Structural Optimization Method Research Articles

Semi-supervised learning method incorporating structural optimization for shear-wall structure design using small and long-tailed datasets

Intelligent structural design based on machine learning represents a novel structural design paradigm and has received extensive attention in recent years. However, the performance of the machine learning models is heavily dependent on the quality and quantity of training data, as the underlying approaches are inherently data-driven. Well-recognized data issues ‒ particularly data insufficiencies and long-tailed data distributions ‒ have become critical impediments in this research area. To address these data issues, this study formulates a schematic structural design task as a semi-supervised learning problem. Specifically, a semi-supervised learning method using small, long-tailed datasets is proposed in which a structural optimization method is incorporated into a self-training framework. As a practical application of the proposed method, a shear-wall layout optimization procedure is devised, based on a two-stage evaluation strategy and the previously established empirical design rules. Results of the numerical experiments indicate that the proposed method can improve the design performance on the tail data by 11.6 % and reduce the performance difference between the head and tail data by 21.3 %, compared to the conventional supervised learning method. A typical case study shows that the shear-wall layout created by the proposed method can satisfactorily resemble that by design engineers whilst meeting key code-specified requirements.

A Patent Review and Current Status of Ultra-thin Vapour Chamber

Background: With the advent and rapid development of 5G technology, many electronic products have been developed in the miniaturized direction. However, excessive operating temperature generated by these electronic products in a small space results in serious runaway problems, such as battery failure and dead equipment. To solve the heat dissipation problem of small electronic products, ultra-thin vapour chambers are widely used in the heat dissipation field of these electronic products due to the characteristic of rapid heat conduction and thermal expansion. Therefore, optimizing the performance of ultra-thin vapour chambers is critical. Over the years, optimizing the performance of ultra-thin vapour chambers has piqued the industry's interest. Objective: This study aimed at exploring the structural features, optimization method, and development status of the ultra-thin vapour chambers. Methods: This study reviews various representative patents related to ultra-thin vapour chambers and discusses the problems existing in the process of achieving ultra-thinning to provide a reference for designers of ultra-thin vapour chambers in the future. Results: Through the investigation of a large number of patents on ultra-thin vapour chamber, some existing problems are summarized and analyzed. Finally, the future trend of ultra-thin vapour chambers is discussed. Conclusion: The optimization of ultra-thin vapour chambers benefits the heat dissipation of small electronic products and improves product safety. More related patents will be published in the future.

Structural reliability-based design optimization with non-probabilistic credibility level

With the increasing diversity of performance requirements for engineering structures, credibility has become an essential prerequisite for ensuring structural safety. This article introduces a reliability-based structural optimization with non-probabilistic credibility (NCRSO) method, to characterize the credibility of the optimization process. First the concept of uncertainty quantification for credible set is introduced. By utilizing a limited number of sample points, structural parameters with a high level of credibility are obtained and maintained throughout the optimization procedure. Additionally, a reliability index is established based on area ratio and credible feature distance, and a credible sequential optimization strategy is developed. Implementation of the proposed method significantly enhances the overall computational efficiency of structural optimization. The reliability index can directly utilized as the translation distance for deterministic constraints in the sequential strategy, minimizing unnecessary calculations and leading to improved convergence. Three engineering examples are eventually presented to effectively illustrate and emphasize the necessity of considering credibility when utilizing the structural optimization method under complex uncertainty from different perspectives.

Practical application of multi-material topology optimization to performance-based architectural design of an iconic building

With the rapid development of architectural design methods and structural analysis techniques, structural performance-based design approaches have become increasingly important in architectural design. Among these approaches, topology optimization is a significant design method. However, most existing topology optimization research and related applications are based on single-material topology optimization techniques, which have limitations when applied to the design of complex and challenging structures. Building upon our previously proposed multi-material bi-directional evolutionary structural optimization (multi-material BESO) method, this paper presents the approaches for achieving diverse and competitive structural designs and then presents a practical application of the multi-material BESO method to the structural design of the core structure of a long-cantilevered building project called “Xiong’an Wings”. After an evolutionary design process based on the multi-material BESO method, an efficient frame with lower overall material costs, better static and dynamic performance compared to the initial design by experienced engineers is achieved. As the first practical application of the multi-material BESO method to a large-scale architectural design, the example of the “Xiong’an Wings” building demonstrates the tremendous prospects for the application of multi-material topology optimization technology to the generative design of innovative and efficient building structures.

