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Structural Optimization Methods and Applications
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Structural Optimization Methods and Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (10 March 2024) | Viewed by 27200

Special Issue Editors

Prof. Dr. Qi Xia

E-Mail Website
Guest Editor
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Interests: topology optimization; composite structure optimization; multiscale structure optimization; level set
Special Issues, Collections and Topics in MDPI journals
Dr. Hui Liu

E-Mail Website
Guest Editor
Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan 430072, China
Interests: computational mechanics; structural and multidisciplinary optimization; multiscale modeling and computation
Special Issues, Collections and Topics in MDPI journals
Dr. Kai Long

E-Mail Website
Guest Editor
State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
Interests: topology optimization; concurrent design; material design; offshore wind turbine
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With structural optimization, all designers need to do is specify their objective and constraints, as well as the design variables of the design problem, and then a structure can be automatically generated which has a suitable performance and is low-cost and easy to manufacture. This is recognized as a powerful tool for solving demanding design problems and is extensively used in engineering. This Special Issue is devoted to topics including but not limited to:

  • Structural optimization methods, numerical techniques, and engineering applications;
  • Optimization method of material or multiscale structures;
  • Structural optimization involving nonlinearity, dynamics, and multiple physical fields;
  • Structural optimization involving manufacturing issues;
  • Structural design considering uncertainties.

Prof. Dr. Qi Xia
Dr. Hui Liu
Dr. Kai Long
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • topology optimization
  • material design
  • multiscale structure optimization
  • composite structure
  • computational mechanics

Published Papers (23 papers)

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16 pages, 2435 KiB  
Article
Hybrid Strategy Improved Beetle Antennae Search Algorithm and Application
by Xiaohang Shan, Shasha Lu, Biqing Ye and Mengzheng Li
Appl. Sci. 2024, 14(8), 3286; https://doi.org/10.3390/app14083286 - 13 Apr 2024
Viewed by 372
Abstract
The multi-dimensional optimization of mechanisms is a typical optimization problem encountered in mechanical design. Herein, the Hybrid strategy improved Beetle Antennae Search (HSBAS) algorithm is proposed to solve the multi-dimensional optimization problems encountered in structural design. To solve the problems of local optimization [...] Read more.
The multi-dimensional optimization of mechanisms is a typical optimization problem encountered in mechanical design. Herein, the Hybrid strategy improved Beetle Antennae Search (HSBAS) algorithm is proposed to solve the multi-dimensional optimization problems encountered in structural design. To solve the problems of local optimization and low accuracy of the high-dimensional solution of the Beetle Antennae Search (BAS) algorithm, the algorithm adopts the adaptive step strategy, multi-directional exploration strategy, and Lens Opposition-Based Learning strategy, significantly reducing the probability of the algorithm falling into the local optimum and improving its global search capability. Comparative experiments of the improved algorithm are carried out by selecting eleven benchmark test functions. HSBAS can reach 1 × 10−22 accuracy from the optimal value when dealing with low-dimensional functions. It can also obtain 1 × 10−2 accuracy when dealing with high-dimensional functions, significantly improving the algorithm’s capability. According to Friedman’s ranking test result, HSBAS ranks first, which proves that HSBAS is superior to the other three algorithms. The HSBAS algorithm is further used to optimize the design of the altitude compensation module of the gravity compensation device for solar wings, controlling the fluctuation of bearing capacity within 0.25%, which shows that the algorithm can be used as an effective tool for engineering structural optimization problems. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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28 pages, 11680 KiB  
Article
Optimizing the Thickness of Functionally Graded Lattice Structures for High-Performance Energy Absorption: A Case Study Based on a Bicycle Helmet
by Thierry Decker and Slawomir Kedziora
Appl. Sci. 2024, 14(7), 2788; https://doi.org/10.3390/app14072788 - 27 Mar 2024
Viewed by 563
Abstract
This study explores the complete production chain of designing, optimizing, and Additive Manufacturing (AM) of a helmet incorporating a functionally graded lattice structure (FGLS). The potential of FGLSs in impact energy absorption tasks is investigated, along with the demonstration of a novel lattice [...] Read more.
This study explores the complete production chain of designing, optimizing, and Additive Manufacturing (AM) of a helmet incorporating a functionally graded lattice structure (FGLS). The potential of FGLSs in impact energy absorption tasks is investigated, along with the demonstration of a novel lattice optimization approach. Fifteen conformal, strut-based lattices are implemented in a realistic mountain bike helmet geometry and simulated in a standardized impact scenario in accordance with EN 1078. One model is subjected to the optimization procedure, produced, and physically tested. The study addresses limitations in prior research, emphasizing manufacturability in an AM context, lattice type exploration, the comparability of different unit cell types, and numerical modeling choices. The findings provide insights into the performance of lattice structures during impact, emphasizing practical engineering aspects such as design choices, optimization approaches, and manufacturing constraints. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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19 pages, 13948 KiB  
Article
Material-Structure Integrated Design and Optimization of a Carbon-Fiber-Reinforced Composite Car Door
by Huile Zhang, Zeyu Sun, Pengpeng Zhi, Wei Wang and Zhonglai Wang
Appl. Sci. 2024, 14(2), 930; https://doi.org/10.3390/app14020930 - 22 Jan 2024
Viewed by 744
Abstract
This paper develops a material-structure integrated design and optimization method based on a multiscale approach for the lightweight design of CFRP car doors. Initially, parametric modeling of RVE is implemented, and their elastic performance parameters are predicted using the homogenization theory based on [...] Read more.
