Optimal Shape Design Research Articles

평균 토크 향상을 위한 단절권 매입형 영구자석 동기전동기의 회전자 배리어 형상 최적 설계

평균 토크 향상을 위한 단절권 매입형 영구자석 동기전동기의 회전자 배리어 형상 최적 설계

Building shape optimization based on interconnected embodied and operational energy and carbon impacts

Strategic building design decisions informed by a comprehensive life cycle impact assessment hold substantial potential in addressing global energy consumption and carbon emissions, with buildings accounting for 40% of energy consumption and 37% of emissions. While building operational energy (OE) has traditionally received greater attention, the dynamic trade-offs between OE and embodied energy (EE) in building design are often overlooked. Design decisions, such material selection and building shape, can present conflicting considerations between OE and EE. Addressing these impacts in isolation may fail to achieve comprehensive reductions in energy consumption and carbon emissions. This study highlights the necessity of a holistic approach to design decisions such as building shape and material selection, emphasizing the importance of considering both OE and EE simultaneously. Our literature review confirms a gap in studies that consider these factors together in the context of building shape optimization. To analyze the interconnectivity of building shape design, material choice, and the trade-offs between OE and EE, we devised two parametric test cases with identical features but using two different insulation materials: hemp-based and glass wool. The analysis allows us to (1) evaluate the impact of integrating total lifecycle impact on building shape design optimization, in comparison to designs that focus solely on OE; (2) assess how the selection of materials, specifically hemp-based versus glass wool insulation, influences optimized building shape and carbon emissions reduction; and explore the benefits of bio-based materials by analyzing performance variations in the two insulations case studies. Our findings reveal that although OE typically has a larger impact over a building’s lifetime, the optimal building shape can still vary significantly based on the EE contribution. The benefit of bio-based material is context-dependent, varying with factors such as the building shape discussed in this paper, as well as other factors such as climate. In our test cases, we observed that shape variations resulted in up to a 17.9% change in OE due to different building shapes, and a 60.7% variation in the envelope’s surface area, while the building area remained unchanged. This expanded understanding will facilitate more informed and sustainable decision-making in the construction and design industries, addressing the often-overlooked interconnectivity of OE and EE.

Computational Shape Design Optimization of Femoral Implants: Towards Efficient Forging Manufacturing

Total hip replacement is one of the most successful orthopedic operations in modern times. Osteolysis of the femur bone results in implant loosening and failure due to improper loading. To reduce induced stress, enhance load transfer, and minimize stress, the use of Ti-6Al-4V alloy in bone implants was investigated. The objective of this study was to perform a three-dimensional finite element analysis (FEA) of the femoral stem to optimize its shape and analyze the developed deformations and stresses under operational loads. In addition, the challenges associated with the manufacturing optimization of the femoral stem using large strain-based finite element modeling were addressed. The numerical findings showed that the optimized femoral stem using Ti-6Al-4V alloy under the normal daily activities of a person presented a strains distribution that promote uniform load transfer from the proximal to the distal area, and provided a mass reduction of 26%. The stress distribution was found to range from 700 to 0.2 MPa in the critical neck area of the implant. The developed computational tool allows for improved customized designs that lower the risk of prosthesis loss due to stress shielding.

Preform cross-section shape optimization design for tube hydroforming with low pressure

Preform design refers to the intermediate geometric design between the initial tube blank and the desired product. A proper preform design can improve the formability of the tubular structure with small fillets. It is difficult to obtain a reasonable preform design based on engineering experience or trial-and-error methods. In this work, a Non-Uniform Rational B-Splines (NURBS) curve control point inversion algorithm-based approach is introduced to define and parameterize the preform cross-section profiles. The corresponding mathematical optimization model of preform cross-section shape design for tube hydroforming with low pressure is established, and an optimization procedure was accordingly proposed. In this procedure, the relationships between the design variables and responses are formulated by combining the DoE techniques with multiple surrogate models. The k-fold cross-validation strategy is adopted to quantify the performance of the candidate surrogate models on fresh datasets. The selected and verified surrogate models are integrated with the heuristic algorithm to determine the optimal preform shape. Compared to the direct hydroforming process, the optimized preform designs decreased the forming pressure of square, trapezoidal, and irregular polygonal tubes by 89.29%, 70.29%, and 32.67%, respectively. The validity of the proposed method is thus verified.