A novel numerical manifold method and its application in parameterized LSM-based structural topology optimization

In this paper, a high-efficiency structural topology optimization framework based on combination of numerical manifold method (NMM) and parameterized level set method (PLSM) is established. The NMM uses two cover systems to discretize the model, which can accurately represent the complex boundary of the design domain. A new numerical manifold element has been derived for the application of NMM in PLSM-based optimization. To obtain enhanced accuracy for structural analysis, a multilevel subdivision technique for numerical manifold element generation is presented, and the related numerical integration scheme coupled with the interpolation point selection strategy is provided. For the proposed topology optimization, the new update method of element stiffness matrix is exclusively formulated as well as the calculation method of volume fraction. Some representative structural optimization problems demonstrate that the proposed structural topology optimization method is very effective for two-dimensional (2D) and three-dimensional (3D) structural topology optimization problems.

An Efficient Optimization Method for Slow Wave Structures Based on Surrogate Model for TWT Applications

An Efficient Optimization Method for Slow Wave Structures Based on Surrogate Model for TWT Applications

Structural Optimization of the Brake Pedal using Artificial Intelligence

In this study, weight reduction was performed on the brake pedal, which is one of the most important parts of the braking system, by using topology and shape optimi-zation, one of the structural optimization methods, respectively. The aim of the study is to develop an optimal design that reduces vehicle weight by finding the optimal material distribution for the brake pedal. The weight reduction process was carried out in two steps. In the first step, static analyses were performed on the starting brake pedal model. Later, topology optimization was performed for weight reduction pur-poses. After the topology optimization, new brake pedal design was created and weight reduction was performed. In the second step, shape optimization was per-formed using a genetic algorithm to obtain the optimal dimensions of the brake pedal. According to the optimization results, the weight of the design was reduced from 437 grams (g) to 326 grams (g) by topology optimization in the first step. So the new de-sign is 25.4% lighter compared to the first design. Later, as a result of shape optimiza-tion performed using a genetic algorithm, the weight was reduced from 326 g to 298 g and the optimal dimensions of the brake pedal were determined. Thus, with shape op-timization, a lighter brake pedal design of about 8.5% was achieved compared to to-pology optimization. As a result, the weight has been reduced from 437 g to 298 g, and the weight of the ideal brake pedal model is 31.8% lighter compared to the main model.

Multi-Scale Concurrent Topology Optimization Based on BESO, Implemented in MATLAB

In multi-scale topology optimization methods, the analysis encompasses two distinct scales: the macro-scale and the micro-scale. The macro-scale refers to the overall size and dimensions of the structural domain being studied, while the micro-scale pertains to the periodic unit cell that constitutes the macro-scale. This unit cell represents the entire structure or component targeted for optimization. The primary objective of this research is to present a simplified MATLAB code that addresses the multi-scale concurrent topology optimization challenge. This involves simultaneously optimizing both the macro-scale and micro-scale aspects, taking into account their interactions and interdependencies. To achieve this goal, the proposed approach leverages the Bi-directional Evolutionary Structural Optimization (BESO) method. The formulation introduced in this study accommodates both cellular and composite materials, dealing with both separate volume constraints and the utilization of a single volume constraint. By offering this simplified formulation and harnessing the capabilities of the multi-scale approach, the research aims to provide valuable insights into the concurrent optimization of macro- and micro-scales. This advancement contributes to the field of topology optimization and enhances its applications across various engineering disciplines.

An efficient LightGBM-based differential evolution method for nonlinear inelastic truss optimization

A metaheuristic-based structural optimization method, whilst being popularly adopted due to its advantages in by-passing gradient function calculations, requires the use of time-consuming advanced analyses for constraint evaluation. To overcome this drawback, the present paper proposes a robust (machine learning-based) optimization method that combines the light gradient boosting machine (LightGBM) with the efficient p-best differential evolution (EpDE) method. In essence, the LightGBM classification model is constructed to assess the constraint (safety and integrity) satisfaction of structures. An efficient framework using a so-called safety parameter is proposed to prevent inaccurate predictions of the LightGBM model. The EpDE processes the optimization procedures on the constructed classification LightGBM model. This enables an enhanced machine learning-based optimization technique that not only maintains the sufficiently accurate optimal design of structures but also significantly reduces the required computing efforts, as compared to standard optimization schemes. Various examples of steel structure designs (i.e., two of which have been provided herein) have been successfully performed by the proposed approach. These illustrate the accuracy and robustness of the proposed method, where good comparisons with reference algorithms (including standard DE with “DE/rand/1” mutational strategy, Jaya, Rao-1 and CaDE) are evidenced. The statistical values collected present the accuracy and reliability of the proposed method in obtaining the minimum total weight designs with substantial (some 60%) reduction of computing efforts required to furnish optimal results.