This paper develops a material-structure integrated design and optimization method based on a multiscale approach for the lightweight design of CFRP car doors. Initially, parametric modeling of RVE is implemented, and their elastic performance parameters are predicted using the homogenization theory based on thermal stress, exploring the impact of RVE parameters on composite material performance. Subsequently, a finite element model of the CFRP car door is constructed based on the principle of equal stiffness, and a parameter transfer across microscale, mesoscale, and macroscale levels is achieved through Python programming. Finally, the particle generation and updating strategies in the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm are improved, enabling the algorithm to directly solve multi-constraint and multi-objective optimization problems that include various composite material layup process constraints. Case study results demonstrate that under layup process constraints and car door stiffness requirements, plain weave, twill weave, and satin weave composite car doors achieve weight reductions of 15.85%, 14.54%, and 15.35%, respectively, compared to traditional metal doors, fulfilling the requirements for a lightweight design. This also provides guidance for the lightweight design of other vehicle body components. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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17 pages, 37995 KiB  
Article
Topological Optimization of Bi-Directional Progressive Structures with Dynamic Stress Constraints under Aperiodic Load
by Yongxin Li, Tao Chang, Weiyu Kong, Fenghe Wu and Xiangdong Kong
Appl. Sci. 2024, 14(1), 322; https://doi.org/10.3390/app14010322 - 29 Dec 2023
Viewed by 485
Abstract
The topology optimization of dynamic stress constraints is highly nonlinear and singular and has been little studied. Dynamic stress based on progressive structural optimization is only available by applying the modal iteration method, but due to the nonlinear limitations of the modal superposition [...] Read more.
The topology optimization of dynamic stress constraints is highly nonlinear and singular and has been little studied. Dynamic stress based on progressive structural optimization is only available by applying the modal iteration method, but due to the nonlinear limitations of the modal superposition method, there is an urgent need to develop a progressive structural optimization method based on dynamic stress sensitivity under direct integration. This method is for the dynamic stresses under non-periodic loading with iterative cycle updating variations. This article proposes a topological optimization method of continuum structures with stress constraints under an aperiodic load based on the Bi-directional Evolutionary Structural Optimization Method (BESO). First, the P-norm condensation function was used to obtain the global stress to approximate maximum stress. By introducing the Lagrange multiplier, the design goal was to increase the P-norm stress on the basis of the smallest volume. After that, based on the dynamic finite element theory, the sensitivity of each cell formula of the objective function and the constraint conditions of the design variables were strictly derived. Then, the performance evaluation index was put forward based on volume and stress, and the convergence criterion based on the performance evaluation index was defined. This method solves the topology optimization problem of stress constraints under a non-periodic load and the topology optimization problem of stress constraints under a periodic load, such as a simple harmonic load. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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16 pages, 21621 KiB  
Article
Multi-Physics and Multi-Objective Optimization for Fixing Cubic Fabry–Pérot Cavities Based on Data Learning
by Hang Zhao, Fanchao Meng, Zhongge Wang, Xiongfei Yin, Lingqiang Meng and Jianjun Jia
Appl. Sci. 2023, 13(24), 13115; https://doi.org/10.3390/app132413115 - 08 Dec 2023
Viewed by 644
Abstract
The Fabry–Pérot (FP) cavity is the essential component of an ultra-stable laser (USL) for gravitational wave detection, which couples multiple physics fields (optical/thermal/mechanical) and requires ultra-high precision. Aiming at the deficiency of the current single physical field optimization, a multi-physics and multi-objective optimization [...] Read more.
The Fabry–Pérot (FP) cavity is the essential component of an ultra-stable laser (USL) for gravitational wave detection, which couples multiple physics fields (optical/thermal/mechanical) and requires ultra-high precision. Aiming at the deficiency of the current single physical field optimization, a multi-physics and multi-objective optimization method for fixing the cubic FP cavity based on data learning is proposed in this paper. A multi-physics coupling model for the cubic FP cavity is established and the performance is obtained via finite element analysis. The key performance indices (V, wF, wF) and key design variables (d, l, F) are determined considering the features of the FP cavity. Different data learning models (NN, RSF, KRG) are established and compared based on 49 sets of data acquired by orthogonal experiments, with the results showing that the neural network has the best performance. NSGA-II is adopted as the optimization algorithm, the Pareto optimal front is obtained, and the optimal combination of design variables is finally determined as {5,32,250}. The performance after optimization proves to be greatly improved, with the displacement under the fixing force and vibration test both decreased by more than 60%. The proposed optimization strategy can help in the design of the FP cavity, and could enlighten other optimization fields as well. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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35 pages, 18518 KiB  
Article
Bisection Constraint Method for Multiple-Loading Conditions in Structural Topology Optimization
by Thi Pham-Truong, Yasumi Kawamura and Tetsuo Okada
Appl. Sci. 2023, 13(24), 13005; https://doi.org/10.3390/app132413005 - 05 Dec 2023
Cited by 1 | Viewed by 926
Abstract
Topology optimization (TO) is currently a focal point for researchers in the field of structural optimization, with most studies concentrating on single-loading conditions. However, real engineering structures often have to work under various loading conditions. Approaches addressing multiple-loading conditions often necessitate subjective input [...] Read more.
