Shape Optimization Research Articles

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

Mitigating solder voids in quad flat no-lead components: A vacuum reflow approach

As global demand for high-efficiency automotive electronics grows, enhanced heat dissipation and reliability are essential to meet the energy demands of high-computation applications. Void formation in solder joints poses significant challenges, reducing thermal conductivity and joint strength. In response, this study optimizes the vacuum reflow process parameters and stencil aperture design to mitigate voids in Quad Flat No-Lead (QFN) packages, which are widely adopted for their heat dissipation capabilities.Using the Taguchi method, we determined the optimal stencil aperture shapes and reflow conditions for two thermal pad sizes in QFNs. For the large thermal pad (5.24 mm × 4.5 mm), the optimal parameters included a fence-type aperture covering 85 % of the pad area, vacuum pressure of 50 mbar, 10-s vacuum duration, and a fully open vacuum valve. For the small thermal pad (1.6 mm × 4.2 mm), optimal parameters were a fully covered aperture at 85 % of the pad area, 50 mbar vacuum pressure, 5-s vacuum duration, and fully open valve. Results demonstrated that these optimized conditions effectively reduced void ratios to 0.7 % for the large pad and 0.5 % for the small pad, meeting industry standards for automotive applications.

Discharge electrode shape optimization for the performance improvement of electrostatic precipitator with six-branched spike discharge electrode and hexagonal collecting plate

Discharge electrode shape optimization for the performance improvement of electrostatic precipitator with six-branched spike discharge electrode and hexagonal collecting plate

Towards cell-adhesive, 4D printable PCL networks through dynamic covalent chemistry.

In recent years, the development of biodegradable, cell-adhesive polymeric implants and minimally invasive surgery has significantly advanced healthcare. These materials exhibit multifunctional properties like self-healing, shape-memory, and cell adhesion, which can be achieved through novel chemical approaches. Engineering of such materials and their scalability using a classical polymer network without complex chemical synthesis and modification has been a great challenge, which potentially can be resolved using biobased dynamic covalent chemistry (DCC). Here, we report a scalable, self-healable, biodegradable, and cell-adhesive poly(ε-caprolactone) (PCL)-based vitrimer scaffold, using imine exchange, free from the limitations of melting transitions and supramolecular interactions in 4D-printed PCL. PCL's typical hydrophobicity hinders cell adhesion; however, our design, based on photopolymerization of PCL-dimethacrylate and methacrylate-terminated vanillin-based imine, achieves a water contact angle of 64°. The polymer network, fabricated in varying proportions, exhibited a co-continuous phase morphology, achieving optimal shape fixity (91 ± 1.7%) and shape recovery (92.5 ± 0.1%) at physiological temperature (37 °C). Additionally, the scaffold promoted cell adhesion and proliferation and reduced oxidative stress at the defect site. This multifunctional material shows the potential of DCC-based research in developing smart biomedical devices with complex geometries, paving the way for novel applications in regenerative medicine and implant design.

A CNN-PINN-DRL driven method for shape optimization of airfoils

A CNN-PINN-DRL driven method for shape optimization of airfoils

Shape Optimization of Harmonic Helicity in Toroidal Domains

Shape Optimization of Harmonic Helicity in Toroidal Domains

A programmable environment for shape optimization and shapeshifting problems.

Soft materials underpin many domains of science and engineering, including soft robotics, structured fluids, and biological and particulate media. In response to applied mechanical, electromagnetic or chemical stimuli, such materials typically change shape, often dramatically. Predicting their structure is of great interest to facilitate design and mechanistic understanding, and can be cast as an optimization problem where a given energy function describing the physics of the material is minimized with respect to the shape of the domain and additional fields. However, shape-optimization problems are very challenging to solve, and there is a lack of suitable simulation tools that are both readily accessible and general in purpose. Here we present an open-source programmable environment, Morpho, and demonstrate its versatility by showcasing a range of applications from different areas of soft-matter physics: swelling hydrogels, complex fluids that form aspherical droplets, soap films and membranes, and filaments.

Pulsation Analysis of Hose Pumps with Different Roller Counts Based on Two-Way FSI

Xinjiang, as a major agricultural region, offers extensive application potential for hose pumps, given their excellent performance as fertilization devices. Analyzing the pulsation characteristics of hose pumps during operation is valuable for reducing noise and extending pump service life. To investigate the pulsation characteristics and unsteady flow of hose pumps with different roller numbers, this study adopts a bidirectional fluid-structure interaction (FSI) method and utilizes ANSYS 19.0 commercial finite element software to analyze the outlet and inlet pressure pulsations, outlet flow velocity pulsations, and the distribution of the flow field at the intermediate plane for both two-roller and three-roller pumps transporting high and low Reynolds number fluids under the same working conditions. It was observed that the three-roller pump exhibited higher outlet pressure compared with the inlet and that the pulsation intensity was lower in the three-roller pump than in the two-roller pump under the same conditions, with an analysis provided on the reasons for this phenomenon. This study offers theoretical support for the selection and further optimization of hose pump designs. To further reduce the negative effects of pulsations, it is recommended to increase the number of rollers in the design while also considering shape optimization of the pump casing or using feedback control systems to adjust and reduce pulsation intensity.

Chamber shape optimization for ultra-high-pressure water-jet nozzle based on computational fluid dynamics method and a data-driven surrogate model

The ultra-high-pressure (UHP) water-jet nozzle acts as one of the key units for the whole rotary sprayers, and its chamber shape plays a decisive role in improving the hydrodynamic performance of water jetting. Unfortunately, comprehensive and effective methods to optimize the nozzles’ chamber shape are still lacking. By coupling a data-driven surrogate model with metaheuristic optimizer, a computational fluid dynamics (CFD)-based optimization scheme aiming at fully enhancing the hydrodynamic performance of UHP nozzles was proposed in this paper. Firstly, to ensure optimization accuracy, an improved whale optimization algorithm (IWOA) was developed. It combines the chaotic opposition-based learning (COBL) and the Cauchy-Gaussian mutation simulated annealing algorithms, incorporating a nonlinear convergence and adaptive inertia weight mechanism. Then, to reduce CFD computational costs and accelerate calculation speed, a data-driven surrogate model based on IWOA-support vector machine (SVM) was proposed. Herein, the parameter gamma and the penalty coefficient in SVM model, are trained using IWOA. The IWOA-SVM model was constructed using optimal Latin hypercube design (Opt. LHD) to sample nozzle structures, with peak wall shear stress (as objective function) calculated via CFD method. Finally, this optimization scheme was applied to optimize the chamber shape of the original nozzle commonly used in ship rust removal. The results reveal that the chamber shape of the optimized nozzle can greatly enhance the water-jet hydrodynamic performance by raising the peak wall shear stress by 13.88%. Additionally, the IWOA-SVM model demonstrates the capability to evaluate hydrodynamic performance with a maximum error of 2.853%. Therefore, the proposed optimization scheme provides novel insights for the overall design and optimization of the UHP water-jet nozzle.

Ameliorated Chameleon Algorithm-Based Shape Optimization of Disk Wang–Ball Curves

The shape design and optimization of complex disk curves is a crucial and intractable technique in computer-aided design and manufacturing (CAD/CAM). Based on disk Wang–Ball (DWB) curves, this paper defines a novel combined disk Wang–Ball (CDWB) curve with constrained parameters and investigates the shape optimization of CDWB curves by using the multi-strategy ameliorated chameleon swarm algorithm (MCSA). Firstly, in order to meet the various shape design requirements, the CDWB curves consisting of n DWB curves are defined, and the G1 and G2 geometric continuity conditions for the curves are derived. Secondly, the shape optimization of CDWB curves is considered as a minimization problem with curve energy as the objective, and an optimization model is developed under the constraints of the splicing conditions. Finally, the meta-heuristic algorithm MCSA is introduced to solve the established optimization model to obtain the minimum energy value, and its performance is verified by comparison with other algorithms. The results of representative numerical examples confirm the effectiveness and competitiveness of the MCSA for the CDWB curve shape optimization problems.

Shape Optimization and Experimental Investigation of Glue-Laminated Timber Beams.

This study investigated the optimal shape of glue-laminated timber beams using an analytical model of a slender beam, taking into account the anisotropy of its strength properties as well as boundary conditions at the oblique bottom face of the beam. A control theory problem was formulated in order to optimize the shape of the modeled beam. Two optimization tasks were considered: minimizing material usage (Vmin) for a fixed load-carrying capacity (LCC) of the beam and maximizing load-bearing capacity (Qmax) for a given volume of the beam. The optimal solution was found using Pontryagin's maximum principle (PMP). Optimal shapes were determined using Dircol v. 2.1 software and then adjusted according to a 3D finite element analysis (FEA) performed in Abaqus. The final shapes obtained through this procedure were used in the CNC-based production of three types of nine beams: three reference rectangular beams, three Vmin beams, and three Qmax beams. All specimens were subjected to a four-point bending test. The experimental results were contrasted with theoretical assumptions. Optimization reduced material usage by ca. 12.9% while preserving approximately the same LCC. The maximization of LCC was found to be rather unsuccessful due to the significant dependence of the beams' response on the highly variable mechanical properties of GLT.

A Leadfield-Free Optimization Framework for Transcranially Applied Electric Currents.

Transcranial Electrical Stimulation (TES), Temporal Interference Stimulation (TIS), Electroconvulsive Therapy (ECT) and Tumor Treating Fields (TTFields) are based on the application of electric current patterns to the brain. The optimal electrode positions, shapes and alignments for generating a desired current pattern in the brain vary between persons due to anatomical variability. The aim is to develop a flexible and efficient computational approach to determine individually optimal montages based on electric field simulations. We propose a leadfield-free optimization framework that allows the electrodes to be placed freely on the head surface. It is designed for the optimization of montages with a low to moderate number of spatially extended electrodes or electrode arrays. Spatial overlaps are systematically prevented during optimization, enabling arbitrary electrode shapes and configurations. The approach supports maximizing the field intensity in target region-of-interests (ROI) and optimizing for a desired focality-intensity tradeoff. We demonstrate montage optimization for standard two-electrode TES, focal center-surround TES, TIS, ECT and TTFields. Comparisons against reference simulations are used to validate the performance of the algorithm. The system requirements are kept moderate, allowing the optimization to run on regular notebooks and promoting its use in basic and clinical research. The new framework complements existing optimization methods that require small electrodes, a predetermined discretization of the electrode positions on the scalp and work best for multi-channel systems. It strongly extends the possibilities to optimize electrode montages towards application-specific aims and supports researchers in discovering innovative stimulation schemes. The framework is available in SimNIBS.

Optimal Shape Design of 1D Fractional Order Heat Equation in Large Time

In this paper, we consider an optimal design problem for the 1D nonlocal heat equations involving the fractional Laplacian . The control here is the shape of the interval on which heat diffuses. We work in the geometric setting introduced by Šverák in [1] where the intervals under consideration are assumed to have a limited number of holes. Based on a -convergence approach, we can prove when \\frac{1}{2}$$\\end{document}]]>, the nonlocal parabolic optimal designs converge, in the complementary Hausdorff topology, to an optimal design for the corresponding stationary nonlocal elliptic equation when time tends to infinity.