Data Handling-type of Artificial Neural Networks is used to predict the relation between the design variables and the objective functions based on a 243-sized set of samples, which are chosen by Factorial method, and the corresponding engine designs are simulated using GT-SUITE as an Engine Simulation Software. The method of simulation is verified by comparison of experiment and simulation results. The verification process shows that the engine simulation code could predict the engine's performance by 4.78% error. Convergence and start point independence of the optimization algorithm (modified NSGA-II) is also investigated. The final results show remarkable improvement in BSFC and torque at 3500 RPM and mean value of BSFC at all working speeds along with a small reduction in mean value of the engine's torque at all working speeds compared to corresponding characteristics of a similar three-cylinder engine.
Article
For hierarchical corrugated sandwich structures with second-order core, the prediction error of failure behavior by existing methods becomes unacceptable with the increase of structure thickness. In this study, a novel analytical model called moderately thick plate model is developed based on Mindlin plate theory, which can be used to analyze the failure behavior of hierarchical corrugated structures with second-order core under compression or shear loads. Then, the analytical expressions of nominal stress for six competing failure modes are derived based on the moderately thick plate model. The results of six different unit structures based on the moderately thick plate model agree quite well the ones by finite element methods. Furthermore, the influence of different structure thicknesses is investigated to validate the applicability of the moderately thick plate model. According to the comparative results with the thin plate model, the proposed moderately thick plate model has a better precision with the increase of the ratio of thickness to width for failure components.
Article
This article presents a hybrid method combining a modified non-dominated sorting genetic algorithm (MNSGA-II) with grey relational analysis (GRA) to improve the static–dynamic performance of a body-in-white (BIW). First, an implicit parametric model of the BIW was built using SFE-CONCEPT software, and then the validity of the implicit parametric model was verified by physical testing. Eight shape design variables were defined for BIW beam structures based on the implicit parametric technology. Subsequently, MNSGA-II was used to determine the optimal combination of the design parameters that can improve the bending stiffness, torsion stiffness and low-order natural frequencies of the BIW without considerable increase in the mass. A set of non-dominated solutions was then obtained in the multi-objective optimization design. Finally, the grey entropy theory and GRA were applied to rank all non-dominated solutions from best to worst to determine the best trade-off solution. The comparison between the GRA and the technique for order of preference by similarity to ideal solution (TOPSIS) illustrated the reliability and rationality of GRA. Moreover, the effectiveness of the hybrid method was verified by the optimal results such that the bending stiffness, torsion stiffness, first order bending and first order torsion natural frequency were improved by 5.46%, 9.30%, 7.32% and 5.73%, respectively, with the mass of the BIW increasing by 1.30%.
Article
In this paper, crashworthiness performance of multi-cell conical tubes with new sectional configuration design (i.e. square, hexagonal, octagonal, decagon and circular) has been evaluated under axial and three different oblique loads. The same weight conical tubes were comparatively studied using an experimentally validated finite element model generated in LS-DYNA. Complex proportional assessment (COPRAS) method was then employed to select the most efficient tube using two conflicting criteria, namely peak collapse force (PCF) and energy absorption (EA). From the COPRAS calculations, the multi-cell conical tube with decagonal cross-section (MCDT) showed the best crashworthiness performance. Furthermore, the effects of possible number of inside ribs on the crashworthiness of the decagonal conical tubes were also evaluated, and the results displayed that the tubes performed better as the number of ribs increased. Finally, parameters (the cone angle, θ, and ratio of the internal tube size to the external one, S) of MCDT were optimized by adopting artificial neural networks (ANN) and genetic algorithm (GA) techniques. Based on the multi-objective optimization results, the optimum dimension parameters were found to be θ=7.9°, S=0.46 and θ=8°, S=0.74 from the minimum distance selection (MDS) and COPRAS methods, respectively.
Article
In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II (NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy (E), peak crushing force (F max) and mass of the structure (W) as three conflicting objective functions. In the multi-objective optimization problem (MOP), E and F max are defined by polynomial models extracted using the software GEvoM based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point (NIP) method and technique for ordering preferences by similarity to ideal solution (TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.