Topology optimization (TO) is currently a focal point for researchers in the field of structural optimization, with most studies concentrating on single-loading conditions. However, real engineering structures often have to work under various loading conditions. Approaches addressing multiple-loading conditions often necessitate subjective input in order to determine the importance of each loading condition, aiming for a compromise between them. This paper proposes a so-called bisection constraint method (BCM), offering a unique, user-preference-independent solution for TO problems amidst multiple-loading conditions. It is well-known that minimizing the system’s compliance is commonly used in TO as the objective. Generally, compliance is not as sufficient as stress to be used as a response to evaluate the performance of structures. However, formulations focusing on minimizing stress levels usually pose significant difficulties and instabilities. On the other hand, the compliance approach is generally simpler and more capable of providing relatively sturdy designs. Hence, the formulation of min–max compliance is used as the target problem formulation of the proposed method. This method attempts to minimize compliance under only one loading condition while compliances under the remaining loading conditions are constrained. During the optimization process, the optimization problem is automatically reformulated with a new objective function and a new set of constraint functions. The role of compliance under different loading conditions, i.e., whether it is to be treated as an objective or constraint function, might be changed throughout the optimization process until convergence. Several examples based on the solid isotropic material with penalization (SIMP) approach were conducted to illustrate the validity of the proposed method. Furthermore, the general effectiveness of the compliance approach in terms of stress levels is also discussed. The calculation results demonstrated that while the compliance approach is effective in several cases, it proves ineffective in certain scenarios. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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22 pages, 10869 KiB  
Article
Local Thickness Optimization of Functionally Graded Lattice Structures in Compression
by Thierry Decker and Slawomir Kedziora
Appl. Sci. 2023, 13(23), 12969; https://doi.org/10.3390/app132312969 - 04 Dec 2023
Cited by 1 | Viewed by 782
Abstract
This paper presents a new method for optimizing the thickness distribution of a functionally graded lattice structure. It links the thickness of discrete lattice regions via mathematical functions, reducing the required number of optimization variables while being applicable to highly nonlinear models and [...] Read more.
This paper presents a new method for optimizing the thickness distribution of a functionally graded lattice structure. It links the thickness of discrete lattice regions via mathematical functions, reducing the required number of optimization variables while being applicable to highly nonlinear models and arbitrary optimization goals. This study demonstrates the method’s functionality by altering the local thickness of a lattice structure in compression, optimizing the structure’s specific energy absorption at constant weight. The simulation results suggest significant improvement potential for the investigated Simple Cubic lattice, but less so for the Isotruss variant. The energy absorption levels of the physical test results closely agree with the simulations; however, great care must be taken to accurately capture material and geometry deviations stemming from the manufacturing process. The proposed method can be applied to other lattice structures or goals and could be useful in a wide range of applications where the optimization of lightweight and high-performance structures is required. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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27 pages, 5680 KiB  
Article
Elastoplastic Analysis of Frame Structures Using Radial Point Interpolation Meshless Methods
by Jorge Belinha, Miguel Aires and Daniel E.S. Rodrigues
Appl. Sci. 2023, 13(23), 12591; https://doi.org/10.3390/app132312591 - 22 Nov 2023
Viewed by 628
Abstract
The need to design structures and structural elements that are more efficient in terms of performance is a key aspect of engineering. For a given material to be used at its maximum capacity, considering non-linear characteristics is mandatory. The non-linear regime is a [...] Read more.