Fatigue life prediction and structural optimization design of the bionic petal non-pneumatic tire with spokes

Fatigue durability of the non-pneumatic tire (NPT) has a decisive influence on vehicle safety and transport economy. This paper aims at the research on the fatigue life prediction method suitable for the flexible spokes of the NPT, and explores the influence of structural parameters on fatigue performance. By simultaneously taking consideration of fatigue performance, bearing capacity, and weight of the NPT, the optimal model parameters are obtained by the proposed structural optimization method. Firstly, based on the Thomas crack model, the fatigue life of the bionic petal non-pneumatic (BP-NPT) is predicted. Then, the influential mechanism of key structural parameters including the curvature, array period, and spoke thickness on tire fatigue durability is investigated by numerical simulation methods. Finally, an optimization method based on the Kriging model and modified NSGA-II is proposed to optimize the structure characteristics of the BP-NPT for better fatigue life and bearing capacity while ensuring lightweight. The results show that the predicted fatigue failure mileage of the BP-NPT is 2.54 × 104 km. By properly increasing the curvature and thickness of the spoke, the maximum strain energy density of the BP-NPT will be reduced, thus improving its fatigue durability. The performance of the optimized structure is significantly improved by the proposed optimization method. The total mass is reduced by 7.44%. The fatigue life and bearing capacity are improved by 9.75% and 4.16%, respectively. It is indicated that a more durable and safer tire configuration is provided for tire safety applications.

Non‐Contact Triboelectric Nanogenerator

AbstractWith the rapid development of science and technology, there is an increasing demand for sustainable energy sources. Although triboelectric nanogenerators (TENGs) can realize self‐powered supply by using various weak mechanical energy, the device's robustness and reliability are seriously affected by frequent, direct, and long‐term mechanical shocks, as well as negative environmental factors during equipment operation. Therefore, researchers have developed non‐contact triboelectric nanogenerators (NC‐TENGs) based on the principle of electrostatic induction. This technology enables electricity generation via relative movement of friction layers even when they are not in direct contact, which consequently leads to enhance device robustness, prolonged service life, and broadened operation scenarios. In this review, the recent progress of NC‐TENG from fundamental theory to practical applications is systematically summarized. The basic structure and working principle of NC‐TENG are first introduced, followed by a discussion of the devices’ structural construction and performance optimization methods. Furthermore, applications of NC‐TENG in automatic force position detection system, non‐contact human‐machine interface, and electrical energy harvesting are reviewed. Finally, a brief prospectus for the future development of NC‐TENG is provided.

A multi‐objective structural optimization method for serviceability design of tall buildings

SummaryStructural optimization design aims to identify optimal design variables corresponding to a minimum objective function with constraints on performance requirements. To this end, many optimization frameworks have been proposed to determine optimal structural systems that are subjected to seismic and wind hazards in isolation. However, some modern tall buildings are sensitive to seismic and wind excitation owing to their complex structural systems and geographic regions. Therefore, a proper structural optimization method for such buildings is required to ensure that the expected performance is achieved in a multi‐hazard scenario. This study proposes a multi‐objective serviceability design optimization methodology for buildings in multi‐hazard seismic and wind environments by combining optimality criteria and the nondominated sorting genetic algorithm II (NSGA‐II). Seismic and wind effects can be instantaneously updated due to changes in the structural dynamic properties during the optimal design process. A neural‐network‐based surrogate model with self‐updating is proposed to predict the structural natural frequency so that the overall computation time of the optimization process can be reduced. The proposed method was used to optimize a 50‐story frame‐tube building and was compared against the general genetic algorithm and general NSGA‐II to verify the feasibility and effectiveness.

Research on topology optimization method of surface support structure based on leaf vein growth process

In this paper, a biomimetic topology optimization design method that simulates the growth pattern of leaf veins is proposed for the design of the support structure of ultra-light airfoil-like solar cells in the solar powered unmanned aerial vehicle. This method simulates the optimal growth process of main vein morphology through the topology change of dynamic point groups to obtain an optimized topological main support structure and then generates a Voronoi grid structure in the area surrounded by the main support structure to increase the local support for the battery. The whole process is combined with genetic algorithm to simulate the optimal distribution strategy of leaf vein growth by inputting a small number of parameters. Compared with the traditional grid support structure, the support structure obtained by simulating the leaf vein growth optimization strategy can provide more efficient support for the solar panel and avoid damage to the solar cell.