Article
Full-text available
In this paper, a new multi-objective uniform-diversity genetic algorithm (MUGA) with a diversity preserving mechanism called the ε-elimination algorithm is used for Pareto optimization of a five-degree of freedom vehicle vibration model considering the five conflicting functions simultaneously. The important conflicting objective functions that have been considered in this work are, namely, seat acceleration, forward tire velocity, rear tire velocity, relative displacement between sprung mass and forward tire and relative displacement between sprung mass and rear tire. Further, different pairs of these objective functions have also been selected for 2-objective optimization processes. The comparison of the obtained results with those in the literature demonstrates the superiority of the results of this work. It is shown that the results of 5-objective optimization include those of 2-objective optimization and, therefore, provide more choices for optimal design of a vehicle vibration model.
Article
Full-text available
As a class of important lightweight structural components, sandwich panels have gained considerable popularity in a range of engineering applications. The crashworthiness of sandwich structures, which signifies a key mechanical property under impact loading, is found largely related to shape and dimensional parameters, such as cell width, wall thickness, structural angle and core height. This study exemplifies corrugated sandwich panels with trapezoidal and triangular cores to determine the relationship between the structural parameters and the crashworthiness under low-velocity local impact and planar impact, further optimizing these structural parameters with the crashworthiness criteria by using multiobjective optimization techniques. The configurations of trapezoidal and triangular core cells are firstly optimized for maximizing energy absorption. The wall thickness of sandwich panels with optimal trapezoidal core shape is then optimized for crashworthiness. Finally, the crashworthiness of these two types of corrugated sandwich panels is compared with each other under the identical face sheet thickness and core density and it is found that the triangular configuration has better performance.
Article
Full-text available
Increasing of head rise (H R) and decreasing of head loss (H L), simultaneously, are important purpose in the design of different types of fans. Therefore, multi-objective optimization process is more applicable for the design of such turbo machines. In the present study, multi-objective optimization of Forward-Curved (FC) blades centrifugal fans is performed at three steps. At the first step, Head rise (H R) and the Head loss (H L) in a set of FC centrifugal fan is numerically investigated using commercial software NUMECA. Two meta-models based on the evolved group method of data handling (GMDH) type neural networks are obtained, at the second step, for modeling of H R and H L with respect to geometrical design variables. Finally, using obtained polynomial neural networks, multi-objective genetic algorithms are used for Pareto based optimization of FC centrifugal fans considering two conflicting objectives, H R and H L . It is shown that some interesting and important relationships as useful optimal design principles involved in the performance of FC fans can be discovered by Pareto based multi-objective optimization of the obtained polynomial meta-models representing their H R and H L characteristics. Such important optimal principles would not have been obtained without the use of both GMDH type neural network modeling and the Pareto optimization approach.
Article
Full-text available
A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their efficiency in solving design optimization problems. In addition, research in multi-objective (MO) and multidisciplinary design optimization (MDO) has focused on developing robust and efficient optimization methods to produce a set of high quality solutions with low computational cost. In this paper, two optimization techniques are considered; the first optimization method uses multi-fidelity hierarchical Pareto optimality. The second optimization method uses the combination of two Game Strategies; Nash-equilibrium and Pareto optimality. The paper shows how Game Strategies can be hybridised and coupled to Multi-Objective Evolutionary Algorithms (MOEA) to accelerate convergence speed and to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid-Game Strategies are clearly demonstrated.
Article
Full-text available
Sandwich plates comprised of truss cores faced with either planar trusses or solid sheets are optimally designed for minimum weight subject to prescribed combinations of bending and transverse shear loads. Motivated by recent ad-vances in manufacturing possibilities, attention is focussed on plates with truss elements and faces made from a single material. The optimized plates are compared with similarly optimized honeycomb core sandwich plates fashioned from the same material. Sandwich plates with solid sheet faces and truss cores are highly ecient from a weight standpoint. These are also studied for their performance as compression panels. Optimized compression panels of this construction compare favorably with the most ecient stringer sti€ened plates.