The need to design structures and structural elements that are more efficient in terms of performance is a key aspect of engineering. For a given material to be used at its maximum capacity, considering non-linear characteristics is mandatory. The non-linear regime is a subject of extreme interest for this reason and is an area with intense research activity. In this work, advanced discretization techniques (i.e., meshless methods) are applied in the elastoplastic analysis of 2D and 3D structural elements. The literature shows that meshless methods are capable of producing more accurate and smoother strain and stress fields, which are the variable fields required in the non-linear models describing elastoplasticity. Thus, in this study, the Radial Point Interpolation Method (RPIM) and the Natural Neighbor Radial Point Interpolation Method (NNRPIM) are combined with a non-linear iterative algorithm, fully developed by the authors, with the objective of analyzing for the first time the elastoplastic behavior of a two-bay asymmetric frame and bowstring bridge considering 2D and 3D analysis. The accuracy and robustness of the RPIM and the NNRPIM are shown in the end, comparing the obtained results with FEM solutions and the available literature. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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29 pages, 10404 KiB  
Article
A Multi-Fidelity Successive Response Surface Method for Crashworthiness Optimization Problems
by Pietro Lualdi, Ralf Sturm and Tjark Siefkes
Appl. Sci. 2023, 13(20), 11452; https://doi.org/10.3390/app132011452 - 19 Oct 2023
Viewed by 738
Abstract
Due to the high computational burden and the high non-linearity of the responses, crashworthiness optimizations are notoriously hard-to-solve challenges. Among various approaches, methods like the Successive Response Surface Method (SRSM) have stood out for their efficiency in enhancing baseline designs within a few [...] Read more.
Due to the high computational burden and the high non-linearity of the responses, crashworthiness optimizations are notoriously hard-to-solve challenges. Among various approaches, methods like the Successive Response Surface Method (SRSM) have stood out for their efficiency in enhancing baseline designs within a few iterations. However, these methods have limitations that restrict their application. Their minimum iterative resampling required is often computationally prohibitive. Furthermore, surrogate models are conventionally constructed using Polynomial Response Surface (PRS), a method that is poorly versatile, prone to overfitting, and incapable of quantifying uncertainty. Furthermore, the lack of continuity between successive response surfaces results in suboptimal predictions. This paper introduces the Multi-Fidelity Successive Response Surface (MF-SRS), a Gaussian process-based method, which leverages a non-linear multi-fidelity approach for more accurate and efficient predictions compared to SRSM. After initial testing on synthetic problems, this method is applied to a real-world crashworthiness task: optimizing a bumper cross member and crash box system. The results, benchmarked against SRSM and the Gaussian Process Successive Response Surface (GP-SRS)—a single-fidelity Gaussian process-driven extension of SRSM—show that MF-SRS offers distinct advantages. Specifically, it improves upon the specific energy absorbed optimum value achieved by SRSM by 14%, revealing its potential for future applications. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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15 pages, 10471 KiB  
Article
A Numerical Method-Based Analysis of the Structural Deformation Behaviour of a Turkish String Instrument (Cura Baglama) under Varying String Tensions
by H. Kursat Celik, Sevilay Gok, Nuri Caglayan and Allan E. W. Rennie
Appl. Sci. 2023, 13(17), 9682; https://doi.org/10.3390/app13179682 - 27 Aug 2023
Viewed by 1111
Abstract
This study focuses on the structural design analysis of a cura baglama, a traditional Turkish string instrument that does not have in place a regulated set of manufacturing standards to follow. The aim therefore is to introduce a structural deformation analysis for a [...] Read more.
This study focuses on the structural design analysis of a cura baglama, a traditional Turkish string instrument that does not have in place a regulated set of manufacturing standards to follow. The aim therefore is to introduce a structural deformation analysis for a sample cura baglama in three different string tensions via a numerical method-based engineering analysis technique. The three-dimensional solid model of a sample cura baglama was created using a 3D scanner and parametric 3D solid modelling software. Based on experimental frequency analysis, structural deformation analyses of the instrument were conducted using finite element method-based engineering simulation techniques. The simulation results revealed useful visual and numerical outputs related to the deformation behaviour of the instrument under pre-defined boundary conditions. A maximum deformation of 0.223 mm on the soundboard (at the D3 tune) and a maximum equivalent stress of 18.325 MPa on the bridge (at the D3 tune) were calculated. The outputs of this research contribute to further research into the usage of numerical method-based deformation simulation studies related to the standardisation, development, and preservation of such traditional string instruments. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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25 pages, 1555 KiB  
Article
An Efficient and Robust Topology Optimization Method for Thermoelastically Damped Microresonators
by Yu Fu, Li Li and Yujin Hu
Appl. Sci. 2023, 13(15), 8811; https://doi.org/10.3390/app13158811 - 30 Jul 2023
Viewed by 813
Abstract
The challenges of computational cost and robustness are critical obstacles in topology optimization methods, particularly for the iterative process of optimizing large-scale multiphysical structures. This study proposes an efficient and robust topology optimization method for minimizing the thermoelastic damping of large-scale microresonators. An [...] Read more.
