Structural Optimization Method Research Articles

Parametric structure optimization of a main rotor blade as an application for FSI analysis in main rotor optimization process

Purpose Modern warfare and modern battlefield are very demanding. The recent conflicts showed that the usage of the helicopters is very limited and only the best constructions are able to provide support for the operations. The purpose of this research is to show the possibilities of new design tool for main rotor aerostructural optimization. It is a next chapter of the research that is aimed at finding new solutions for rotorcraft constructions. Design/methodology/approach This work presents a method of preliminary structure optimization of the main rotor blade using parametric modeling. It is the next step in the main rotor optimization studies. It is the next step after preparing the parametric model for the external shape CFD analysis. As a basis for parametric blade structure calculations, the analytical model is provided in this paper. The equations of rigid blade loads and, as a consequence of the strength elements, stresses are shown. The parametric blade modeling is conducted using the Graphic Integrated Programming language. The parametric design method is shown to be used for various blade planform models and different section airfoils. The structure of a blade is generated automatically after the user enters the parameters. The code-inbuilt analysis systems provide a quick inertia examination of the generated geometry, which is the basis for further optimization. The program calculates the blade loads and verifies them with the given material conditions and proposed safety factors. In the analysis, composite materials for the strength elements were proposed. Findings The results of this research showed the application of parametrization into the main rotor blade design loop. It was presented that the main rotor blade structure can be enhanced using fluid-structure interaction (FSI) methods. The time saving with the implementation the process into design loop is shown. Practical implications This work can be practically used in the main rotor blade design process. It provides the possibilities to check various blade aerodynamic configuration in a structure strength aspect. Originality/value To the best of the authors’ knowledge, there were no published research that combines the main rotor FSI analysis. The method, which is presented in the work, provides a new approach to a rotorcraft design. The application of the parametrization and combining it with the FSI method gives a novel solution for helicopters construction enhancement.

New shape optimization method for tree structures based on BP neural network

To realize the intelligent optimization for the tree structures supporting freeform surface roof or bearing uneven load, a new shape optimization method based on the back-propagation (BP) neural network is proposed. This method enables the intelligent positioning of hierarchical nodes through a recursive approach from top-down, with the aim of satisfying the zero bending moment and structural stability. Using three-dimensional tree structures as an example, this study provides a detailed description of the implementation method and steps of intelligent shape optimization, along with a comparative analysis with the reverse-hang recursive approach. Results indicate that the proposed approach effectively addresses the challenge of locating load-bearing centers in tree structures with uneven loads or freeform surface roofs. It not only demonstrates universality for tree structures under complex engineering conditions, but also enhances efficiency and intelligence in the structure optimization design.

A one-time training machine learning method for general structural topology optimization

Machine learning (ML) methods have found some applications in structural topology optimization. In the existing methods, however, the ML models need to be retrained when the design domains and supporting conditions have been changed, posing a limitation to their wide applications. In this paper, we propose a one-time training ML (OTML) method for general topology optimization, where the self-attention convolutional long short-term memory (SaConvLSTM) model is introduced to update the design variables. An extension–division approach is used to enrich the training sets. By developing a splicing strategy, the training results of a small design space (i.e., a basic cell of either two- or three-dimensions) can be extended to tackling the optimization problem of a large design domain with arbitrary geometric shapes. Using the OTML method, the ML model needs to be trained for only one time, and the trained model can be used directly to solve various optimization problems with arbitrary shapes of design domains, loads, and boundary conditions. In the SaConvLSTM model, the material volume of the post-processed thresholded designs can be precisely controlled, though the control precision of the gray-scale designs might be slightly sacrificed. The effects of model parameters on the computational cost and the result quality are examined. Four examples are provided to demonstrate the high performance of this structural design method. For large-scale optimization problems, the present method can accelerate the structural form-finding process. This study holds a promise in the high-resolution structural form-finding and transdisciplinary computational morphogenesis.