Article
A semi-analytical method for bending analysis of corrugated-core, honeycomb-core and X-core sandwich panels is presented. The real displacement of sandwich panels is divided into the global displacement field and local displacement field. The discrete geometric nature of the core is taken into account by treating the core sheets as beams and the sandwich panel as composite structure of plates and beams with proper displacement compatibility. In the global displacement field, the governing equations of these sandwich panels are derived using energy variation principle and solved by employing Fourier series and the Galerkin approach. In the local displacement field, the face sheets under external loads are taken as a multi-span thin plate and the local bending response are then computed. Then the real bending responses are obtained by superposing these bending responses calculated in the two displacement fields and the structural stress fluctuation can be captured. Results from the proposed method agree well with available results in the literature and those from detailed finite element analysis. Furthermore, the mechanical properties of the three kinds of sandwich panels have been compared.
Article
In the present study, multi-objective optimization of a cyclone vortex finder is performed in three steps. In the first step, collection efficiency (η) and the pressure drop (Δ p) in a set of cyclones with different vortex finder shapes are numerically investigated using CFD techniques. Two meta-models based on the evolved group method of data handling (GMDH) type neural networks are obtained in the second step, for modelling of η and Δ p with respect to geometrical design variables. Finally, using the obtained polynomial neural networks, multi-objective genetic algorithms are used for Pareto-based optimization of a vortex finder considering two conflicting objectives, η and Δ p.
Article
In order to maximise the impact automotive energy-absorbing capacity considering uncertainties in the parameters of the design, it is desired to perform a robust optimum design process. Moreover, the optimum design of such absorption system is inherently a multi-objective optimisation problem. In this paper, a multi-objective optimisation approach is thus proposed to consider the robustness issue of those objective functions in the presence of parameter uncertainties. First, the axial impact crushing behaviour of the S-shaped box beams, as a highly simplified model of the front member of a vehicle body, is studied by the finite-element method using the software ABAQUS. Two polynomial meta-models based on the evolved group method of data handling (GMDH) neural networks are then obtained to simply represent both the absorbed energy (E) and the peak crushing force (F max) with respect to geometrical and material design variables using the training and testing data obtained from the finite-element study. Using such obtained polynomial neural network models and the Monte Carlo simulation, a multi-objective genetic algorithm is then used for the reliability-based robust Pareto design of the S-shaped box beams having probabilistic uncertainties in material and geometrical parameters. In this way, the statistical moments of mean and variances of the important crashworthiness criteria functions, namely the specific energy absorption (SEA) and the peak crushing force (F max), are considered as the conflicting objectives. It is shown that some useful optimal design principles involved in the performance of the S-shaped box beams can be discovered by the reliability-based robust Pareto optimisation.
Article
Lightweight metallic sandwich plates comprising periodic truss cores and solid facesheets are optimally designed against minimum weights. Constitutive models of the truss core are developed using homogenization techniques which, together with effective single-layer sandwich approaches, form the basis of a two-dimensional (2D) single-layer sandwich model. The 2D model is employed to simulate the mechanical behaviors of truss-cored sandwich panels having a variety of core topologies. The types of loading considered include bending, transverse shear and in-plane compression. The validities of the 2D model predictions are checked against direct FE simulations on three-dimensional (3D) truss core sandwich struc-tures. Optimizations using the 2D sandwich model are subsequently performed to determine the minimum weights of truss-cored sandwiches subjected to various failure constraints: overall and local buckling, yielding and facesheet wrinkling. The performances of the optimized truss core sandwiches with 4-rod unit cell and solid truss members and pyramidal unit cell with hollow truss members are compared with benchmark lightweight structures such as honeycomb-cored sandwiches, tetrahedral core sandwiches and hat-stiffened single layer plates.
Article
In this paper, evolutionary algorithms (EAs) are deployed for multi-objective Pareto optimal design of group method of data handling (GMDH)-type neural networks which have been used for modelling an explosive cutting process using some input–output experimental data. In this way, multi-objective EAs (non-dominated sorting genetic algorithm, NSGA-II) with a new diversity-preserving mechanism are used for Pareto optimization of such GMDH-type neural networks. The important conflicting objectives of GMDH-type neural networks that are considered in this work are, namely, training error (TE), prediction error (PE), and number of neurons (N) of such neural networks. Different pairs of theses objective functions are selected for 2-objective optimization processes. Therefore, optimal Pareto fronts of such models are obtained in each case which exhibit the trade-off between the corresponding pair of conflicting objectives and, thus, provide different non-dominated optimal choices of GMDH-type neural networks models for explosive cutting process. Moreover, all the three objectives are considered in a 3-objective optimization process, which consequently leads to some more non-dominated choices of GMDH-type models representing the trade-offs among the training error, prediction error, and number of neurons (complexity of network), simultaneously. The overlay graphs of these Pareto fronts also reveal that the 3-objective results include those of the 2-objective results and, thus, provide more optimal choices for the multi-objective design of GMDH-type neural networks in terms of minimum training error, minimum prediction error, and minimum complexity.