The challenges of computational cost and robustness are critical obstacles in topology optimization methods, particularly for the iterative process of optimizing large-scale multiphysical structures. This study proposes an efficient and robust topology optimization method for minimizing the thermoelastic damping of large-scale microresonators. An evolutionary structural optimization method is adopted to passively determine the search direction of optimizing large-scale thermoelastic structures. To efficiently reduce the computational cost of the iterative process of an optimizing process, a model reduction method is developed based on the projection-based model reduction method whose reduced basis is generated within the Neumann series subspace. However, the projection-based model reduction method may be unstable when topology modifications are made during an iteration optimization process. To ensure robustness, a modal validation technique is first implemented in the iterative process to stabilize the iteration and narrow down the search domain, and a posterior evaluation of the Neumann series expansion is then developed to retain the convergence of the projection-based model reduction method. Furthermore, the efficiency and accuracy of the proposed topology optimization method are validated through numerical examples. Two large-scale numerical models are also used to demonstrate the advantage of the proposed method. It is found that large-scale thermoelastic structures with a phase-lag heat conduction law can be designed passively, precisely, and efficiently by using the proposed topology optimization method. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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19 pages, 9022 KiB  
Article
Intelligent Assembly Method of the Profiled Thermal Battery Pack Based on Improved DE Algorithm
by Yingyu Zhou, Ling He, Jiangchuan Zhong and Dan Liu
Appl. Sci. 2023, 13(9), 5280; https://doi.org/10.3390/app13095280 - 23 Apr 2023
Viewed by 1115
Abstract
An intelligent assembly method was designed to realize the intelligent assembly of the profiled thermal battery pack and improve its assembly accuracy. Firstly, as the number and size of different monomer batteries vary, this paper takes the monomer thermal battery assembly as the [...] Read more.
An intelligent assembly method was designed to realize the intelligent assembly of the profiled thermal battery pack and improve its assembly accuracy. Firstly, as the number and size of different monomer batteries vary, this paper takes the monomer thermal battery assembly as the object, with a common shape circle assembly screw arrangement and an established process model. Then, the assembly also has an improved differential evolution algorithm for assembly arrangement and process on the number, location, tightening of the screw assembly, torque, and the order of solutions. According to this scheme, the assembly and the flatness test were carried out. The results showed that the bottom plate of the assembly frame was “concave in the middle and warped around”, and the flatness error was large. The scheme was optimized by numerical simulation analysis. After optimization, the average offset of the floor plane was 0.04 mm, and the offset accounted for 0.028% of the overall height; the maximum offset was 0.094 mm and the offset was reduced by 0.312%. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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19 pages, 5148 KiB  
Article
Topology Optimization Design of Multi-Input-Multi-Output Compliant Mechanisms with Hinge-Free Characteristic and Totally Decoupled Kinematics
by Shouyu Cai, Wenshang Zhou, Hongtao Wei and Mingfu Zhu
Appl. Sci. 2023, 13(7), 4627; https://doi.org/10.3390/app13074627 - 06 Apr 2023
Viewed by 1580
Abstract
A new multi-constraint optimization model with the weighted objective function is proposed to design the multi-input-multi-output (MIMO) compliant mechanisms. The main feature of this work is that both the two notable problems related to the de facto hinge and the movement coupling are [...] Read more.
A new multi-constraint optimization model with the weighted objective function is proposed to design the multi-input-multi-output (MIMO) compliant mechanisms. The main feature of this work is that both the two notable problems related to the de facto hinge and the movement coupling are tackled simultaneously in the topological synthesis of MIMO compliant mechanisms. To be specific, the first problem is the severe stress concentration in the flexible hinge areas, and it is solved by the introduction of input and output compliances into the objective function, which could facilitate the optimization to strike a good balance between structural flexibility and stiffness. The second problem is the high degree of control complexity caused by the coupled outputs and inputs, and it is addressed by achieving the complete decoupling with two groups of extra constraints that are used to suppress the input coupling and the output coupling, respectively. As the most common and effective topology optimization method, the Solid Isotropic Material with Penalization (SIMP)-based density method is adopted here to obtain the optimized configurations. After the analytical sensitivity deduction related to the weighted objective function and constraints, two typical numerical examples are presented to demonstrate the validity of the proposed topology optimization framework in designing the hinge-free and completely decoupled MIMO compliant mechanisms. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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13 pages, 2185 KiB  
Article
Topology Optimization Based on SA-BESO
by Liping Chen, Hui Zhang, Wei Wang and Qiliang Zhang
Appl. Sci. 2023, 13(7), 4566; https://doi.org/10.3390/app13074566 - 04 Apr 2023
Cited by 2 | Viewed by 1741
Abstract
Bidirectional asymptotic structure methods have long been used to solve topological optimization problems, but are prone to being stuck in local optimal solutions. To solve this problem, this paper proposed a topology optimization method based on the Bi-directional Evolutionary structure Structural Optimization and [...] Read more.
Bidirectional asymptotic structure methods have long been used to solve topological optimization problems, but are prone to being stuck in local optimal solutions. To solve this problem, this paper proposed a topology optimization method based on the Bi-directional Evolutionary structure Structural Optimization and Simulated Annealing algorithm (SA-BESO). First, the structural elements of the structural partition are encoded by a dual encoding, where elements are assigned with density values and binary strings. Second, binary strings are crossed and mutated, while criteria for adding and removing structural units are formulated. Then, structures are updated randomly. Finally, the structural compliance of the current structure is evaluated. If the structural compliance of the original structure increases, it will be accepted with a certain probability, thus jumping out of the local optimal solution. Related examples show that the SA-BESO method improves the smoothness of the optimization process and can obtain optimized structures with lower structural compliance and computational cost. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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15 pages, 5807 KiB  
Article
Multiscale Design of Graded Stochastic Cellular Structures for the Heat Transfer Problem
by Lianxiong Chen, Ran Zhang, Xihua Chu and Hui Liu
Appl. Sci. 2023, 13(7), 4409; https://doi.org/10.3390/app13074409 - 30 Mar 2023
Cited by 3 | Viewed by 926
Abstract
Advancesin additive manufacturing technology have expanded the development prospect of structures with complex configurations. Cellular structures have been a hot research topic in recent years for their superior performance and characteristics, such as being lightweight and having high specific strength and good permeability. [...] Read more.