Novel Paradigm for Steel Joints in Gridshell Structures: from Structural Optimization to Advanced Construction

AbstractNovel integrated computer‐aided paradigm/workflow for the topology optimization (TO) and additive manufacturing (AM) of steel joints in gridshell structures is proposed. The architecture scheme of gridshell structure was first established and numerically analyzed through Grasshopper parametric platform. Based on the extracted joint geometric parameters and the corresponding loading conditions, the initial joint structures were parametrically modelled using the subdivision surface method. Further parametric TO design was accomplished by the bi‐directional evolutionary structural optimization (BESO) method on the basis of cloud computing server. A series of mesh smoothing and reverse modelling algorithms were applied to the optimized joint to obtain a closed smooth surface in the NURBS form, which was then output as STL file for additive manufacturing. One typical optimized joint was additively manufactured using selective laser melting. The proposed workflow can be extended to a much wider range of spatial structures with various joint types.

An enhanced proportional topology optimization with virtual elements: Formulation and numerical implementation

This paper presents an improved non-sensitivity structural topology optimization method incorporating virtual elements with unstructured polygonal meshes. Specifically, we employ the recently developed gradient-free proportional topology optimization (PTO) approach, for the first time, together with a new material distribution formula suitable for both minimum compliance and compliant mechanism problems. In order to improve performance, we integrate a linear virtual element method (VEM) module into the PTO algorithm. The linear VEM has a desirable characteristic: it does not require numerical integration and, more importantly, is less sensitive to small-edge elements, thus, significantly reducing computational time. Additionally, we utilize virtual elements with unstructured polygonal meshes inside PTO to suppress one-node connection instabilities. Furthermore, the Heaviside-type operator in the main PTO algorithm loop enhances the optimized results by encouraging the density variables to approach discrete (0/1) solutions more effectively. We demonstrate the performance of our developed method in terms of computational speed, diversity of applications, and improved black-and-white (0/1) structures through several benchmark examples of compliance and compliant mechanism designs.

On the optimal design of staved water-lubricated bearings driven by tribo-dynamic mechanism

In this study, a structural optimization method driven by tribo-dynamic mechanism is proposed for the staved water-lubricated bearings (SWLBs). To this end, a tribo-dynamic model considering mass conservation cavitation is established, and the accuracy of this model is verified by comparing it with the experimental and numerical results in published literature studies. The comparative studies emphasize the significant role of mass conservation cavitation on the tribo-dynamic responses of SWLBs under the mixed lubrication regime. Based on numerical simulations, the optimal stave structure for a specific working operation under heavy load condition is identified from the perspective of the tribo-dynamic mechanism. Furthermore, in order to evaluate the applicability of the proposed optimization method, the influences of key parameters, including the rotational speed, the radial clearance, and the surface roughness, on the optimization results are comparatively analyzed. The comparative results reveal that the optimal stave structure is highly dependent on the mentioned key parameters, and the optimal method is effective for a wide range of working conditions. Moreover, the effects of the stave parameters, including stave width and number, on tribo-dynamic characteristics of SWLBs are also investigated, suggesting a more comprehensive optimization scheme for SWLBs.

An explicit structural optimization method for temperature-sensitive hydrogel actuation devices

Hydrogel actuation devices are commonly composed of responsive and passive materials, and their actuation effect depends on their unique structure. In this paper, an explicit optimization method is proposed for the design of temperature-sensitive hydrogel-based soft devices involving swelling and shrinking to achieve specific actuation effects. In this method, the outline of configuration and the responsive layer are explicitly described by the ordered B-spline curve and movable hydrogel patch, respectively. The parametric modeling method is proposed to construct the geometric model with local features, which can transform the complex patch stacking problem into the fusion problem of three-dimensional geometry. Based on the large deformation theory of temperature-sensitive hydrogel, the deformation behavior of soft device is accurately simulated. The adaptive mesh division method is applied to numerical simulation of complex structures to avoid mesh distortion. Furthermore, the optimization problem is effectively solved by combining the gradient optimization algorithm. Several numerical examples are presented to verify the accuracy of the method, and interesting structures such as the Miura-ori structure, switch and bionic structures are designed. The method can significantly reduce the optimization design variables, and the explicit optimization results can be used as the basis for the additive manufacturing of soft devices.