Numerical methods for shape optimal design of fluid–structure interaction problems

We consider the method of mappings for performing shape optimization for unsteady fluid–structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes several theoretical results into account, such as regularity requirements on the transformations and a differential geometrical point of view on the manifold of shapes. Moreover, we discretize the problem such that we can compute exact discrete gradients. This allows for the use of general purpose optimization solvers. We focus on problems derived from an FSI benchmark to validate our numerical implementation. The method is used to optimize parts of the outer boundary and the interface. The numerical simulations build on FEniCS, dolfin-adjoint and IPOPT. Moreover, as an additional theoretical result, we show that for a linear special case the adjoint attains the same structure as the forward problem but reverses the temporal flow of information.

Shape Design Optimization and Comparative Analysis of a Novel Synchronous Reluctance Machine With Grain-Oriented Silicon Steel

Shape Design Optimization and Comparative Analysis of a Novel Synchronous Reluctance Machine With Grain-Oriented Silicon Steel

Second-order Arnoldi accelerated boundary element method for two-dimensional broadband acoustic shape sensitivity analysis

This paper proposes a novel approach for broadband acoustic shape sensitivity analysis based on the direct differentiation approach. Since the system matrices of the boundary element method (BEM) for the analysis of acoustic state and acoustic sensitivity have frequency dependence, repeated calculations are needed at different frequencies. This is very time-consuming, especially for sensitivity calculations used in shape optimization design. The Taylor series expansion of the Hankel function is carried out to separate the frequency-dependent and frequency-independent terms in the acoustic shape sensitivity boundary integral equation to construct a frequency-independent system matrix. In addition, due to the formation of asymmetric full-coefficient matrices in acoustic shape sensitivity equations based on the BEM, repeatedly solving system equations is also extremely time-consuming at broadband frequencies for large scale issues. The second-order Arnoldi approach was employed to create a reduced-order model that maintains the key features of the initial full-order model. The strong singular and supersingular integrals within the sensitivity equations can be calculated directly utilizing the singularity elimination technique. Finally, several numerical examples confirm the accuracy and efficiency of the proposed algorithm.

Kriging Surrogate-based Optimization for Shape Design of Thin Electric Propeller

Kriging Surrogate-based Optimization for Shape Design of Thin Electric Propeller

Micromechanical analysis for effective elastic moduli and thermal expansion coefficient of composite materials containing ellipsoidal fillers oriented randomly

In this study, we examine to derive the solutions of effective elastic moduli and thermal expansion coefficient for composite materials containing ellipsoidal fillers oriented randomly in the material using homogenization theories, which are the self-consistent method and the Mori–Tanaka method. This analysis is carried out by micromechanics combining Eshelby’s equivalent inclusion method for each theory. The solutions for effective elastic moduli and thermal expansion coefficient obtained on each theory are expressed by common coefficients composed of both the physical properties of the constituents of the composite material and geometrical factors depending upon the shape of the fillers. Moreover, these solutions enable us to calculate effective elastic moduli and thermal expansion coefficient for composite materials that contain randomly oriented fillers of various shapes and physical properties. By taking the limit of eliminating the existence of the matrix for these solutions, we can derive effective physical properties of polycrystalline materials. Using the obtained solutions, we investigate the effects of the shape of the fillers on the effective elastic moduli and thermal expansion coefficient. As a result, we confirm that these effective properties fall within the lower and upper bounds, and find that a characteristic result appears when the shape of the fillers is flake or oblate. Through comparisons between the analytical and experimental results, we confirm the practical usability of the solutions obtained in this analysis. Furthermore, we determine originally the shape factor for the filler and can show that this factor has the potential to provide guidelines for the optimal design of filler shape to improve the effective elastic properties of materials.

Optimal shape design to improve torque characteristics of interior permanent magnet synchronous motor for small electric vehicles

Optimal shape design to improve torque characteristics of interior permanent magnet synchronous motor for small electric vehicles

Curved Domains in Magnetics: A Virtual Element Method Approach for the T.E.A.M. 25 Benchmark Problem

In this paper, we are interested in solving optimal shape design problems. A critical challenge within this framework is generating the mesh of the computational domain at each optimisation step according to the information provided by the minimising functional. To enhance efficiency, we propose a strategy based on the Finite Element Method (FEM) and the Virtual Element Method (VEM). Specifically, we exploit the flexibility of the VEM in dealing with generally shaped polygons, including those with hanging nodes, to update the mesh solely in regions where the shape varies. In the remaining parts of the domain, we employ the FEM, known for its robustness and applicability in such scenarios. We numerically validate the proposed approach on the T.E.A.M. 25 benchmark problem and compare the results obtained with this procedure with those proposed in the literature based solely on the FEM. Moreover, since the T.E.A.M. 25 benchmark problem is also characterised by curved shapes, we utilise the VEM to accurately incorporate these “exact” curves into the discrete solution itself.