Advancesin additive manufacturing technology have expanded the development prospect of structures with complex configurations. Cellular structures have been a hot research topic in recent years for their superior performance and characteristics, such as being lightweight and having high specific strength and good permeability. With a high specific surface area, cellular structures perform noticeably well in heat transfer applications when subjected to a body heat source. In this paper, a scale-separated multiscale design of theVoronoi graded stochastic cellular structure (Voronoi-GSCS) that considers the heat transfer problem is proposed. The design method is composed of three steps: the offline calculation on the microscale, the online optimization on the macroscale, and geometry reconstruction on the full scale. Numerical examples are given to show the effectiveness and superiority of the developed method for designing the Voronoi-GSCS. The results obtained by the solid isotropic material with penalization (SIMP) approach are used for comparison. The size effect analysis was conducted to research the influence of the size of the microstructure on the Voronoi-GSCS. It should be stressed that the smallest struts were larger than the minimum print size of the additive manufacturing so that the Voronoi-GSCS could be conveniently exploited in heat transfer applications. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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26 pages, 19630 KiB  
Article
Structure Design and Optimization Algorithm of a Lightweight Drive Rod for Precision Die-Cutting Machine
by Jing Wang, Xian Chen and Yong Li
Appl. Sci. 2023, 13(7), 4211; https://doi.org/10.3390/app13074211 - 26 Mar 2023
Viewed by 1143
Abstract
In order to solve the problems of excessive elastic deformation and excessive inertia force existed in the drive mechanism of traditional die-cutting machine, a lightweight drive rod with full symmetrical structure is proposed as the main force bearing component of the drive mechanism [...] Read more.
In order to solve the problems of excessive elastic deformation and excessive inertia force existed in the drive mechanism of traditional die-cutting machine, a lightweight drive rod with full symmetrical structure is proposed as the main force bearing component of the drive mechanism based on the kinematics analysis. The elastic deformation and inertia force of the lightweight drive rod are verified by static simulation analysis, and show that the weight of the drive rod is significantly reduced under the same deformation conditions, the traditional one. Further compared with, taking the minimum elastic deformation and lightweight as the optimization objectives, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used to optimize the structural parameters of the drive rod. The results show that under the working conditions of 350 T die-cutting force and 125 r/min rotating speed, the elastic deformation of lightweight drive rod after structural optimization is smaller (the maximum deformation is 0.00988 mm) and the weight is lighter (27% less). The research data presented in this paper can be used as the theoretical basis for future research on die-cutting mechanism. The lightweight drive rod proposed in this study can be used in die-cutting devices with high die-cutting speed and high die-cutting accuracy. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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15 pages, 4474 KiB  
Article
Simulation-Based Reliability Design Optimization Method for Industrial Robot Structural Design
by Li-Xiang Zhang, Xin-Jia Meng, Zhi-Jie Ding and Hong-Xiang Han
Appl. Sci. 2023, 13(6), 3776; https://doi.org/10.3390/app13063776 - 15 Mar 2023
Cited by 1 | Viewed by 1425
Abstract
Robots are main elements in Industry 4.0. Research on the design optimization of robots has a great significance in manufacturing industries. There inevitably exist various uncertainties in robot design that have an important influence on the reliability of robots. At present, the design [...] Read more.
Robots are main elements in Industry 4.0. Research on the design optimization of robots has a great significance in manufacturing industries. There inevitably exist various uncertainties in robot design that have an important influence on the reliability of robots. At present, the design optimization of robots considering the uncertainties is mainly focused on joints design and trajectory optimization. However, for the structural design of robots, deterministic design optimization still plays a leading role. In this paper, a simulation-based reliability design optimization method is proposed to improve the reliability of robots’ structural design. In the proposed method, the Latin hypercube sampling (LHS), computer simulation, response surface method (RSM) and SORA (Sequential Optimization and Reliability Assessment) algorithm are integrated to complete the structural design of the robot. Firstly, samples of the uncertainty design variables were obtained by LHS, and then, the reliability performance constraint functions were firstly constructed through the RSM in which the joint simulation of MTLAB and ANSYS was adopted. Afterwards, the reliability design optimization model was established on the basis of the probabilistic reliability theory. At last, the SORA algorithm was employed to realize the optimization. The design optimization problems of the big arm and the small arm of a 6 Kg industrial robot were considered to verify the proposed method. The results showed that the weights of the big arm and the small arm were, respectively, reduced by 7.73% and 25.70% compared with those of the original design, and the design was more effective in ensuring the reliability requirements compared with the deterministic optimization. Moreover, the results also demonstrated that the proposed method has a better computational efficiency compared with the reliability design optimization of the double-loop method. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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17 pages, 19304 KiB  
Article
Structural Design of Aerostatic Bearing Based on Multi-Objective Particle Swarm Optimization Algorithm
by Biqing Ye, Guixin Yu, Yidong Zhang and Gang Li
Appl. Sci. 2023, 13(5), 3355; https://doi.org/10.3390/app13053355 - 06 Mar 2023
Cited by 1 | Viewed by 1041
Abstract
Aerostatic bearings are considered crucial components that can improve the measurement accuracy of ground simulation tests of space equipment. A structural optimization design method is proposed to enhance the static performance of aerostatic bearings. A mathematical model which can quickly calculate the aerostatic [...] Read more.