Article
A minimum-weight flexural actuator is designed. The actuator comprises a triangular corrugated core with shape memory alloy (SMA) faces. It is clamped at one end and free at the other. For design and optimization, the temperature history of the face sheets upon heating and subsequent cooling is first obtained as a function of the cooling efficiency (Biot number) and the operational frequency deduced. Based upon this response, a phenomenological model is employed to represent the martensite evolution. Thereafter, the end deflection is calculated as a function of temperature. The minimum weight is calculated subject to the provisos that: (i) the end deflection attains a specified value; (ii) the power consumed is less than the upper limit of the supply; and failure is averted by (iii) face/core yielding and (iv) face/core buckling; (v) the operational frequency of the panel achieves a specified limit.
Article
Multifunctional sandwich panels with corrugated and prismatic diamond cores have been analyzed and their behavior compared with panels designed using truss and honeycomb cores. Failure mechanism maps have been devised that account for interactions between core and face members during buckling. The optimal dimensions and the minimum weight have been evaluated. The load capacities predicted for near-optimal designs have been validated by conducting selected finite element calculations. Designs that use diamond prismatic cores (with corrugation order 4) are slightly more weight efficient than trusses, when optimized for a specific loading direction. Honeycomb cores, while somewhat more weight efficient, especially at lower load capacities, are not amenable to the fluid flows needed for cooling. We conclude that the diamond prismatic topology is the most weight efficient among designs amenable to simultaneous load bearing and active cooling.
Article
Metallic sandwich panels with periodic, open-cell cores are important new structures, enabled by novel fabrication and topology design tools. Fabrication protocols based on the sheet forming of trusses and shell elements (egg-boxes) as well as textile assembly have allowed the manufacture of robust structures by inexpensive routes. Topology optimization enables control of failure mechanisms at the truss length scale, leading to superior structural performance. Analysis, testing and optimization have demonstrated that sandwich panels constructed with these cores sustain loads at much lower relative densities than stochastic foams. Moreover, the peak strengths of truss and textile cores are superior to honeycombs at low relative densities, because of their superior buckling resistance. Additional benefits of the truss/textile cores over honeycombs reside in their potentially lower manufacturing cost as well as in their multifunctionality.
Article
Multi-objective optimization has recently emerged as a useful technique in sustainability analysis, as it can assist in the study of optimal trade-off solutions that balance several criteria. The main limitation of multi-objective optimization is that its computational burden grows in size with the number of objectives. This computational barrier is critical in environmental applications in which decision-makers seek to minimize simultaneously several environmental indicators of concern. With the aim to overcome this limitation, this paper introduces a systematic method for reducing the number of objectives in multi-objective optimization with emphasis on environmental problems. The approach presented relies on a novel mixed-integer linear programming formulation that minimizes the error of omitting objectives. We test the capabilities of this technique through two environmental problems of different nature in which we attempt to minimize a set of life cycle assessment impacts. Numerical examples demonstrate that certain environmental metrics tend to behave in a non-conflicting manner, which makes it possible to reduce the dimension of the problem without losing information.
Article
Solving multi-objective problems requires the evaluation of two or more conflicting objective functions, which often demands a high amount of computational power. This demand increases rapidly when estimating values for objective functions of dynamic, stochastic problems, since a number of observations are needed for each evaluation set, of which there could be many. Computer simulation applications of real-world optimisations often suffer due to this phenomenon. Evolutionary algorithms are often applied to multi-objective problems. In this article, the cross-entropy method is proposed as an alternative, since it has been proven to converge quickly in the case of single-objective optimisation problems. We adapted the basic cross-entropy method for multi-objective optimisation and applied the proposed algorithm to known test problems. This was followed by an application to a dynamic, stochastic problem where a computer simulation model provides the objective function set. The results show that acceptable results can be obtained while doing relatively few evaluations.
Article
Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN<sup>3</sup>) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN<sup>2</sup>) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed