Structural Optimization Research Articles

Framework of acoustic analysis and shape optimization for three-dimensional doubly periodic multilayered structures

In this research, a framework of acoustic analysis and shape optimization, based on isogeometric boundary element method (IGA-BEM), is proposed for three-dimensional doubly periodic multilayered structures. The study addresses a gap in the literature by focusing on the shape optimization of such structures, which has not been extensively explored previously. The interface between different acoustic media is an infinite doubly periodic surface, which can be constructed by an open non-uniform rational B-splines. A periodic IGA-BEM is developed for the sound field analysis of the doubly periodic multilayered structure, in which the Ewald method is used to accelerate the calculation of periodic Green function. Furthermore, the shape derivative of the doubly periodic multiple boundaries is derived by imposing boundary perturbation and using the adjoint variable method. The control points of the NURBS surfaces are defined as the shape design variables, and all shape sensitivities can be quickly calculated by discretizing the shape derivative formula. Finally, in according with shape sensitivities, the corresponding shape optimization problem is solved by the method of moving asymptotes, so that the optimized shape design can be obtained. A series of numerical examples validates the accuracy and applicability of the proposed approaches.

Regulating Intermolecular Hydrogen Bonds in Organic Cathode Materials to Realize Ultra-stable, Flexible and Low-temperature Aqueous Zinc-organic Batteries.

Rational design of molecular structures is one of the effective strategies to obtain high-performance organic cathode materials. However, besides the optimization of single-molecule structures, the influence of the "weak" interaction forces (e.g. hydrogen bonds) in organic cathode materials on the performance of batteries should be fully considered. Herein, three organic small molecules with different numbers of hydroxyl groups (namely nitrogen heterocyclic tetraketone (DAB), monohydroxyl nitrogen heterocyclic dione (HDA), dihydroxyl nitrogen heterocyclic dione (DHT)) were selected as the cathodes of aqueous zinc ion batteries (AZIBs), and the effect of the intermolecular hydrogen bonds on their electrochemical performance was studied for the first time. Clearly, the stable hydrogen-bond networks built through the hydroxyl groups significantly enhance the cycle stability of organic small-molecule cathodes and facilitate rapid proton conduction between the hydrogen-bond networks through the Grotthuss mechanism, thereby endowing them with excellent rate performance. In addition, a larger and more dense two-dimensional hydrogen-bond network can be constructed through multiple hydroxyl groups, further enhancing the structural stability of organic small-molecule cathodes, giving them better cycle tolerance, excellent rate performance, and extreme environmental tolerance.

Quantum computational and experimental spectroscopic investigation (FT-IR, Raman, UV–Vis), PES, LHE and topological investigations of 7-[(2R)-2-hydroxypropyl]-1,3-dimethylpurine-2,6-dione

The current research explored the structural optimization, electrical and vibrational characteristics, and quantum chemical calculations via the procedure of DFT for a purine derivative, 7-[(2R)-2-hydroxypropyl]-1,3-dimethylpurine-2,6-dione (2HDPD). Functional groups were found by correlating FT-IR with simulated spectra. TD-DFT calculations were done for UV–vis absorption and to ascertain the electronic properties of both the solvent and the gas phase, enabling additional study of the compounds LHE. The experimental outcomes and theoretic parameters are in good agreement. LUMO and HOMO band gaps spectacle that the molecule is chemically reactive and that there is adequate charge transfer. Polar solvent exhibits the highest band gap value, 5.057 eV. Numerous topological considerations were accomplished using the Multiwfn tool. Charge transfer investigations have demonstrated the most imperative states. Weak intermolecular interactions were investigated using RDG analysis, LOL, NBO, and ELF. The 2HDPD compounds reactive areas were discovered by applying the MEP and Fukui investigations. Hyperpolarizability characteristics were used to calculate NLO behavior. The drug-like characteristics of the molecule follow Lipinski five rules. After docking with the proteins 1NG2, 2DVV, 3CAF, and 7OEX, the compound 2HDPD showed moderate binding affinities of −5.28, −5.04, −4.96, and −5.66 kcal/mol, in that order. The Ramachandran plot verified the proteins stability and advantageous locations. The Docking results show compound 2HDPD exhibited a COPD property.

Numerical thermal analysis and structural optimization of cascaded PCM heat sinks for thermal management of electronics

In the present study, an innovative cascaded phase change material (PCM) heat sink using organic PCMs was proposed for electronic thermal management. The design arranges multiple PCMs with progressively lower melting points along the heat transfer path, allowing active control of the melt front. A numerical model with 5 % accuracy was developed to evaluate thermal performance. Based on the validated model, the effects of PCM stage numbers, PCM volume fractions, fin types, and fin volume fractions were analyzed. The fin volume fractions were further optimized using a support vector machine (SVM) and genetic algorithm (GA) methods. Results showed that a three-stage PCM heat sink with pin fins and increasing configurations outperformed single-stage PCM heat sinks, enhancing heat transfer by up to 36.7 %. Additionally, the innovative cascaded PCM heat sink with a uniform 20 % fin volume fraction across the three stages achieved a 38.8 % improvement compared to single-stage configurations. When the fin volume fractions were set to 24.1 %, 17.6 %, and 13.0 % for the three stages, thermal performance of the innovative cascaded PCM heat sink was enhanced by up to 39.8 % compared to single-stage configurations. The findings provide valuable insights for the design and application of PCM-based thermal management systems, potentially leading to more efficient solutions for various engineering fields.

Enhanced Special Relativity Search Algorithm Based Lorentz Force for Structural Optimization

Enhanced Special Relativity Search Algorithm Based Lorentz Force for Structural Optimization

Structural Performance Analysis and Optimization of Small Diesel Engine Exhaust Muffler

In recent years, the optimization of diesel engine exhaust mufflers has predominantly targeted acoustic performance, while the impact on engine power performance has often been overlooked. Therefore, this paper proposes a parallel perforated tube expansion muffler and conducts a numerical analysis of its acoustic and aerodynamic performance using the finite element method. Then, a Kriging model is established based on the Design of Experiments to reveal the impact of different parameter couplings on muffler performance. With transmission loss (TL) and pressure loss (PL) as the optimization objectives, a multi-objective optimization study is carried out using the competitive multi-objective particle swarm optimization (CMOPSO). The optimization results indicate that this method can simplify the optimization model and improve optimization efficiency. After CMOPSO calculation, the average TL of the muffler increased from 27.3 dB to 31.6 dB, and the PL decreased from 1087 Pa to 953 Pa, which reduced the exhaust noise and improved the fuel economy of the engine, thus enhancing the overall performance of the muffler. This work provides a reference and guidance for the optimal design of mufflers for small agricultural diesel engines.

Grid Optimization of Free-Form Spatial Structures Considering the Mechanical Properties

In recent years, the application of free-form surface spatial grid structures in large public buildings has become increasingly common. The layouts of grids are important factors that affect both the mechanical performance and aesthetic appeal of such structures. To achieve a triangular grid with good mechanical performance and uniformity on free-form surfaces, this study proposes a new method called the “strain energy gradient optimization method”. The grid topology is optimized to maximize the overall stiffness, by analyzing the sensitivity of nodal coordinates to the overall strain energy. The results indicate that the overall strain energy of the optimized grid has decreased, indicating an improvement in the structural stiffness. Specifically, compared to the initial grid, the optimized grid has a 30% decrease in strain energy and a 43.3% decrease in maximum nodal displacement. To optimize the smoothness of the grid, the study further applies the Laplacian grid smoothing method. Compared to the mechanically adjusted grid, the structural mechanical performance does not significantly change after smoothing, while the geometric indicators are noticeably improved, with smoother lines and regular shapes. On the other hand, compared to the initial grid, the smoothed grid has a 21.4% decrease in strain energy and a 28.3% decrease in maximum nodal displacement.

New Active Ingredients for Sustainable Modern Chemical Crop Protection in Agriculture.

Today, the agrochemical industry faces enormous challenges to ensure the sustainable supply of high-quality food, efficient water use, low environmental impact, and the growing world population. The shortage of agrochemicals due to consumer perception, changing needs of farmers and ever-changing regulatory requirements is higher than the number of active ingredients that are placed on the market. The introduction of halogen atoms into an active ingredient molecule offers the opportunity to optimize its physico-chemical properties such as molecular lipophilicity. As early as 2010, around four-fifths of modern agrochemicals on the market contained halogen atoms. In addition, it becomes clear that modern agrochemicals have increasingly complex molecular structures with one or more stereogenic centers in the molecule. Today, almost half of modern agrochemicals are chiral molecules (herbicides, insecticides/acaricides/nematicides ≪ fungicides) and most of them consist of mixtures such as racemic mixtures of enantiomers, followed by mixtures of diastereomers and mixtures of pure enantiomers. Therefore, it is important that halogen-containing substituents or stereogenic centers are considered in the structural optimization of the active ingredients to ultimately develop sustainable agrochemicals in terms of efficacy, ecotoxicology, ease of use and cost-effectiveness.

Optimization of atomization performance of external mixing air atomizing nozzle based on response surface agent model

Based on the finding that the atomization performance of the nozzle is affected by its structural parameters, a combination of finite element analysis and structural optimization calculations is used. Finite element analysis was performed through the VOF (Volume of Fluid) module of Fluent software to determine the structural parameters affecting the performance of the atomizing nozzle. The liquid cyclone tank inclination, the length of the flat section at the gas outlet, and the mixing chamber outlet diameter were used as optimization factors. The atomization cone angle and fuel atomization circumferential distribution uniformity index were used as the evaluation indexes of atomization performance. An orthogonal experimental design was carried out based on the above. Proxy model for atomization cone angle and fuel atomization circumferential distribution uniformity index based on response surface method. The optimal structure of the nozzle was obtained by optimization calculation of the agent model by genetic algorithm. The results show that the atomization performance is optimal when the inclination angle of the liquid rotating tank is 42.9, the length of the flat section at the gas outlet is 3.3, and the diameter of the mixing chamber outlet is 5.0. The atomization cone angle increased by 23.07 % compared with the original model, and the fuel atomization circumferential distribution uniformity index decreased by 45.06 %. A new solution for the design of externally mixed air atomizing nozzles is provided.

Multi-scale topology optimization of periodic structures with orthotropic multiple materials using the element-free Galerkin method

ABSTRACT A multi-scale topology optimization model is proposed for orthotropic multi-material periodic structures using the element-free Galerkin method. The macro multi-material distribution is optimized with the alternating active-phase algorithm, and the effective elastic tensor of multi-type microstructures is determined by energy-based homogenization. The feasibility of the model is verified and the effects of the quantities of material types and design subdomains, the Poisson's ratio factor and the multi-material off-angle on topological configuration and compliance are studied. The results indicate that the quantity of material types affects the mechanical properties of the periodic structure, and different microstructure configurations can be obtained under different numbers of design subdomains. The increase in the Poisson's ratio factor and decrease in the off-angle can enhance the effective elastic properties of the microstructure and reduce the compliance. Reasonable values of the Poisson's ratio factor and multi-material off-angle are suggested to be 2–4 and 0–45°.

Computational study of substituent effects on molecular structure, vibrational and electronic properties of fluorene molecule using density functional theory

Density functional theory (DFT) provides a powerful tool for investigating the effects of halogen (F, Cl and Br) substitution on the electronic and structural properties of fluorene. The B3LYP/6-31G (d,p) protocol is a commonly used method in DFT calculations for the optimisation of molecular structures and the calculation of various molecular properties by Gaussian 09 W program. In the case of the fluorene molecule with halogen substitutions, (TD–DFT) calculations can be used to predict its UV–Vis spectrum. The B3LYP density functional model with a 6-31G(d,p) basis set is a common choice for performing (TD–DFT) calculations on molecules. The results showed a decrease in gap energies when electron-withdrawing groups were present in the molecule. A decrease in the gap energy indicates that the molecule is less stable and more reactive.

Structural topology optimization for plastic-limit behavior of I-beams, considering various beam-column connections

This work proposes topology optimization for steel I-beams, including consideration of bolted beam-column connections with geometric and material nonlinear analysis. The aim is to assess and compare the topological configurations influenced by different connections, examining their stress distribution and rotational stiffness to illustrate the potential of structural optimization. The bi-directional evolutionary structural optimization (BESO) approach is implemented. Furthermore, several bolted steel beam-column configurations were validated based on experimental tests. Subsequently, a series of finite element models were developed, contributing to a comprehensive understanding of the plastic-limit behavior of I-beams under different loading conditions. The proposed method could potentially use a lesser quantity of material while maintaining the same level of structural performance. The results indicate that the implementation of structural topology optimization on I-beams while considering various beam-column connections, yields structural performance similar to that of solid web configurations, achieved through material reduction.

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.

An enhanced proportional topology optimization method with new density filtering weight function for the minimum compliance problem

This article proposes an enhanced proportional topology optimization (EPTO) method to solve the structural topology optimization problem of minimizing compliance under material volume constraints. In the proposed method, a new filtering weight function based on the improved Heaviside threshold function is adopted to filter element density during the optimization process. The optimization process of the EPTO method consists of an inner loop and an outer loop. In the inner loop, density distribution is modified in combination with a new filtering weight function. By locally averaging the weighted element compliance, an improved density distribution function in the inner loop is put forward to make the topology configuration of the optimized structure more reasonable. In addition, the projection method is used to reduce the number of intermediate density elements, thereby obtaining optimization results with clear boundaries. In the outer loop, a new termination criterion is adopted, which terminates the optimization process by determining that the relative error of the objective function in several consecutive iterations is less than the specified value. The effectiveness and efficiency of the proposed method are demonstrated through several numerical examples involving two-dimensional (2D) and three-dimensional (3D) topology optimization problems. The results of numerical examples show that the proposed method can not only accelerate the convergence of optimization iterations, but also obtain optimized structures with smaller objective function values and better topology configurations. HIGHLIGHTS A new density filtering weight function is proposed based on an improved Heaviside threshold function. An improved inner loop density distribution formula is proposed by combining a new filtering weight function. Using projection based methods to suppress the appearance of intermediate density elements. Verify the effectiveness of the proposed algorithm by comparing the optimization results with existing algorithms such as top88 and PTO.

An efficient single-loop strategy for time-variant reliability sensitivity analysis based on Bayes’ theorem

Time-variant reliability sensitivity analysis aims to measure the effect of input variables on the time-variant failure probability, which can then be used to guide structural design and optimization. The traditional methods for calculating the sensitivity index require a nested sampling procedure and their computational complexity depends on the number of input variables, making them computationally the most expensive. To address the above limitations, an efficient single-loop strategy is developed for time-variant reliability sensitivity (TRS) analysis. Based on Bayes' theorem, the TRS index is represented by the difference between the probability density function (PDF) and failure-conditional PDF of the variable. This derivation enables TRS analysis to be implemented using only a single set of samples, with computational costs that don’t depend on the number of input variables. Then, the sensitivity index is normalized to identify influential variables effectively. Several case studies involving numerical and engineering problems are employed to verify the feasibility and effectiveness of the proposed strategy. The direct Monte Carlo simulation is introduced to assess the accuracy of the obtained results. The results indicate that the proposed strategy provides acceptable sensitivity analysis for time-variant events, while greatly conserving computational resources and enhancing efficiency.

Crashworthiness performance of novel thin-walled tubes with spiral cross section

This study proposes two innovative thin-walled structures: the spiral tube (ST) and the multi-cell spiral tube (MCST), with MCST demonstrating better energy absorption performance. Through numerical simulation, geometric parameters of MCST are analyzed for their effect on crashworthiness performance. MCST with inner diameter of 15 mm, rotating angle of 4π, pitch of 18 mm and 6 ribs has the best energy absorption performance, and the SEA of MCST increases by up to 16.2% compared to the multi-cell circular tube, indicating superior energy absorption performance. The findings promote the optimization and application of structures in automotive energy absorption components.

Iterative eigenvalue method coupled with RSM for structural acoustic analysis and optimization of the CLD-damped orthotropic steel deck

In the present work, an iterative eigenvalue method (IEM) is proposed and combined with the boundary element method (BEM) to perform the structural acoustical analysis of the orthotropic steel deck (OSD) damped with constrained layer damping (CLD), through which the frequency-dependent properties of the viscoelastic core can be accurately considered. Then, a series of hammer tests are carried out in a semi-anechoic chamber to verify the acoustic prediction method. It shows that the simulated structural noises basically agree with the test results, and the overall deviations at the field points M2 and M8 are merely 2.4 and 2.3 dB, respectively. Subsequently, taking the thicknesses of the damping layer and the constraining layer, as well as the material properties of the constraining layer as design variables, a central composite experiment is designed and combined with response surface methodology (RSM) to fit the relationship between analysis objectives and design variables. With the objective of minimizing the acoustic radiation power, a program for finding the optimal values of design variables is developed based on the interior penalty function method. Through iterative computations, the optimal points are numerically determined as t 1 = 2.3 mm and t 2 = 0.3 mm for the thicknesses of the damping layer and the constraining layer, respectively. Steel alloy is found to be the optimal material for the constraining layer. After optimizing CLD treatment, the overall acoustical power level can be reduced from 97.7 dB to 93.1 dB and the overall sound pressure levels (SPLs) at the field points M2 and M8 can be reduced from 89.2 dB to 83.5 and 76.9 dB to 70.3 dB, respectively, indicating that the optimization of CLD design parameters can significantly improve acoustic performance of the CLD-damped structures.

Innovative simplified approach and numerical investigation for flow and heat transfer in internally threaded tubes

Internally threaded tubes exhibit exceptional heat transfer capabilities, holding paramount significance in enhancing energy efficiency, reducing energy consumption, and tackling thermal challenges across aerospace, automotive, and environmental domains. Nonetheless, their intricate structural features, software modelling intricacies, extensive grid requirements, and challenges in maintaining grid quality render numerical simulation investigations a demanding endeavor. This study elucidates the influence mechanisms of thread spacing on the distribution of single-phase and two-phase flows. It delves into the condensation heat transfer of the R32 refrigerant and the single-phase heat transfer of water within internally threaded tubes. At the same Reynolds number, the heat transfer rate can be improved by approximately 19.61% with the optimized internally threaded parameters. When the Reynolds number varies from 18,626 to 51,222, the heat transfer rate per unit length for Tube-5 remains around 2,478.9 W/m, with a variation of less than 5.19%. Furthermore, it presents a simplified numerical simulation approach tailored for internally threaded pipes. This method manipulates wall roughness and regulates wall rotation speed to mimic fluid dynamics phenomena akin to conventional numerical simulation techniques. The findings reveal that the proposed simplified numerical simulation approach yields heat transfer and pressure drop predictions with less than 3% discrepancies compared to traditional numerical simulation predictions. Simultaneously, compared to directly simulating threaded pipes through conventional means, this approach significantly mitigates grid generation complexities, slashing computational time costs by at least 85% and facilitating efficient thermal design and structural optimization processes.

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.

High-performance Waterproof Flexible Thermoelectric Generators for Self-powered Electronics

Flexible and wearable thermoelectric generators (TEG) have emerged as promising energy sources for wearable health-monitoring devices. However, common thermoelectric generators are difficult to be applied to a wide range of application scenarios due to their poor durability, low output power, and susceptibility to human sweat or underwater environments. Here, we propose a waterproof wearable TEG with a gap structure. Through structural optimization and full-coverage elastomer encapsulation, the wearable TEG has a maximum power density of 4.38mW∙cm-2 at a temperature difference (ΔT) of 30K and exhibits good stability under aqueous environments, which is capable of supplying power to electronic devices even under submerged conditions. The internal resistance of wearable TEG changes by less than 10% at 50% stretch or 900 degrees of torsion, showing good flexibility and mechanical stability. Based on this, we designed an energy harvesting and management system to help wearable TEG collect and utilize energy on demand, and successfully implemented wireless transmission of human skin temperature data for underwater environments and real-time electrocardiograms (ECG) tests for health detection in air environments. This research provides a reliable method for powering wearable electronic devices using thermoelectric generators.