Aerostatic bearings are considered crucial components that can improve the measurement accuracy of ground simulation tests of space equipment. A structural optimization design method is proposed to enhance the static performance of aerostatic bearings. A mathematical model which can quickly calculate the aerostatic bearing capacity and gas consumption is established, and the influence of structural parameters on bearing performance is analyzed using simulation software. By comparing the convergence time and convergence results of the algorithm using different initialization methods, the Latin hypercube initialization method is selected instead of the random initialization method. The multi-objective particle swarm optimization algorithm is used to obtain the optimal solution set distributed in the objective space. It is found that the optimized structural parameters meet the requirements of improving the capacity and reducing gas consumption, which verifies the method’s effectiveness in designing the structural parameters of aerostatic bearings. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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22 pages, 6716 KiB  
Article
A Crossrate-Based Approach for Reliability-Based Multidisciplinary Dynamic System Design Optimization
by Li Lu, Yizhong Wu, Qi Zhang and Ping Qiao
Appl. Sci. 2023, 13(3), 1600; https://doi.org/10.3390/app13031600 - 26 Jan 2023
Cited by 1 | Viewed by 976
Abstract
In practical applications, the multidisciplinary dynamic system design optimization (MDSDO)-based solution is limited by uncertainty, which causes random variation in the physical design variable in the static discipline and the equation of state in the dynamic discipline. To address the lack of reliability [...] Read more.
In practical applications, the multidisciplinary dynamic system design optimization (MDSDO)-based solution is limited by uncertainty, which causes random variation in the physical design variable in the static discipline and the equation of state in the dynamic discipline. To address the lack of reliability of the MDSDO solution, a crossrate-based MDSDO approach (C-MDSDO), consisting of the MDSDO stage and a reliability assessment stage, is proposed in this paper. In the reliability assessment stage, a sub-optimization problem based on the crossrate of the objective reliability index sample trajectory is designed to obtain the shifting vector, which is employed to obtain a sufficiently reliable solution. In addition, the proposed approach adopts a sequential problem-solving framework that avoids nested optimization and a reliability assessment. One numerical case and two engineering cases were employed to validate the effectiveness of the proposed method. The results show that the reliability of the proposed solutions significantly improved. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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26 pages, 7013 KiB  
Article
Topology Optimization for Minimum Compliance with Material Volume and Buckling Constraints under Design-Dependent Loads
by Yuanteng Jiang, Ke Zhan, Jie Xia and Min Zhao
Appl. Sci. 2023, 13(1), 646; https://doi.org/10.3390/app13010646 - 03 Jan 2023
Cited by 3 | Viewed by 3213
Abstract
Stability is a critical factor in structural design. Although buckling-constrained topology optimization has been investigated in previous work, the problem has not been considered under design-dependent loads. In this study, a model of buckling constraints in topology optimization problems under design-dependent loads was [...] Read more.
Stability is a critical factor in structural design. Although buckling-constrained topology optimization has been investigated in previous work, the problem has not been considered under design-dependent loads. In this study, a model of buckling constraints in topology optimization problems under design-dependent loads was proposed to solve the above problem. First, the Kreisselmeier–Steinhauser aggregation function was employed to reduce multiple constraints to a single constraint. Then, the problem was sequentially approximated using the optimality criteria method tailored to update the variables. After that, a gradient-based optimization algorithm was established based on finite element and sensitivity analyses for the topology optimization problem with design-dependent loads. Finally, four numerical examples with design-dependent loads were comparatively analyzed, with and without bucking-constrained solutions. The calculation results proved the effectiveness and reliability of the optimization algorithm. Therefore, in this study, it was suggested that the developed optimization algorithm gained improved applicability. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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19 pages, 5000 KiB  
Article
Research on Non-Circular Raceway of Single-Row Four-Point Contact Ball Bearing Based on Life Optimization
by Yanjie Zhao, Guanci Chen, Wenbin Zhang and Yinke Ding
Appl. Sci. 2022, 12(24), 13027; https://doi.org/10.3390/app122413027 - 19 Dec 2022
Cited by 1 | Viewed by 1164
Abstract
The traditional slewing bearing with circular raceway has the problem of stress concentration under the large overturning moment. In this paper, a new non-circular raceway of a slewing ball bearing was presented to conquer this problem. To obtain the new non-circular raceway, first, [...] Read more.