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A novel method for concurrent dynamic topology optimization of hierarchical hybrid structures

This paper proposes a feature-decoupled method for concurrent dynamic topology optimization of the Hierarchical Hybrid Structure (HHS) to minimize the steady-state dynamic response. First, a novel single-variable uniform multiphase material interpolation model is established based on the Gaussian function and normalization method, which achieves the decoupled description of the macroscopic topology, substructure topology, and the spatial distribution of the substructures for HHS. Second, by combining the extended multiscale finite element method (EMsFEM), which overcomes the limitations of the scale separation assumption and periodic boundary conditions in HHS response analysis, a concurrent dynamic topology optimization mathematical formulation for HHS is constructed. Finally, the sensitivity scheme is established based on the adjoint method, and the MMA algorithm was employed to update the model. Numerical examples verify the correctness and feasibility of the proposed method, demonstrate its advantages in solving HHS concurrent topology optimization problem compared to traditional methods, and explore the impact of the number of substructure types on the optimization results of HHS.

Numerical simulation and structural optimization of the diffusion furnace for crystal silicon solar cells

The diffusion furnace is an important device for crystalline silicon solar cell production. Given the rapid evolution of solar cell technology, large-scale, high-efficiency and mass-produced diffusion furnaces are required by the market. This puts forward higher requirements for the diffusion furnaces. In this study, a large-scale 3D model is established and validated by measured data in practical diffusion furnace. Its internal temperature, velocity and gas concentration fields are analyzed. The silicon wafer temperatures are found to be high at the top but low at the bottom. The temperature uniformity at both ends of silicon wafer groups is poor. To solve these problems, three structural optimization methods, namely the inlet pipe optimization, adding uniform-flow plates and the quartz boat optimization, are proposed and analyzed. The average mass fraction in the diffusion furnace is improved by 6.311% using the two-tube forked intake pipe. The uniform flow plates with evenly distributed pores on the lower half effectively improve the gas concentration uniformity on silicon wafer surfaces. The optimized quartz boat can improve the temperature uniformity of silicon wafers, though its deformation slightly increases by 0.338%. The silicon wafer temperature differences after quartz boat optimization are 13.77–50.27% smaller than those before optimization, which are conducive to reducing the thermal stress, the risk of thermal damage and the failure during manufacture and utilization of silicon wafers. Results in this study give guidelines for design and utilization of crystal silicon solar cell diffusion furnaces, some of which have been successfully used in Trina Solar Energy Co., China.

Directed evolution-based non-gradient method for structural topology optimization

Existing non-gradient optimizers often rely on stochastic search strategies, which require a large number of finite element analyses to evaluate the objective function. In this study, a directed evolution-based non-gradient topology optimization method is proposed to reduce the high computational cost. A directed generation strategy of load path components is presented, based on the idea of fixed-point enumeration. This strategy determines the position and direction of components by locating the region with the maximum stress and enumerating samples with different orientations at each iteration step. Then, an element removal criterion is developed to gradually eliminate the redundant elements from the components. Consequently, an adaptive adjustment technique of component size is presented to overcome the numerical instability. The applicability and effectiveness of the proposed method are illustrated through numerical examples. The results show that the proposed method can reasonably generate structural load paths with exceptional efficiency compared to existing non-gradient algorithms.

Multidisciplinary optimization methodology for truss-braced wing aircraft using high-fidelity structure sizing

In this research, a method is developed to optimize the truss-braced wing aircraft configuration in a multidisciplinary design framework. Physics-based high-fidelity methods, that can capture the nature of the configuration changes, are employed for the disciplines where the existing classical methods are not reliable. High-fidelity geometry modeling, structure loading, structure optimization, and aeroelastic sizing methods are integrated into the aircraft multidisciplinary design and optimization. The developed algorithm is applied for the multi-objective optimization of a regional jet aircraft to minimize the cost and weight. The results demonstrate that the cost-optimum solution converges to a higher aspect ratio wing equipped with a higher bypass ratio engine, and a 7.94% reduction in the direct operating cost can be achieved. On the other hand, the weight-optimum wing planform tends to a slightly lower aspect ratio wing with a lower bypass ratio engine, while a 6.18% reduction in take-off weight is achieved. In addition to that, the findings of this study highlight the considerable effect that the engine technology has on the optimum layout, which suggests that the engine technology and its performance should also be a part of the design optimization process. The developed modular framework offers further optimization potential for the truss-braced wing aircraft, as more detailed models can be integrated.

Nature's Load-Bearing Design Principles and Their Application in Engineering: A Review.

