Shape Optimization Research Articles

Analysis of stress-strain curve of POM fiber reinforced concrete

ABSTRACT As a new type of synthetic fiber, polyoxymethylene (POM) fiber has the advantages of high tensile strength, good dispersibility, and high bonding strength with cement interface. It has broad application prospects. However, there is limited research on POM fiber reinforced concrete. In order to provide scientific basis for promoting the application of POM fiber, this paper adopts a combination of indoor experiments and numerical simulations to obtain the axial stress-strain complete curves of POM fiber reinforced concrete with different volume dosages and studies the uniaxial compressive properties of POM fiber reinforced concrete. Finally, the constitutive equation parameters of POM fiber reinforced concrete were fitted using the Guo Zhenhai model, and the optimal fiber content was determined. The results indicate that at a POM fiber content of 1.5 kg/m3, the load-displacement curve exhibits optimal shape with the highest residual strength. With increasing fiber content, compressive stress-strain curve parameters initially increase and then decrease, peaking at 1.5 kg/m3, optimizing the mechanical properties of concrete. POM fiber has minimal impact on initial elastic modulus. Thus, optimal mechanical property enhancement is achieved with 1.5 kg/m3 POM fiber content.

Synthesis of a Hard Anodic Oxide Coating with a Structure Allowing for Its Modification by Nanoparticles

A hard anodic oxide coating’s characteristic porous structure allows for its modification by the incorporation of nanoparticles. However, achieving an appropriate microstructure requires an optimal pore arrangement and shape, which is influenced by the electrolyte composition, current densities, temperature, and processing time. To achieve pores with a diameter of about 50 nm and the most regular structure, a range of these parameters were tested. Using a two-stage manufacturing process had a beneficial effect on increasing the microporosity of the coating. The addition of phthalic acid at 0 °C did not increase the pore diameter, but allowed for the process to be carried out at higher temperatures. However, the coating produced at 20 °C had a larger pore diameter, but numerous defects. The coating obtained from the three-component solution had the most regular structure, but the smallest pore diameter.

Optimization of condensing tray shapes for a multi‐effect solar still coupled with parabolic solar collectors for domestic wastewater treatment: A comparative study

AbstractThe issue of water depletion emerged as a life‐threatening problem for the world due to urbanization, groundwater over‐extraction, industrialization, and global warming. Current study aimed to address this issue by proposing a solution to distill wastewater using a multi‐effect solar still. The study optimizes two condensation tray shapes, U and V, based on the yield produced and the temperatures achieved. Two solar still units with four stages of U and V‐shaped trays were connected to a parabolic solar collector. To determine the optimal tray shapes, a rigorous optimization process was carried out using SolidWorks 2020. The optimization process yielded optimum heat flux values of 3.04e01 and 2.84e01 W/m2 for U and V‐shaped trays, respectively. Higher the value of heat flux suggested more energy available for condensation. Which was corroborated by physical findings that the U‐shaped condensation tray was more efficient, producing an average per day yield of 2.519 L/m2 h compared to the V‐shaped tray's yield of 2.041 L/m2 h. The findings provide strong evidence that the U‐shape is a better tray shape for condensation purposes. Maximum yield for both units was observed during the peak temperature time between (13:00–15:00 h), indicating a direct correlation between yield and atmospheric temperature.

Transverse Magnetic ENZ Resonators: Robustness and Optimal Shape Design

Transverse Magnetic ENZ Resonators: Robustness and Optimal Shape Design

Shape optimized acoustic metagratings for anomalous refraction under strong thermoviscous effects