The traditional slewing bearing with circular raceway has the problem of stress concentration under the large overturning moment. In this paper, a new non-circular raceway of a slewing ball bearing was presented to conquer this problem. To obtain the new non-circular raceway, first, the static equilibrium equations of the slewing ball bearing was established by the vector method, which is a constraint condition for life optimization; secondly, the life optimization function was established to calculate the contact load distribution in the bearing when the bearing life is at its maximum; finally, through the contact deformation with the contact load, the non-circular inner raceway corresponding to the maximum bearing life was obtained, and the non-circular shape corresponding to the raceway under axial load and overturning moment was studied. The results show that the non-circular raceway devised by this method can evenly reduce the contact force of the raceway and effectively improve the bearing capacity. Moreover, the position where the non-circular raceway deformation occurs is the position where the contact force is different before and after optimization. Therefore, the overturning moment has an effect on the shape of the raceway, whereas the axial load only affects the amplitude of the deformation, and has no obvious effect on the shape of the raceway. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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30 pages, 8750 KiB  
Article
Analysis and Optimization of Dynamic and Static Characteristics of Machining Center Direct-Drive Turntable
by Bo Huang, Jian Wang, Bangyu Tan, Jianguo Zhao, Kang Liu and Junxiong Wang
Appl. Sci. 2022, 12(19), 9481; https://doi.org/10.3390/app12199481 - 21 Sep 2022
Cited by 3 | Viewed by 1359
Abstract
There are few studies on optimizing the dynamic and static characteristics of direct-drive turntables. In terms of dynamic and static characteristic analysis, most studies only analyze the dynamic and static characteristics of direct-drive turntables in a single machining position and working condition. The [...] Read more.
There are few studies on optimizing the dynamic and static characteristics of direct-drive turntables. In terms of dynamic and static characteristic analysis, most studies only analyze the dynamic and static characteristics of direct-drive turntables in a single machining position and working condition. The optimization is mainly for individual parts without considering the overall structure of the turntable. A multi-objective optimization method based on the back-propagation neural network (BP) and the non-dominated sorting genetic algorithm is proposed to ensure the machining accuracy of the direct-drive turntable, reduce the total mass, and improve its dynamic and static characteristics. In this paper, the workpiece and direct-drive turntable are studied as a whole. Static and modal analyses determine the maximum deformation locations and vulnerable parts of the turntable. Topology optimization analysis was used to find the redundant mass parts. We determined the optimization objectives and dimensional parameters based on the direct-drive turntable’s structural and topology optimization results. Using a central composite experimental design, we obtained test points and fitted them to a response surface model using a BP neural network. A multi-objective genetic algorithm then obtained the optimal solution. After multi-objective optimization, we reduced the mass of the direct-drive turntable by 9.02% and 21.394% compared with the topologically optimized and original models, respectively. The dynamic and static characteristics of the direct-drive turntable increased, and a lightweight design was achieved. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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Review

Jump to: Research

23 pages, 3757 KiB  
Review
Lattice Structures Built with Different Polygon Hollow Shapes: A Review on Their Analytical Modelling and Engineering Applications
by Munashe Ignatius Chibinyani, Thywill Cephas Dzogbewu, Maina Maringa and Amos Muiruri
Appl. Sci. 2024, 14(4), 1582; https://doi.org/10.3390/app14041582 - 16 Feb 2024
Viewed by 697
Abstract
Lattice structures are useful in the aerospace, automotive, infrastructural, and medical fields due to the way they incorporate a lightweight design and good mechanical properties, because of their hollow shapes. This review paper documents work carried out using various analytical models for lattice [...] Read more.
Lattice structures are useful in the aerospace, automotive, infrastructural, and medical fields due to the way they incorporate a lightweight design and good mechanical properties, because of their hollow shapes. This review paper documents work carried out using various analytical models for lattice structures designed with different polygon hollow shapes, for loading in the in-plane and out-of-plane directions, in order to advise their ranking in terms of mechanical behaviour. A primer on lattice structures and polygon hollow shapes is first provided. This is followed by a review of relevant analytical models applied to lattice structures with various polygon hollow shapes that are available in the literature, and then a ranking of the polygon hollow structures in terms of their mechanical properties is performed. Following on from this, a review of the mechanical properties of polygon hollow structures is given. Engineering applications of different polygon hollow structures are then identified. A next-generation structural optimisation and design guide is then highlighted, and some of the primary prospective areas to be focused on when designing lattice parts are pointed out. The last section highlights current challenges, as well as recommendations for extending the use of design for the additive manufacturing of lattice parts. Full article
(This article belongs to the Special Issue Structural Optimization Methods and Applications)
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