Biological structures optimized through natural selection provide valuable insights for engineering load-bearing components. This paper reviews six key strategies evolved in nature for efficient mechanical load handling: hierarchically structured composites, cellular structures, functional gradients, hard shell-soft core architectures, form follows function, and robust geometric shapes. The paper also discusses recent research that applies these strategies to engineering design, demonstrating their effectiveness in advancing technical solutions. The challenges of translating nature's designs into engineering applications are addressed, with a focus on how advancements in computational methods, particularly artificial intelligence, are accelerating this process. The need for further development in innovative material characterization techniques, efficient modeling approaches for heterogeneous media, multi-criteria structural optimization methods, and advanced manufacturing techniques capable of achieving enhanced control across multiple scales is underscored. By highlighting nature's holistic approach to designing functional components, this paper advocates for adopting a similarly comprehensive methodology in engineering practices to shape the next generation of load-bearing technical components.

Perturbation approaches to achieving diverse and competitive designs in topology optimisation

Utilising topology optimisation to generate diverse and competitive structures enables designers to create elegant and efficient designs according to their aesthetic intuition and functional needs. This study proposes load and support perturbation approaches based on the bi-directional evolutionary structural optimisation (BESO) method to achieve diverse designs. During the optimisation process, noise is introduced to the sensitivity calculations by randomly perturbing the load angles or material properties near the supports, leading to a variety of local optima. Numerical results demonstrate that the proposed approaches are capable of creating designs with similar stiffness but distinct geometries. In addition, the diversity of the obtained solutions can be controlled by utilising different perturbation functions. This work is of significant practical importance in both architecture and engineering, where multiple design options of high structural performance are in demand.

Electromagnetic Fields Calculation and Optimization of Structural Parameters for Axial and Radial Helical Air-Core Inductors

To improve the current density distribution and electromagnetic performance of air-core inductors, a structural optimization method combining back-propagation(BP) neural network and genetic algorithm(GA) is proposed for the study of axial and radial spiral multi-winding inductors. The Monte Carlo method was used to extract the structural size samples of the inductors, and the training dataset was obtained through the finite element calculation of electromagnetic fields. Based on BP neural networks, nonlinear mapping models between the inductance value, volumetric inductance density, current distribution non-uniformity coefficient, and inductor structural parameters were constructed. A sensitivity analysis of the inductor inductance value affected by the structural parameters was conducted using the Sobol index calculation. Using the current distribution non-uniformity coefficient as the fitness function and the volumetric inductance density as the constraint condition, a genetic algorithm was applied to globally optimize the structural parameters of the inductor. The optimization results were verified through a finite element comparison. The results show that, under the requirement of satisfying the volumetric inductance density, the current distribution non-uniformity coefficient of the Axial Helical Inductor (AHI)-type inductor was reduced by 4.57% compared with the best sample in the sampling, while that of the Radial Helical Inductor (RHI)-type inductor was reduced by 5.33%, demonstrating the practicality of the BP-GA joint algorithm in the structural optimization design of inductors.

Research on topology optimization strut-and-tie model and prestress construction for cable-pylon anchorage zone of Fengshuba Bridge

To address the challenges associated with accurate load-bearing capacity calculation and prestress design for the cable-pylon anchorage zone of cable-stayed bridges, a case study focusing on the Fengshuba Bridge is conducted. Utilizing the Solid Isotropic Material with Penalization (SIMP) variable density topology optimization method, a strut-and-tie model (STM) is constructed for the cable-pylon anchorage zone. This model is subsequently employed to verify load-bearing capacity of the struts and nodes within the cable-pylon anchorage zone, as well as to calculate the required quantity of circumferential prestressing tendons. Additionally, a spatial segmental finite element model is established for the cable-pylon anchorage zone to perform a detailed analysis of prestressed structural optimization. This analysis determines various structural details, including the arrangement of prestressing tendons along the height, the design for prestressing blind zones, and the quantity of prestressing tendons. Subsequently, the optimized model is subjected to stress verification. The research results indicate that the adoption of dispersed tendon arrangement results in reduced principal tensile stress within the cable-pylon anchorage zone, in contrast to the concentrated tendon arrangement. The introduction of short prestressing steel bundles within the conduit of prestressing blind zones uniformly enhances the pre-compressive stress on the cable-pylon side wall. Due to the Poisson effect of materials, it is necessary to arrange prestressing tendons appropriately within the cable-pylon anchorage zone. Arranging prestressing steel bundles according to the proposed STM and structural optimization method adequately fulfills the structural force requirements of the cable-pylon anchorage zone.

