Shape Optimization Research Articles

RANS-Based Aerodynamic Shape Optimization of a Wing with a Propeller in Front of the Wingtip

Accounting for propeller–wing interaction allows for the design of more efficient propeller aircraft through strategic propulsion integration. In this paper, the cruise drag of a wing with a propeller located in front of the wingtip is minimized using twist and airfoil-shape design variables. Reynolds-averaged Navier–Stokes computational fluid dynamics with an actuator-disk approach is used for the flow simulations, and a gradient-based algorithm is used for the optimization. Changing the rotation direction of the propeller and optimizing the twist and airfoil shapes of the wing are found to impact the aerodynamic performance significantly, as expected. However, optimizing the wing while accounting for the propeller slipstream during optimization provides little benefit over optimizing it without accounting for the propeller slipstream—a difference of less than one drag count.

Scalar Field Prediction on Meshes Using Interpolated Multi-Resolution Convolutional Neural Networks

Abstract Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field prediction can be faster than traditional finite element methods. However, current data-driven techniques to predict scalar fields are limited to a fixed grid domain, instead of arbitrary mesh structures. In this work, we propose a method to predict scalar fields on arbitrary meshes. It uses a convolutional neural network whose feature maps at multiple resolutions are interpolated to node positions before being fed into a multilayer perceptron to predict solutions to partial differential equations at mesh nodes. The model is trained on finite element von Mises stress fields, and once trained it can estimate stress values at each node on any input mesh. Two shape datasets are investigated, and the model has strong performance on both, with a median R-squared value of 0.91. We also demonstrate the model on a temperature field in a heat conduction problem, where its predictions have a median R-squared value of 0.99. Our method provides a potential flexible alternative to finite element analysis in engineering design contexts. Code and datasets are available at: https://github.com/kevinferg/sfp-cnn.

Structural Optimization Design of Magnetoelectric Thin-Film Antenna for Bandwidth and Radiation Enhancement.

The acoustically actuated nanomechanical magnetoelectric (ME) antennas represent a promising new technology that can significantly reduce antenna size by 1-2 orders of magnitude compared to traditional antennas. However, current ME antennas face challenges such as low antenna gain and narrow operating bandwidth, limiting their engineering applications. In this paper, we enhance the bandwidth and radiation performance of ME antennas through structural optimization, leveraging theoretical analysis and numerical simulations. Our findings indicate that optimizing the inner diameter of the ring-shaped ME antenna can elevate the average stress of the magnetic layer, leading to improved radiation performance and bandwidth compared to circular ME antennas. We establish an optimization model for the radiation performance of the ME antenna and conduct shape optimization simulations using COMSOL Multiphysics. The results of the Multiphysics field optimization align with the stress concentration theory, demonstrating a strong correlation between the radiation performance and bandwidth of the ME antenna with the average stress of the magnetic film. The resonant frequency in the thickness vibration mode is determined to be 170 MHz. Furthermore, shape optimization can enhance the bandwidth by up to 104% compared to circular ME antenna structures of the same size.

Fuel consumption and trailing-edge noise tradeoff studies via mission-based airfoil shape optimization

Aerodynamic drag is often used as a proxy for fuel consumption in aircraft design. However, the aeroacoustic byproduct of airfoil design, such as trailing-edge noise (TEN), is yet to be considered in aircraft applications, despite its inclusion in wind turbine designs. To explore the impact of TEN in airfoil design for aircraft, we establish a mission-based aerodynamic shape optimization framework. A surrogate-based detailed flight mission analysis (that can simulate a flight mission from takeoff to landing) is incorporated into the optimization framework to obtain realistic flight conditions during takeoff and landing—which are important to assess TEN metrics—and calculate accurate fuel consumption, where both are used to evaluate the objective function. To assess its effectiveness, we compare the results against those of the conventional single-point optimization. Not surprisingly, the mission-based optimization simultaneously reduces fuel consumption and TEN, while the single-point optima (performed at the low Mach region) reduce TEN at the expense of higher fuel consumption. This is due to the tradeoff between aerodynamic performance in the transonic region and aeroacoustic performance in the low Mach region, which cannot be properly analyzed without including flight mission analysis in the optimization loop.

Optimization of cantilever piezoelectric harvester to triangular shape with material reduction using finite element analysis

The paper studies the piezoelectric output performance of a piezoelectric harvester with four piezoceramic layers, assessing if the piezoelectric material can be reduced. The shape optimization regards cantilevers with trapezoidal or triangular longitudinal sections, maintaining comparable electric response with the original rectangular structure. The piezoelectric material is subjected to maximum mechanical stress in the fixed constrained area, decreasing gradually down to null stress towards the free tip. It is worthwhile to study if the material reduction would result in an increased effectiveness in terms of voltage output per unit volume of piezoelectric material. The simulations conducted in COMSOL Multiphysics employ Structural Mechanics – Piezoelectric Devices module, in a Multiphysics approach through Piezoelectric Effect, coupling Solid Mechanics with Electrostatics. It was found that the electric response increases per unit volume of piezoelectric material in triangular configuration with material reduction. A comparable voltage output is obtained after reducing the amount of piezoceramic material towards the free tip, while using an inertial mass of the same value. Hence, the piezoelectric material is used more effectively in the case of triangular cantilever with material cutdown than the traditional rectangular shaped cantilever. The paper also addresses shape optimization while maintaining the same mechanical stress, studying the response when increasing the tip mass for the purpose. All the structures render an even more significantly increased power output for matching optimum load resistor.