The recent development of microacoustic metagratings opens up promising possibilities for manipulating acoustic wavefronts passively, particularly in applications such as flat acoustic lenses and ultra-high frequency ultrasound imaging. The emergence of two-photon polymerization has made it feasible to precisely manufacture microscopic structures, as required when metagratings are scaled to MHz frequencies in airborne ultrasound. Nevertheless, the downsizing process presents another hurdle as the increased thermoviscous effects result in substantial losses that must be considered during the design phase. In this study, we propose two designs for microacoustic metagratings that refract a normally incident wave towards –35 ° at 2 MHz, consisting of single-body and two-body meta-atoms. The designs are created by employing shape optimization techniques that incorporate the linearized Navier–Stokes equations in every iteration starting from a neutral geometry. This ensures that the evolution of geometric key features responsible for anomalous refraction fully accounts for thermoviscous effects, as would be the case during evolution in nature where the full set of physics is always active. Subsequently, we experimentally evaluate the effectiveness of these metagratings by employing a capacitive micromachined ultrasonic transducer as the sound source and an optical microphone as the detector, covering a frequency range from 1.8 to 2.2 MHz. Our findings confirm the single-body geometry reported in the literature and show an alternative geometry for two-body design, showcasing the successful utilization of two-photon polymerization for manufacturing microscopic acoustic metamaterials.

Hydrodynamic Shape Optimization of a Naval Destroyer by Machine Learning Methods

This paper explores the integration of advanced machine learning (ML) techniques within simulation-based design optimization (SBDO) processes for naval applications, focusing on the hydrodynamic shape optimization of the DTMB 5415 destroyer model. The use of unsupervised learning for design-space dimensionality reduction, combined with supervised learning through active learning-based multi-fidelity surrogate modeling, allows for significant improvements in computational efficiency while addressing complex, high-dimensional design spaces. By applying these ML techniques to both single- and multi-objective optimizations, aimed at minimizing resistance and enhancing seakeeping performance, the proposed framework demonstrates its practical value in hydrodynamic design. This approach provides a scalable and efficient solution, reducing the reliance on high-fidelity simulations while accelerating the optimization process, without substantial modifications to existing toolchains. A design-space dimensionality reduction of approximately 70% is achieved, reducing the design variables from 22 to 7 while retaining 95% of the original geometric variance. Additionally, computational cost reductions of 65% to 98% are observed, compared to using the full design space and high-fidelity simulations only.

Discretization-independent node-based shape optimization with the Vertex Morphing method using design variable scaling

AbstractThe Vertex Morphing method is a node-based shape parameterization that uses an explicit filtering approach to regularize the optimization problem and generate smooth shapes. It has been successfully applied to shape optimization problems of industrial size in recent years. This work investigates in detail how irregular discretizations, design surface boundaries, and complex geometries can influence the progress of a gradient-based optimization using the standard Vertex Morphing formulation. A sensitivity weighting approach based on the available shape morphing functions is presented, which eliminates all of the aforementioned influences. Subsequently, a design variable scaling strategy is developed that transforms the optimization problem into an alternative design space and allows the use of arbitrary, even highly irregular surface discretizations in combination with black-box optimization algorithms for shape optimization with the Vertex Morphing method. Illustrative academic examples and an application case of an additively manufactured part are presented to support the work.

Development of a novel rotational metallic damper as a dissipative connector in rocking steel core systems: Cyclic behavior and seismic demand

Rocking systems with stiff rocking cores have been proposed as a promising solution for mitigating concentrations of story drift and enhancing structural seismic resilience. This study introduces a novel rotational metallic damper, termed the rotational steel rod damper (RSRD), developed for use in rocking steel core systems to improve energy dissipation capacity. The configuration, working mechanism, and application of the RSRD in rocking steel core systems are described. Three critical energy-dissipating elements, low-yield-point steel rods with different edge shapes, were isolated from the RSRD and tested to validate the efficacy of an optimal hourglass shape, defined through cubic equations, in enhancing low-cycle-fatigue performance. Two RSRD specimens were then tested and analyzed, focusing on failure modes, cyclic behavior, rotational strength, and energy dissipation. Both specimens demonstrated positive and stable hysteretic performance and energy dissipation capacity, with maximum equivalent viscous damping ratios of 0.51 and 0.53. Subsequently, structural models of seven steel frames were developed in OpenSees for case studies. Nonlinear response history analyses were performed under 20 ground motion records scaled to DBE and MCE levels. Dynamic behaviors, particularly the seismic demand on RSRDs, were examined. Numerical results confirmed the efficacy of the RSRD in mitigating inter-story drift. The location of the pivoting point of the rocking core significantly influenced the rotational demand on the RSRD. The proposed RSRD presents an innovative energy-dissipating alternative for the development of rocking steel core systems.

Efficient aerodynamic shape optimization using transfer learning based multi-fidelity deep neural network

Computational efficiency and precision pose a classic contradiction in aerodynamic shape optimization. To address this challenge, this study introduces an effective optimization framework based on multi-fidelity fully connected neural network (MFFCN). The framework utilizes transfer learning (TL) to train a multi-fidelity surrogate model that establishes direct mappings between geometric configuration parameters and aerodynamic performance by adaptively capturing linear or nonlinear relationships concealed between high-fidelity (HF) and low-fidelity (LF) information. The HF and LF data are derived from fine and coarse grids, respectively, evaluated using the same computational fluid dynamics (CFD) model. The MFFCN-TL framework is applied to optimize the National Advisory Committee for Aeronautics 0012 (NACA0012) airfoil (12 design variables) and the Office National d'Études et de Recherches Aérospatiales M6 (ONERA M6) wing (50 design variables). Simulation results demonstrate that the NACA0012 airfoil achieves a 69.47% enhancement in lift–drag ratio in 1.069 s, compared to a 12.76% gain over 24.8 h in single-fidelity CFD-based optimization. The ONERA M6 wing achieves a 24.66% reduction in drag coefficient in 694 ms compared to 18.37% over 237.3 h in the CFD model. Statistical results show that the MFFCN-TL framework can reduce optimization cost by more than 90% compared to the single-fidelity CFD-based model. These findings suggest that the MFFCN-TL framework significantly enhances optimization efficiency and provides superior feasible solutions over single-fidelity methods.

Ship Forebody Optimization Based on Rankine Source Method

Abstract The shape of the ship’s forebody has a greater impact on the ship’s resistance, and a reasonable optimization of the forebody can play a role in reducing the propulsion power and optimizing the resistance performance. Under the premise of Rankine source method of potential flow wave theory as the theoretical basis, SHIPFLOW software is used as the calculation tool, and CAESES software is used as the optimization tool to study the optimal design of the ship with minimum wave resistance. In the optimization process, a real ship is taken as the object, and the optimal solution of the rising wave resistance coefficient is calculated with the rising wave resistance coefficient as the objective function and the ship speed and displacement as the constraints. The real ship is selected as the mother ship, the parameters of the hull shape are taken as the design variables, and the shape of the forebody is optimized by the Lackenby shift method, so as to obtain a ship shape with less wave resistance at the same speed and within the displacement limit. The results show that the improved ship shape has obvious effect of reducing the wave resistance, which verifies the effectiveness and feasibility of this method for ship shape optimization

Multi‐Stage Optimization of Pore Size and Shape in Pore‐Space‐Partitioned Metal–Organic Frameworks for Highly Selective and Sensitive Benzene Capture

AbstractCompared to exploratory development of new structure types, pushing the limits of isoreticular synthesis on a high‐performance MOF platform may have higher probability of achieving targeted properties. Multi‐modular MOF platforms could offer even more opportunities by expanding the scope of isoreticular chemistry. However, navigating isoreticular chemistry towards best properties on a multi‐modular platform is challenging due to multiple interconnected pathways. Here on the multi‐modular pacs (partitioned acs) platform, we demonstrate accessibility to a new regime of pore geometry using two independently adjustable modules (framework‐forming module 1 and pore‐partitioning module 2). A series of new pacs materials have been made. Benzene/cyclohexane selectivity is tuned, progressively, from 4.5 to 15.6 to 195.4 and to 482.5 by pushing the boundary of the pacs platform towards the smallest modules known so far. The exceptional stability of these materials in retaining both porosity and single crystallinity enables single‐crystal diffraction studies of different crystal forms (as‐synthesized, activated, guest‐loaded) that help reveal the mechanistic aspects of adsorption in pacs materials.

Multi-Stage Optimization of Pore Size and Shape in Pore-Space-Partitioned Metal-Organic Frameworks for Highly Selective and Sensitive Benzene Capture.

Compared to exploratory development of new structure types, pushing the limits of isoreticular synthesis on a high-performance MOF platform may have higher probability of achieving targeted properties. Multi-modular MOF platforms could offer even more opportunities by expanding the scope of isoreticular chemistry. However, navigating isoreticular chemistry towards best properties on a multi-modular platform is challenging due to multiple interconnected pathways. Here on the multi-modular pacs (partitioned acs) platform, we demonstrate accessibility to a new regime of pore geometry using two independently adjustable modules (framework-forming module 1 and pore-partitioning module 2). A series of new pacs materials have been made. Benzene/cyclohexane selectivity is tuned, progressively, from 4.5 to 15.6 to 195.4 and to 482.5 by pushing the boundary of the pacs platform towards the smallest modules known so far. The exceptional stability of these materials in retaining both porosity and single crystallinity enables single-crystal diffraction studies of different crystal forms (as-synthesized, activated, guest-loaded) that help reveal the mechanistic aspects of adsorption in pacs materials.

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

Shape optimization for high efficiency metasurfaces: theory and implementation

Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction often imposes performance limitations. On the other extreme, inverse design based on topology optimization leverages non-local coupling to achieve high efficiency, but leads to complex and difficult to fabricate structures. In this paper, we demonstrate numerically and experimentally a shape optimization method that enables high efficiency metasurfaces while providing direct control of the structure complexity through a Fourier decomposition of the surface gradient. The proposed method provides a path towards manufacturability of inverse-designed high efficiency metasurfaces.

Jet mixing optimization using a bio-inspired evolution of hardware and control

Jet mixing is a critical factor in various engineering applications, influencing pollutant dispersion, chemical processes, medical treatments, and combustion enhancement. Hitherto, jet mixing has typically been optimized by either passive or active control techniques. In this experimental study, we combine simultaneous optimization of active control with 12 inward-pointing minijets and a tuneable nozzle exit shape commanded by 12 stepper motors. Jet mixing is monitored at the end of the potential core with an array of 7 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 7 Pitot tubes. This high-dimensional actuation space is conquered with Particle Swarm Optimization through Targeted, Position-Mutated Elitism. Our results underscore the significant impact of combining control techniques, illustrating the complex interactions of both passive and active control on jet flow dynamics. The mixing area of the combined control optimization is 4.5 times larger than the area of the unforced state. This mixing increase significantly outperforms the effect of shape optimization of the nozzle alone. Our study points at the potential of optimization in high-dimensional design spaces for shapes as well as passive and active control—leveraging the rapid development of flow control hardware and the increasingly powerful tools of artificial intelligence for optimization.

Improving transonic performance with adjoint-based NACA 0012 airfoil design optimization

This study delves into the discrete adjoint method, a powerful tool in high-fidelity aerodynamic shape optimization that efficiently computes derivatives of a target function for different design variables. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables. It is implemented to a NACA0012 airfoil at a transonic speed. This designated test case is qualitatively evaluated, considering specified Mach number and Reynolds number values of 0.7 and 15.96 million, respectively. The standard Spalart-Allmaras turbulence model is adapted to improve computational cost efficiency. The results validate the efficiency of Discrete Adjoint with OpenFOAM, showcasing its capability to generate optimal configurations. The achieved optimized performance is evidenced by minimizing the drag coefficient value (Cd) to an impressive value of 0.00871, 62.2 % lower than the previous studies, thus securing a novelty. While this research does not consider the post-processing of sensitivity calculations, it enables the potential for future research. The primary target of this paper is to assess the educational and training needs of researchers, engineers, and graduate students, offering a comprehensive introduction to discrete adjoint aerodynamic design optimization, presenting a novel methodology, and contributing to future advancements in the design optimization field.

A preoperative planning procedure of septal myectomy for hypertrophic obstructive cardiomyopathy using image-based computational fluid dynamics simulations and shape optimization.