Surrogate-based Shape Optimization Design for the Stable Descent of Mars Parachutes

The crucial role that the supersonic parachute plays in space exploration missions has been widely recognized, as it directly impacts the safe landing of probes. However, parachute models with optimization on different aerodynamic performances often involve design conflicts with each other. Additionally, the parachute design focusing on a single point cannot fully adapt to different speed ranges during stable descent. This complexity makes it challenging to use traditional shape design methods, which rely on empirical knowledge, to address these coupled design issues. Faced with the design challenges of Mars parachutes, this study, inspired by aircraft aerodynamic optimization principles, establishes a shape design method specifically for the stable descent phase of Mars parachutes. The method combines numerical simulation and surrogate-based optimization strategies, aiming to enhance the overall performance during stable descent and meet various demands of different exploration missions. Meanwhile, by providing a rapid estimate of the shape during the design phase, the method significantly improves computational efficiency. The optimal models effectively balance comprehensive performance in the supersonic-transonic-subsonic speed domain by conducting shape optimization research on the disk-gap-band parachute using the surrogate-based optimization strategy. Also, it exhibits better deceleration and stability across the entire speed range compared to the base model, even when deviating from the design Mach number. Importantly, the advantages of canopy-only optimization for drag performance extend to the capsule-canopy two-body system, enhancing the drag performance of the canopy in the two-body system. This strategic approach reduces the transient calculation time for the two-body system, further improving computational efficiency. The method provides a practical and forward-thinking solution for the design of Mars parachutes.

Fast Aerodynamic Prediction of Airfoil with Trailing Edge Flap Based on Multi-Task Deep Learning

Conventional methods for solving Navier–Stokes (NS) equations to analyze flow fields and aerodynamic forces of airfoils with trailing edge flaps (TEFs) are known for their significant time cost. This study presents a Multi-Task Swin Transformer (MT-Swin-T) deep learning framework tailored for swift prediction of velocity fields and aerodynamic coefficients of TEF-equipped airfoils. The proposed model combines a Swin Transformer (Swin-T) for flow field prediction with a multi-layer perceptron (MLP) dedicated to lift coefficient prediction. Both networks undergo gradient updates through the shared encoder component of the Swin Transformer. Such a trained network model for computational fluid dynamics simulations is both effective and robust, significantly improving the efficiency of complex aerodynamic shape design optimization and flow control. The study further investigates the impact of integrating multi-task learning loss functions, skip connections, and the network’s structural design on prediction accuracy. Additionally, the effectiveness of deep learning in improving the aerodynamic simulation efficiency of airfoils with TEF is examined. Results demonstrate that the multi-task deep learning approach provides accurate predictions for TEF airfoil flow fields and lift coefficients. The strategic combination of these tasks during network training, along with the optimal selection of loss functions, significantly enhances prediction accuracy compared with the single-task network. In a specific case study, the MT-Swin-T model demonstrated a prediction time that was 1/7214 of the time necessitated by CFD simulation.

Shape Optimization Design Method of High-Performance Multibeam Antenna for Mixed-Payload Communication Satellite

Shape Optimization Design Method of High-Performance Multibeam Antenna for Mixed-Payload Communication Satellite

Multi-objective optimization of variable-stiffness composite for CFRP-winding buckle arrestor by using NSGA-Ⅲ

This study introduces a multi-objective optimization method utilizing the NSGA-III algorithm to tailor the fiber shape of variable-stiffness CFRP (Carbon Fiber Reinforced Plastics) shell structures. Combined with offshore oil and gas engineering, this method is employed to perform fiber shape optimization design for CFRP-winding buckle arrestors. Based on cubic polynomial path functions' contour lines, curved fibers are represented and fitted using the Curvature Minimum Bi-Arc (CMBiArc) interpolation NURBS curve method. Employing the NSGA-III algorithm, the fiber shapes of a CFRP laminate are optimized under manufacturing constraints, targeting mean compliance, fundamental frequency, and fiber curvature. With the study of numerical modeling, buckling crossover mode and arresting efficiency, multi-objective optimization is carried out for fiber shape of CFRP-winding buckle arrestors designed for subsea pipelines. With the goal of maximizing arresting efficiency, structural fundamental frequency, and minimizing fiber curvature, the method yields an enhanced CFRP-winding arrestor design, which demonstrates a high practicability through a layered design approach. By parametric study of optimization result and comparison with slip-on arrestor, the feasibility of the optimization method and the practical value of the novel improved arrestor are substantiated.

