Shape Optimization Research Articles

Bidirectional Pattern Recognition and Prediction of Bending-Active Thin Sheets via Artificial Neural Networks

Currently, active-bending structures and their shape optimization techniques have become a hot topic in the design of spatial structures and freeform buildings. However, their form-finding process is usually time-consuming, and the application of finite element methods (FEM) requires huge computational effort. In the face of these challenges, artificial intelligence techniques have great potential for application and bring many important advantages to this field. In this paper, we propose a novel, data-driven, bidirectional prediction method based on artificial neural networks. It can both forward infer the bending deformation shapes of a thin plate under specific complex conditions and reverse infer the boundary conditions necessary for a given bending shape. In comparison to traditional active-bending simulation, the proposed method is quicker and simpler to utilize during the design process and facilitates reverse predictions. Communication between design and construction can be facilitated to ensure quality and efficiency in the construction of relevant bent structural components. It is experimentally demonstrated that the network can control the mean value of prediction deviation below 40 mm for a 4 m × 0.5 m aluminum plate.

Simulation Study on the Navigation Resistance and Shape Optimization of a New Type of Amphibious Vehicle

Amphibious vehicles are important equipment used by emergency rescue teams to quickly pass through water networks. A numerical model of amphibious vehicle underwater navigation in the lower shell was established in this study using computational fluid dynamics, the Reynolds-averaged Navier–Stokes model, and the volume-of-fluid method to investigate the navigation performance of a new all-terrain all-water amphibious emergency rescue vehicle. The navigation resistance was calculated at different speeds. The characteristics of the flow field around the vehicle body were analyzed, and optimization measures for drag reduction by installing a stern flap were proposed. The simulation results show that the existing vehicle body has a relatively high navigation resistance, and the flow field of the amphibious vehicle body is significantly improved after using stern flaps with larger angles and sizes. When the stern flap angle was 38°, the drag-reduction effect was 23%, which effectively improved the navigation performance of the amphibious vehicle.

Enhancing Optical Sectioning in Structured Illumination Microscopy With Axially Confined Fringe Modulation

AbstractOptical sectioning structured illumination microscopy (OS‐SIM) is a fast, minimally invasive 3D imaging technique that has found widespread application in the biosciences. It is based on sample illumination with several illumination fringe patterns featuring distinct mutual phase shifts, from which an axially sectioned image is reconstructed. Its optical sectioning capability is commonly attributed to the attenuation of the fringe modulation of light collected from planes displaced from the focal plane. However, in addition to this effect, which is governed solely by the detection optics, optical sectioning can be further enhanced by confining the fringe modulation axially via partially coherent illumination (PCI). To establish guidelines for optimal illumination field shaping, both theoretically and experimentally are investigated, the optical sectioning strength of OS‐SIM upon variation of the two key parameters, modulation period and angular spectrum of the incident illumination. By using PCI with OS‐SIM, nearly fivefold and 1.4‐fold enhanced axial resolution have achieved for scattering (non‐fluorescent) and fluorescent samples, respectively. This work elucidates the optical sectioning mechanism of OS‐SIM and provides a perspective for further optimization.

Optimizing Designs of Structurally Stable Open-graded Aggregate Bases (OGAB) in Concrete Pavements