Bamboo-inspired hierarchical microlattice structures (BHMSs) for high strength and energy absorption

Mechanical metamaterials as a category of lightweight materials have exhibited superior specific mechanical properties and energy absorption. However, lack of reasonable structural design always results in weakening or failure to achieve the optimal mechanical performance of metamaterials. Here, we firstly adopted bio-inspired and structural optimization methods to guideline the design of microlattice structures. Inspired by the strong and ductile ‘Moso’ bamboo, three bamboo-inspired hierarchical microlattice structures (BHMSs) were initially designed, and the bamboo’s features, viz., hollow, gradient distribution, and cellular, were imitated by designed BHMSs. Optimization design with the objective of maximum ratio of strain energy and reaction force was carried out to furthermore improve the mechanical properties of BHMSs. Afterwards, the optimal BHMSs were printed via Stereolithography. The compressive responses of BHMSs were elaborated by experiments and simulation. Results show that these designed biomimetic structures can be easily tailored via tuning the geometric sizes of unit cell, achieving high compressive specific modulus and strength 48.16 kPa m3 kg−1 and 1389.23 Pa m3 kg−1 and the energy-absorbing efficient 85.43% in the octet bamboo-inspired hierarchical microlattice structures (OCT BHMSs). The design strategies and findings shed light on the realization of advanced metamaterials with tailored mechanical properties. How to design ordered cellular structures for lightweight structures with high mechanical strength and energy absorption efficiency remains a crucial challenge in automation, aerospace and lightweight construction fields. Inspired by the lightweight and high load-bearing capacity of nature bamboos and metamaterials in the previous researches (Song et al., Materials & Design, 2019, 173: 107773; Song et al., International Journal of Fatigue, 2017, 100: 126), here a comprehensive approach of bionics and optimization was proposed to design hierarchical microlattice structures with lightweight, good mechanical properties and high energy absorption efficiency. The bamboo’s characteristics, including hollow, gradient enhancement, and cellular, were completely copied to reasonably produce hierarchical microlattice configurations, while the optimal sizes were obtained though the optimization design.

Research on Structural Parameter Optimization and Springback Compensation Methods of a Steel Bar Hoop Bending Machine

After being processed into a certain shape by a stirrup bending machine, steel bars are used as the skeleton of reinforced concrete in construction. The accuracy of their bending directly affects the bearing capacity of reinforced concrete. In order to improve the accuracy of the springback angle of steel bars after bending, this paper focuses on optimizing the structural parameters of the steel bar bending machine and controlling the springback angle of steel bars. The influence of the support shaft diameter, bending crankshaft diameter, and bending crankshaft radius on the springback angle of steel bars is analyzed using ANSYS explicit dynamic simulation and experimental analysis. By combining orthogonal experimental methods, the bending structural parameters were optimized, including a support shaft diameter of 20 mm, a crankshaft bending diameter of 40 mm, and a crankshaft bending radius of 80 mm. This can effectively reduce the springback angle of the steel bars and improve the accuracy of the bending angle after bending. In addition, in order to improve the control accuracy of the steel bar springback angle, a cubic spline interpolation method was proposed, and the collected steel bar springback angle data were fitted using Matlab. At the same time, comparisons were made between the least squares method, polynomial interpolation method, and cubic spline interpolation method. The results show that the compensation formula obtained by using the cubic spline interpolation method can effectively improve the control accuracy of the steel bar bending springback angle.

Chaotic heterogeneous comprehensive learning PSO method for size and shape optimization of structures

This paper proposes a novel chaotic heterogeneous comprehensive learning particle swarm optimization (CLPSO) method for the simultaneous size and shape design of structures. The heterogeneous CLPSO divides the particles into two explorative and exploitative subpopulations. The exploration performs the global searches for the set of best particles experienced solely within its own subpopulation, whilst the exploitation refines the deep searches learnt from the global best particle over an entire population. In essence, the proposed method maintains a good balance between the global explorative and local exploitative optimization schemes. The global searches within the explorative subpopulation are independent to the exploitative simulations even if the latter scheme prematurely converges to the local swarm position. For both subpopulations, the comprehensive learning approach constructs the particles through a cross-positioning process on the individual variable space and avoids the local optimal pitfall. Moreover, the chaotic logistic map within the exploitative optimization tests the global best particle through the set of diversely generated samples and hence enhances the local search ability. Various enriching techniques, including automatic adaptive (inertial weight and acceleration) parameters with dynamic space reduction, are incorporated to improve the likelihood of finding the optimal solution of practical-scale problems at modest computing efforts. The accuracy and robustness of the proposed method are illustrated through a number of planar and spatial truss design benchmarks subjected to the challenging nonconvex and/or nonsmooth programs.