Although septal myectomy is the preferred treatment for medication-refractory hypertrophic obstructive cardiomyopathy (HOCM), the procedure remains subjective. A preoperative planning procedure is proposed using computational fluid dynamics simulations and shape optimization to assist in the objective assessment of the adequacy of the resection. 3 patients with HOCM were chosen for the application of the proposed procedure. The geometries of the preoperative left ventricular outflow tract (LVOT) of patients in the systolic phase were reconstructed from medical images. Computaional fluid dynamics (CFD) simulations were performed to assess hemodynamics within LVOT. Sensitivity analysis was performed to determine the resection extent on the septal wall, and the depth of the resection was optimized to relieve LVOT obstruction while minimizing damage to the septum. The optimized resection was then transferred from systole to diastole to provide surgeons with instructive guidance for septal myectomy. Comparison between preoperative and postoperative hemodynamics showed an evident improvement with respect to the pressure gradient throughout the LVOT. The resected myocardium in the diastolic phase is more extended and thinner than its state in the systolic phase. The proposed preoperative planning procedure may be a viable addition to the current preoperative assessment of patients with HOCM.

Space-time shape optimization of rotating electric machines

Space-time shape optimization of rotating electric machines

An adaptive snow ablation-inspired particle swarm optimization with its application in geometric optimization

In response to the shortcomings of particle swarm optimization (PSO), such as low execution efficiency and difficulty in overcoming local optima, this paper proposes a multi-strategy PSO method incorporating snow ablation operation (SAO), known as SAO-MPSO. Firstly, Cubic initialization is performed on particles to obtain a good initial environment. Subsequently, SAO and PSO are combined in parallel, and a balanced search mechanism led by multiple sub-populations is devised, significantly improving the search efficiency of overall population. Finally, the degree day method of SAO is introduced, and particles are endowed with memory of environmental changes to prevent premature convergence of PSO, while balancing the exploration and exploitation (ENE) capabilities in later phases. All adaptive parameters are used throughout this method in place of fixed parameters to improve the robustness and adaptability. For a comprehensive analysis of SAO-MPSO, its good ENE ability is verified on CEC 2020 and CEC 2022 and this method is compared with existing improved PSO versions on both test sets. The results show that SAO-MPSO has certain advantages in the comparison of similar improved algorithms. In order to further validate the strength of SAO-MPSO in dealing with nonlinear optimization problems (OPs) with strong constraints, firstly, based on the ball Wang-Ball (BWB) curve, a combined BWB (CBWB) curve is constructed, and a construction method for CBWB curves that satisfy G1 and G2 continuity is derived. Then, with the energy minimization and scale parameters of the CBWB curve as the optimization objective and variables respectively, a shape optimization model that satisfies G2 continuity is established. Finally, three numerical optimization examples based on this model are solved using SAO-MPSO and compared with 10 other methods. The results show that the energy obtained by SAO-MPSO is the smallest, which verifies the effectiveness of this method applied to shape OPs of CBWB curve.

Optimization of vehicle conceptual design problems using an enhanced hunger games search algorithm

Abstract Electric vehicles have become a standard means of transportation in the last 10 years. This paper aims to formalize design optimization problems for electric vehicle components. It presents a tool conceptual design technique with a hunger games search optimizer that incorporates dynamic adversary-based learning and diversity leader (referred to as HGS-DOL-DIL) to overcome the local optimum trap and low convergence rate limitations of the Hunger Games search algorithm to improve the convergence rate. The performance of the proposed algorithms is studied on six widely used engineering design problems, complex constraints, and discrete variables. For the HGS-DOL-DIL practical feasibility analysis, a case study of shape optimization of an electric car suspension arm from the industry is carried out. Overall, the inclusion of the OL strategy has proven its superiority in solving real-world problems, especially in solving real-world problems such as shape optimization of an electric vehicle automobile suspension arm, showing that the algorithm improves the search space improves the solution quality, and reflects its potential to find global optimum solutions in a well-balanced exploration and exploitation phase.