Assembly Simulation and Optimization Method for Underconstrained Frame Structures of Aerospace Vehicles

Aerodynamic contour dimensional accuracy is very important for the stable and safe flight of aerospace vehicles. Nevertheless, due to the influence of various factors such as material properties, machining and manufacturing deviations, and assembly and installation deviations, key structural geometric dimensions are frequently exceeded. Therefore, this paper investigates a data-driven combined vector loop method (VLM)–Skin Model Shapes (SMS) method to realize aerospace vehicle structural geometric accuracy analysis; assembly optimization targeting contour deviation is also achieved. Tests are carried out on a typical aerospace vehicle’s underconstrained structural workpieces to validate the effectiveness of the proposed method.

Dynamic Resistance and Energy Absorption of Sandwich Beam via a Micro-Topology Optimization

The current research of sandwich structures under dynamic loading mainly focus on the response characteristic of structure. The micro-topology of core layers would sufficiently influence the property of sandwich structure. However, the micro deformation and topology mechanism of structural deformation and energy absorption are unclear. In this paper, based on the bi-directional evolutionary structural optimization method and periodic base cell (PBC) technology, a topology optimization frame work is proposed to optimize the core layer of sandwich beams. The objective of the present optimization problem is to maximize shear stiffness of PBC with a volume constraint. The effects of the volume fraction, filter radius, and initial PBC aspect ratio on the micro-topology of the core were discussed. The dynamic response process, core compression, and energy absorption capacity of the sandwich beams under blast impact loading were analyzed by the finite element method. The results demonstrated that the over-pressure action stage was coupled with the core compression stage. Under the same loading and mass per unit area, the sandwich beam with a 20% volume fraction core layer had the best blast resistance. The filter radius has a slight effect on the shear stiffness and blast resistances of the sandwich beams. But increasing the filter radius could slightly improve the bending stiffness. Upon changing the initial PBC aspect ratio, there are three ways for PBC evolution: The first is to change the angle between the adjacent bars, the second is to further form holes in the bars, and the third is to combine the first two ways. However, not all three ways can improve the energy absorption capacity of the structure. Changing the aspect ratio of the PBC arbitrarily may lead to worse results. More studies are necessary for further detailed optimization. This research proposes a new topology sandwich beam structure by micro-topology optimization, which has sufficient shear stiffness. The micro mechanism of structural energy absorption is clarified, it is significant for structural energy absorption design.

Performance optimization of a printed circuit heat exchanger for the recuperated gas turbine

To further improve the thermal efficiency of gas turbines, the recuperator needs to be employed and the printed circuit heat exchanger with airfoil fins meets the recuperator's requirements of high heat transfer capacity, low flow resistance, and high reliability. However, the effect of airfoil fin pitches is not clear and the structure optimization method should be developed. In this study, the heat transfer quantity and pressure drop per length of the flue gas in the airfoil channels are numerically investigated under different Reynolds numbers and airfoil fin pitches. The results show that the effect of the airfoil transverse pitch has a great effect on the performance of the flue gas and the heat transfer quantity is increased by 82.39 %–96.08 % when the transverse pitch is decreased from 6.0 mm to 1.2 mm. At the same time, the pressure drop per length is increased to 189.39–842.47 Pa/m. The heat transfer performance is varied not obviously when the airfoil longitudinal pitch is varied from 4 mm to 15 mm. Based on the numerical data, the multiple-objective genetic algorithm combined with the backpropagation neural network is proposed for the performance predictions and optimizations. The corresponding Pareto front is obtained and the technique for order preference by similarity to the ideal solution method is employed to obtain the optimal point. Under the current conditions, the heat transfer quantity of the optimal point is 521.25 kW/m2, which is decreased by 34.5 % compared to the highest value, and the pressure drop per length of the optimal point is 108.45 Pa/m, which is decreased by 85.2 % compared to the highest value.