Experimental optimization of butterfly-shaped film cooling hole configuration with a 30 degree injection angle

Film cooling is one of the external cooling techniques that is widely applied to the hot-gas path components of a gas turbine, forming a thin film of a coolant on the surface to prevent the direct convective heat transfer between combustion gas and components. The film cooling effectiveness (FCE) is significantly influenced by the geometry of the injection hole. Therefore, it is important to adjust the shape parameters in order to derive the optimal hole configuration under given flow conditions. In a previous study, a butterfly-shaped film cooling hole configuration (BSHC), which combines the advantages of fan-shaped holes and anti-vortex holes, was proposed. In this study, an investigation into the optimal shape design of the BSHC was performed using the design of experiments. The forward expansion angle, lateral expansion angle, and twisted angle were defined as design variables. Before the optimization, the effect of each design variable on local and averaged FCE was analysed. Generally, a high FCE could be obtained when the forward expansion angle was small within a range of 7⁰ - 15⁰. However, at high blowing ratios, high effectiveness was also observed even with a large forward expansion angle. Both the lateral expansion angle and the twisted angle had high FCE near the centre point, 11⁰ and 20⁰, respectively. The response surface of the overall averaged FCE was predicted using the Kriging model. The optimized BSHC under a density ratio of 2.0 and blowing ratio of 2.0 was determined and named OPT BSHC. The OPT BSHC showed 8.6 % and 10.5 % higher FCE respectively, compared to two types of the optimized fan-shaped holes that were optimized under the same conditions.

Optimal shape design of printing nozzles for extrusion-based additive manufacturing

The optimal design seeks the best possible solution(s) for a mechanical structure, device, or system, satisfying a series of requirements and leading to the best performance. In this work, optimized nozzle shapes have been designed for a wide range of polymer melts to be used in extrusion-based additive manufacturing, which aims to minimize pressure drop and allow greater flow control at large extrusion velocities. This is achieved with a twofold approach, combining a global optimization algorithm with computational fluid dynamics for optimizing a contraction geometry for viscoelastic fluids and validating these geometries experimentally. In the optimization process, variable coordinates for the nozzle’s contraction section are defined, the objective function is selected, and the optimization algorithm is guided within manufacturing constraints. Comparisons of flow-type and streamline plots reveal that the nozzle shape significantly influences flow patterns. Depending on the rheological properties, the optimized solution either promotes shear or extensional flow, enhancing the material flow rate. Finally, experimental validation of the nozzle performance assessed the actual printing flow, the extrusion force and the overall print control. It is shown that optimizing the nozzle can significantly reduce backflow-related pressure drop, positively impacting total pressure drop (up to 41 %) and reducing backflow effects. This work has real-world implications for the additive manufacturing industry, offering opportunities for increased printing speeds, enhanced productivity.

Tuning of idiophones using shape optimization on finite and boundary element 1D models

We address the multi-modal tuning of idiophones and approach it as a shape optimization design problem. The Finite Element Method (FEM) and the Boundary Element Method (BEM), are adopted to discretize continuous models and lead to eigenvalue problems for the shape optimization of both the idiophone vibrating bars and the resonators. The methods presented here consist of two main components. The first component involves solving the eigenproblem of a discrete dynamical system that approximates a real idiophone bar (beam) or a resonator (acoustic tube), while the second component is the implementation of an appropriate design procedure to achieve the desired frequency ratios of the bar and resonator eigenfrequencies through optimization. For the shape optimization problem, both a gradient algorithm and a population–based algorithm are tested. We introduce the use of analytically computed sensitivity indices, which significantly accelerate the optimization when gradient–based algorithms are used in conjunction with the FEM. For illustrative purposes, the presented methods are applied to 1D formulation however, these can be expanded in a straightforward way to more involved/realistic 2D or 3D models.

The Current Design for Additive Manufacturing Research Frontier

Design for additive manufacturing (DFAM) seeks to develop designs that take advantage of the unique capabilities of additive manufacturing (AM) processes to maximize benefits. In this paper, several issues at the frontier of DFAM research are highlighted. First, the need is described to include as-manufactured mechanical and other physical properties, such as topology and shape optimization and generative design, during computational design. AM processes rarely produce parts with homogeneous composition and isotropic properties, so design methods and tools should not assume them. Second, the topic of designing for the AM process chain is important since AM-fabricated parts typically need postprocessing operations, such as support removal, finish machining, heat treatments, etc. DFAM methods need to incorporate the entire process chain, not just the AM process, which is explored with an example from metal powder bed fusion. Third, potentially, the largest benefit of AM can be realized by radically rethinking product architectures. Examples of an electric motorcycle and an assistive exosuit illustrate the ideas and potential benefits. Finally, some thoughts on design for 4D printing are offered, specifically for 3D printed morphing and deployable systems that utilize the shape memory effect.

The Key Path of the Shape Optimization Design of Isotropic Material Pressure Vessels

The Key Path of the Shape Optimization Design of Isotropic Material Pressure Vessels