A stable, non-erodible, drainable base layer is crucial to maintain uniform support under concrete pavements and ensure satisfactory performance. This paper presents findings from a recent study aimed at investigating possible improvements in concrete pavement base layers in terms of stability, stiffness, and permeability. Moisture regimes in PCC pavement foundation layers and corresponding predicted pavement performance were first evaluated using different types of base course materials with varying hydraulic and mechanical properties. A previously validated discrete element method (DEM) model was subsequently employed for evaluating the gradation effect on both packing characteristics and load-carrying performance of unbound aggregate materials. The calibrated DEM model has the potential for optimizing the selection of size and shape properties of various types of unbound aggregates to achieve desired shear strength (stability) and drainage characteristics (drainability) for open-graded permeable aggregate base. DEM simulations were performed on different gradations chosen from the current Minnesota Department of Transportation (MnDOT) specified gradation band for unbound permeable aggregate base (UPAB). It was found that depending on the specific gradation and material hydraulic properties, different types of unbound permeable aggregate bases resulted in varying performance improvements. The benefits of maintaining adequate permeability and stability of base course proved to be evident. The DEM model simulation results indicated that a gravel to sand (G/S) ratio of 1.6 yielded the highest coordination number due to the achieved densest packing (indicated by the lowest porosity). Therefore, the optimal G/S ratio of 1.6 also determined previously from experimental results agreed well with the results of DEM simulations, which utilized three-dimensional polyhedral particles with realistic size distributions and aggregate shape properties. The use of such optimal size and shape properties is expected to achieve cost-effective open-graded aggregate base designs for long-life concrete pavements.

Parametric Search for Optimal Channel Shape for Swirling Blood Flow in the Heart and Main Vessels.

The study presents a numerical parametric investigation of flow structures in channels with a longitudinal-radial profile zRN = Const and a spherical dome at the base. The goal of the study was to examine the flow structures in these channels depending on the exponent N of the profile and the height of the dome, to determine the conditions that provide optimal centripetal swirling flow, analogous to blood flow in the heart chambers and major vessels. The investigation was conducted using a comparative analysis of flow structures in channel configurations zRN = Const, carried out in two stages. In the first stage, the convergence parameter N was varied from 1.25 to 2.75 to identify the value that ensures optimal flow conditions. In the second stage, for the established value of N, the dome height was varied from 2.5 to 15 mm to identify the beneficial effects associated with its presence. The method of investigation involved numerical modeling in a steady-state regime. The results of the study on the influence of the convergence parameter revealed that the profile zR2 = Const provides optimal conditions for the formation of swirling flow with minimal specific losses and a uniform distribution of velocity gradients. This channel configuration also showed the best agreement with the analytical solutions for Burgers' vortex, confirming its effectiveness in the static approximation of flows. The parametric investigation of dome height indicated that an optimal dome height of 7 mm contributes to the smoothing of velocity gradients and the reduction of viscous losses due to the optimal enhancement of the centripetal swirling flow scale.

Immediate Hybrid Breast Reconstruction: Dual-plane approach using prepectoral implants and retro-pectoral fat grafting

Background: Implant-based breast reconstruction (BR) is to date the most popular reconstructive modality. The aim of the study was to evaluate the immediate hybrid one-stage BR technique, with a dual-plane approach, using prepectoral implants and retro-pectoral autologous fat transfer (AFT). Methods: We prospectively enrolled patients scheduled for immediate BR using a hybrid approach, which included retro-pectoral AFT and prepectoral breast implants (Group-A). This cohort was compared with a retrospective control group of patients who underwent immediate direct-to-implant BR without AFT (Group-B). Complications, hospitalization days, number of AFT procedures for a complete BR, aesthetic outcomes and patient’s satisfaction were analysed. Fat survival rate was assessed through comparison of preoperative and 6-months postoperative MRI. Results: 30 immediate BR were included in each group. The average amount of AFT in the retro-pectoral plane was 106.30 cc (SD 16.54), while the mean breast implant size was statistically higher in group B (p=0.00026). MRI assessment confirmed an average of 47.90 % (SD 0.14) retro-pectoral fat survival at 6 postoperative months. No statistically significant differences in term of complications and hospitalization days were observed (p>0.05), while a significant difference was observed regarding additional AFT sessions (p=0.00062). After a propensity score weighted analysis, surgeons and patients assessment showed a significant higher overall satisfaction in the active group. Conclusions: Immediate hybrid approach for one-stage BR, enabled the use of smaller breast implants, a decrease in AFT procedures with costs reduction, and yielded optimal breast shape and contour, by reducing step-off deformity and rippling alterations, without adding complications. Level of Evidence II

Analytical solutions for optimal photon absorption into inhomogeneous spin memories