A dimensionality reduction optimization method for thin-walled parts to realize mass center control and lightweight design

Structural lightweight design has attracted growing attention. However, most studies have ignored the impact of lightweight design on the location of mass centres, which is an important factor affecting the dynamic performance of structures. This article proposes a structural optimization method for thin-walled parts to achieve both mass centre control and lightweight design. First, mass centre and volume are taken as the constraints for structural optimization, and a mathematical model for multi-constrained topology optimization is developed. Secondly, a dimensionality reduction method based on a 3D spatial filter is introduced for the optimization of thin-walled parts. The maximum error between the mass centre of the optimized structure and the target mass centre is only 1.03%, which indicates that the method has high accuracy in mass centre control. Numerical analysis shows that adjusting the mass centre can achieve regulation of the moment of inertia and can also suppress flutter.

Evolutionary topology optimization of fiber reinforced composite laminates for maximum stiffness

In this study, a topology optimization technique based on the bi-directional evolutionary structural optimization (BESO) method is developed to maximize the stiffness of fiber reinforced composite laminates. The elastic properties of single-layer and multi-layer composite laminates are characterized and a composite material interpolation scheme is introduced. The effectiveness of the developed BESO method for the single-layer and multi-layer composite laminates are verified by three classical examples, namely a cantilever, a Michell-type structure, and an L-bracket. Then, based on the analysis of the topological results, a selection suggestion and verification criteria for layers with appropriately matched fiber angles are proposed and verified by two additional examples. This study proves that the BESO method is an effective technique for the topology optimization of composite laminates for maximum stiffness, and the proposed suggestion and criteria are useful for avoiding large computational costs and empirical selection of layers.

A concurrent optimization method of compliant structures embedded with movable piezoelectric actuators considering fundamental frequency constraints

A concurrent optimization method of compliant structures embedded with movable piezoelectric actuators considering fundamental frequency constraints

Enhancing structural stability in civil structures using the bi-directional evolutionary structural optimization method

Topology optimization techniques are increasingly utilized in structural design to create efficient and aesthetically pleasing structures while minimizing material usage. Many existing topology optimization methods may generate slender structural members under compression, leading to significant buckling issues. Consequently, incorporating buckling considerations is essential to ensure structural stability. This study investigates the capabilities of the bi-directional evolutionary structural optimization method, particularly its extension to handle multiple load cases in buckling optimization problems. The numerical examples presented focus on three classical cases relevant to civil engineering: maximizing the buckling load factor of a compressed column, performing buckling-constrained optimization of a frame structure, and enhancing the buckling resistance of a high-rise building. The findings demonstrate that the algorithm can significantly improve structural stability with only a marginal increase in compliance. The detailed mathematical modeling, sensitivity analyses, and optimization procedures discussed provide valuable insights and tools for engineers to design structures with enhanced stability and efficiency.

Parametric Optimization of Structural Frame Design for High Payload Hexacopter

For drones, the use of which has been increasing recently for load carrying, lightweight drone frame design is significant for increased flight time and payload capacity. Drones are produced in different configurations with three, four or six rotors, and in different sizes depending on the purpose of use. While agility is more important in three and four rotor drone applications, six-rotor and relatively large-bodied drones are preferred in cases such as load carrying. When the body structure has to be large, lightening the design becomes very critical. Lightweight designs can be achieved by two commonly used methods for structural optimization: topology optimization and parametric optimization. Topology optimization is an advanced method that can significantly reduce weight but is expensive and time-consuming. Parametric optimization is a more practical approach for conventional manufacturing methods and was used in this study. This study aims to first simplifying the hexacopter frame model and defining key geometric parameters for mass-decreasing optimization. Finite element analysis simulations were used to evaluate the strength and deformation of the frame under various design scenarios. The results showed that parametric optimization successfully reduced the weight of the hexacopter frame while maintaining structural integrity. The maximum Von Mises stress was found as approximately one quarter of the yield strength of the frame material. The maximum total deformation was achieved below 0.3 mm, and deformation under 1 mm is considered safe in the literature. As a result, the optimized design offers a lighter drone structure in line with conventional manufacturing methods, providing better flight time and payload capacity while maintaining cost effectiveness. In future studies, comparisons can be made based on this study by performing weight optimizations suitable for current methods such as topology optimization or generative design. the cost factor and the availability of existing production lines should be taken into consideration when comparing the mentioned methods with parametric optimization.