Abstract We investigate for optimal photon absorption a quantum electrodynamical model of an inhomogeneously-broadened spin ensemble coupled to a single-mode cavity. Solutions to this problem under experimental assumptions are developed in the Schr"odinger picture without using perturbation theory concerning the cavity-spin interactions. Furthermore, we exploit the possibility of modulating the frequency and coupling rate of the resonator. We consider a one-photon input pulse and show some optimal scenarios, where exact formulas and numerical results are obtained for the absorption probabilities and the optimal pulse shapes. In particular, if the external loss dominates the internal loss of the cavity, we find the optimal cooperativity for different parameters and identify cases where absorption with a success probability larger than $99\%$ is achieved.

Optimization of Environmental Conditioning Equipment Based on Particle Swarm Optimization Algorithm and Genetic Algorithm

The purpose of this paper is to systematically analyze and design the appearance of the 3-in-1 environmental conditioning device by using particle swarm optimization algorithm and genetic algorithm. Firstly, the particle swarm optimization algorithm (PSO) is applied to simulate the indoor temperature change for the placement of air conditioners, the location of the inlet and outlet, and the direction of airflow to design the optimal shapes and sizes to improve the temperature control efficiency. Second, a genetic algorithm optimization model was constructed for the relationship between the shape of the air purifier and the purification effect, aiming to determine the best design that can maximize the purification effect. Next, an optimization analysis of the shape of the humidifier is introduced, and a multi-objective optimization model for the 3-in-1 device is developed using PSO to maximize energy efficiency, comfort, and air quality. The algorithms and models used in this paper not only enhance the comprehensive performance of the device, but also provide a scientific basis for future product development and promote the innovation and application of smart home devices.

Study on vortex-induced vibration response of large-scale two-lay steel trusses bridge under large wind angle of attack

With the advancement of urbanization, two-lay trusses bridges are widely used because of their good traffic capacity and structural performance. However, the aerodynamic behavior of this beam type is still in the exploratory stage. The local microclimate characteristics at the bridge site in mountainous cities are obvious, and it is easy to form a large wind angle of attack, which has a significant impact on the vortex-induced vibration (VIV) performance of the bridge. Therefore, this study takes a long-span two-lay steel trusses bridge in a mountainous city as the engineering background, and uses wind tunnel test and numerical calculation methods to study the changes of the static three-component force coefficient and VIV response of the main beam in the construction and completion state under the action of high wind angle of attack. The results show that the three-component force coefficient curves under different wind speeds are close to each other, and the Reynolds number effect is not obvious. The vibration test shows that the vertical bending VIV first occurs at +3° and +5°, and then two torsional VIV with different amplitudes occur. Both vertical bending and torsional VIV are simple harmonic vibrations with a single frequency, and the vertical bending VIV frequency is locked at 2.227 Hz, and the torsional VIV frequency is locked at 4.289 Hz, which are close to the natural frequency of the test model. Compared with +3°, the maximum amplitude of vertical bending VIV under +5° increases by 30.0 %, while the maximum amplitude of torsional VIV under high and low wind speed increases by 16.6 % and 12.7 % respectively, and the locking range is longer. It can be seen that the wind angle of attack has a significant effect on the VIV response of the main beam in the completion state. Especially, the trusses beam at a large angle is more sensitive to VIV, and it is more prone to large-scale and large-amplitude VIV. The research results can provide a theoretical basis for the aerodynamic shape optimization and provide a reference for the design of related bridges.

Curvature Determination Method for Diverging Acoustic Lens of Underwater Acoustic Transducer.

Underwater acoustic transducers need to expand the coverage of acoustic signals as much as possible in most ocean explorations, and the directivity indicators of transducers are difficult to change after the device is packaged, which makes the emergence angle of the underwater acoustic transducer limited in special operating environments, such as polar regions, submarine volcanoes, and cold springs. Taking advantage of the refractive characteristics of sound waves propagating in different media, the directivity indicators can be controlled by installing an acoustic lens outside the underwater acoustic transducer. To increase the detection range of an underwater acoustic transducer in a specific marine environment, a curvature-determining method for the diverging acoustic lens of an underwater acoustic transducer is proposed based on the acoustic ray tracing theory. The relationship equation between the original directivity indicators of the underwater acoustic transducer and the emergence angle in the specific environment is constructed, and the slope of the acoustic lens at different positions of the underwater acoustic transducer is obtained by a progressive solution. Then, the least squares polynomial fitting of the acoustic lens slope at all the refractive positions is carried out to obtain the optimal curvature of the acoustic lens. Experiments are designed to verify the effectiveness of the curvature determination method for the diverging acoustic lens of an underwater acoustic transducer, and the directivity indicators of acoustic lenses under different materials and different marine environments are analyzed. The experimental results show that the acoustic lens can change the directivity of the underwater acoustic transducer without changing the acoustic unit array, and the curvature of the acoustic lens directly affects the directivity indicators after refraction, so the method proposed in this paper has important reference value for determining the optimal shape of the diverging acoustic lens.

Gâteaux semiderivative approach applied to shape optimization of obstacle problems

Abstract Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs, as well as distributed, non-linear, non-convex and infinite-dimensional aspects, due to the shapes, which complicate setting up an optimality system and, thus, developing efficient solution algorithms. In this paper, we consider Gâteaux semiderivatives for the purpose of formulating optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the obstacle problem.

Analysis and application of a lower envelope method for sharp-interface multiphase problems

Abstract We introduce and analyze a lower envelope method (LEM) for the tracking of motion of interfaces in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides with exactly one of the functions. We show that a variety of complex lower-dimensional interfaces naturally appear in the process. The evolution of phases is then achieved by solving a set of transport equations. In the first part of the paper, we show several theoretical properties, give conditions to obtain a well-posed behaviour, and show that the level set method is a particular case of the LEM. In the second part, we propose a LEM-based numerical algorithm for multiphase shape optimization problems. We apply this algorithm to an inverse conductivity problem with three phases and present several numerical results.

Riemannian Shape Optimization of Thin Shells Using Isogeometric Analysis

ABSTRACTIn this contribution, we consider the optimal shape design of thin elastic shell structures based on a linearized shell model of Koiter's type, whose shape can be described by a surface immersed in three‐dimensional Euclidean space. We regard the set of unparametrized immersions of the surface as an infinite‐dimensional Riemannian shape space and perform optimization in this setting using the Riemannian shape gradient. Nonuniform rational basis splines (NURBS) are employed to discretize the shell and numerically solve the underlying equations that govern its mechanical behavior via isogeometric analysis. By representing NURBS patches as B‐spline patches in real projective space, NURBS weights can also be incorporated into the optimization routine. We discuss the practical implementation of the method and demonstrate our approach on the compliance minimization of a half‐cylindrical shell under static load and fixed area constraint.

Dust removal on solar panels of exploration rovers using Chladni patterns

The buildup of dust on solar panels has significantly reduced the operational lifespan and mission performance of exploration rovers, and traditional dust removal techniques have proven inadequate for the Martian environment. The present study proposes a novel method for removing dust from the solar panels of Mars exploration rovers using Chladni patterns, addressing the persistent issue of efficiency loss due to Martian dust accumulation. To overcome these challenges, the proposed method leveraged Chladni patterns, generated by specific frequencies, to effectively clear dust from the panels. We conducted experiments that identified optimal frequencies, frequency sequences, and plate shapes for dust removal, demonstrating the method’s effectiveness. In conclusion, our approach not only enhances the efficiency of solar panels but also has the potential to improve the overall performance and longevity of Mars exploration missions.

Mathematical modeling of occlusion load on a screw-retained bridge prosthesis on straight universal conical and flat abutments

In this mathematical experiment, a comparative study of microdeformations and von Mises equivalent stresses arising in the elements of two orthopedic bridge structures with different abutment shapes was conducted using the finite element method. The strength limits of both structures were also compared. The structures under study had the same external geometry and corresponded to two premolars and the first molar. The difference between the models under study was in the superstructures that are inserted and fixed in the implants and serve as a support for artificial crowns. The first model used flat superstructures (or flat abutments), while the second model used conical superstructures (or universal multi-units). The data obtained indicate the clinical significance of choosing the optimal abutment shape when planning surgical interventions and predicting subsequent patient treatment results.

Optimising surgical efficiency by designing lightweight skull-PSI assemblies and curved fixture plates for cranial reconstruction using FEA

Cranial reconstruction using implants is critical for protecting intracranial structures and restoring cerebral hemodynamics in cases of cranial defects caused by accidents, diseases or cancer. Patient-specific implants (PSIs) made from materials such as polyether-ether-ketone (PEEK), are required to be lightweight, high in strength and capable of mimicking the natural bone structure. Effective fastening mechanisms using the required number of fixture plates are essential for seamless integration between the PSI and the cavity of a defected skull for successful cranial reconstruction. This study explores the optimal number and shape of fixture plates required to join a Skull-PSI assembly, such that the overall weight of the PSI remains minimal, and to ensure that these assemblies do not fail when subjected to heavy external loads of 950 N. PEEK material was used for PSI, natural bone for the defected skull and Titanium Alloy (Ti-6Al-4 V) for the fixture plates. Conventional straight shaped fixture plates often require manual bending for correct fitment on the Skull-PSI curved surface, which increases a surgeon's time and effort. Curved shaped fixture plates were designed, to save on this time and effort and enhance the contact surface area with the Skull-PSI surface. Four, three and two numbered, straight and curved shaped fixture plates were investigated using Finite Element Analysis (FEA) techniques. Three numbered, curved shaped fixture plates were found to be optimal, to generate a 7-gram lightweight PSI that could successfully sustain external loads up-to 950 N without failure. Ultimately, these design improvements would benefit both patient and surgeon in aspects of surgery time and patient comfort.

A new tool for shape and structure optimization of soft materials.

A new tool for shape and structure optimization of soft materials.

Correction: Combined parameter and shape optimization of electric machines with isogeometric analysis

Correction: Combined parameter and shape optimization of electric machines with isogeometric analysis

How does optimal prey abundance shape space use by a territorial raptor?

Understanding predator-prey interactions is important to determine the inter-relationships between species. Optimal foraging theory states that predators balance out energy expended with the energy gained from their prey. In the Iberian Peninsula, the European rabbit (Oryctolagus cuniculus) is a key prey species for endangered Bonelli’s eagle (Aquila fasciata). Thus, it is vital to understand how changes in rabbit abundance can influence habitat selection and territory use by Bonelli’s eagle. We studied 11 radio-tagged Bonelli’s eagles in their territories in Catalonia (NE Iberian Peninsula) and analysed the relationship between rabbit relative abundance, habitat selection and territory use of eagles. Rabbit relative abundance varied between territories, with shrublands hosting more rabbits, and eagles preferred shrublands and open areas for foraging and avoided dense forests. Spatial use by territorial eagles correlated positively with rabbit abundance in rabbit-rich territories, thereby supporting the idea that prey availability influences habitat selection. This result confirms optimal foraging strategies given that open habitats including shrublands tended to host more rabbits, thus providing better opportunities for prey detection and capture. Therefore, maintaining rabbit populations and their habitats (i.e., preserving open Mediterranean shrublands) would seem to be crucial for Bonelli’s eagle conservation. Our findings improve our understanding of predator-prey interactions and highlight the relationship between habitat structure, prey abundance and predator behaviour. In addition, our results emphasize the need for targeted conservation strategies designed to safeguard endangered species such as Bonelli’s eagle and maintain ecosystem integrity.

Topology, Size, and Shape Optimization in Civil Engineering Structures: A Review

Topology, Size, and Shape Optimization in Civil Engineering Structures: A Review