2-D shape optimization of auxiliary anode for ICCP

In this paper, to determine the influence of the shape of the auxiliary anode on the protection potential distribution in an impressed current cathodic protection (ICCP) system, an electrochemical and a level-set optimization method were combined to optimize the shape of the auxiliary anode. To accomplish this, the square of the deviation between the potential of the structure and the protection potential was used as the objective function, and the level set theory was employed to develop the anode shape. Following a set number of iterations, the optimized anode shape was obtained. Using the optimized anode, a current was injected into the anode surface, and the potential distribution was calculated. The experimental results showed that the potential distribution of the protected surface was uniform, and it could fully protect the protected structure's surface, which helped to avoid overprotection or underprotection.

Data-driven aerodynamic shape design with distributionally robust optimization approaches

We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. DRO aims to minimize the worst-case expected performance in a set of distributions that is informed by observed data with uncertainties. Building on the findings of the work Gotoh, et al. (2018), we study the connections between a class of DRO and robust design optimization, which is classically based on the mean–variance (standard deviation) optimization formulation pioneered by Taguchi. Our results provide a new perspective to the understanding and formulation of robust design optimization problems. It enables data-driven and statistically principled approaches to quantify the trade-offs between robustness and performance, in contrast to the classical robust design formulation that captures uncertainty only qualitatively. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

Optimal potential shaping on SE(3) via neural ordinary differential equations on Lie groups

This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization problem on Lie groups. A gradient descent optimization algorithm is presented to tackle the optimization numerically. Our algorithm is scalable, and applicable to any finite-dimensional Lie group, including matrix Lie groups. By representing the system at the Lie algebra level, we reduce the computational cost of the gradient computation. In an extensive example, optimal potential energy shaping for control of a rigid body is treated. The optimal control problem is phrased as an optimization of a neural ODE on the Lie group SE(3), and the controller is iteratively optimized. The final controller is validated on a state-regulation task.

Shape optimization of autonomous underwater helicopters based on different parameter curves and various optimization algorithms

This study aimed to compare the non-uniform rational B-spline (NURBS) and Bezier curves to design the shape of an autonomous underwater helicopter (AUH). Currently, there is no established method for AUH shape design. The optimal solutions obtained from both curves were compared to evaluate their performance. A parametric model was constructed to determine the design variables of the two curves. Computational fluid dynamics was used to solve the resistance values of different shapes. Sample points were generated using the design of the experimental approach, and an approximate model was established using the radial basis function neural network method. Based on the combinatorial optimization strategy, three intelligent optimization algorithms were used for the global search. Then, the resulting solution was used as the starting point for a local search to obtain the global optimal solution. The resistance optimal solutions achieved by employing the NURBS and Bezier curves were 25.2% and 24.1% smaller than the initial values, respectively. These findings indicate that, within the design parameters of this study, the shape design approach using the NURBS curve yields superior performance for the AUH.

Improving the energy efficiency and carbon dioxide reduction of a long-haul bus through aerodynamic design optimization

<p>Exhaustion of fossil fuel resources, inconsistent fuel costs and the difficulty of adopting electric vehicle technology in commercial vehicles support the idea that there is an opportunity for research in public transit regarding the correlation between energy efficiency and aerodynamic drag. The turbulent external airflow over a bus at high speeds impacts acceleration, speed, and fuel economy. The fundamental bus's design is intended to carry enough passengers for a reasonable run. Envisaging the factors influencing aerodynamic drag is defiant due to the convoluted relationship between the moving bus and the air. Consequently, a comprehensive numerical and experimental exploration is executed on the bodywork of a bus to improve its aerodynamic efficiency. The aerodynamic drag is directly proportional to the variations in the air density, frontal area, freestream velocity and the drag coefficient. Minimal design reforms are performed on a distinctive long-haul bus. The exertion aims to minimize the drag coefficient, thereby improving the flow characteristics of the bus's bodywork. Through the shape optimization of the bus's bodywork, the modified design has attained a forty-five percent reduction in the drag coefficient. This substantial reduction in drag coefficient directly impacts the reduction of drag force, energy efficiency improvement, and carbon emissions reduction.</p>

End-to-end optimization of optical communication systems based on directly modulated lasers

The use of directly modulated lasers (DMLs) is attractive in low-power, cost-constrained short-reach optical links. However, their limited modulation bandwidth can induce waveform distortion, undermining their data throughput. Traditional distortion mitigation techniques have relied mainly on the separate training of transmitter-side pre-distortion and receiver-side equalization. This approach overlooks the potential gains obtained by simultaneous optimization of the transmitter (constellation and pulse shaping) and receiver (equalization and symbol demapping). Moreover, in the context of DML operation, the choice of laser-driving configuration parameters such as the bias current and peak-to-peak modulation current has a significant impact on system performance. We propose, to our knowledge, a novel end-to-end optimization approach for DML systems, incorporating the learning of bias and peak-to-peak modulation current to the optimization of constellation points, pulse shaping, and equalization. The simulation of the DML dynamics is based on the use of the laser rate equations at symbol rates between 15 and 25 Gbaud. The resulting output sequences from the rate equations are used to build a differentiable data-driven model, simplifying the calculation of gradients needed for end-to-end optimization. The proposed end-to-end approach is compared to three additional benchmark approaches: the uncompensated system without equalization, a receiver-side finite impulse response equalization approach, and an end-to-end approach with learnable pulse shape and nonlinear Volterra equalization but fixed bias and peak-to-peak modulation current. The numerical simulations on the four approaches show that the joint optimization of bias, peak-to-peak current, constellation points, pulse shaping, and equalization outperforms all other approaches throughout the tested symbol rates.

Noninterferometric rotational test of the continuous spontaneous localization model: Enhancement of the collapse noise through shape optimization

Noninterferometric rotational test of the continuous spontaneous localization model: Enhancement of the collapse noise through shape optimization

Numerical two-dimensional optimization of a cylindrical fuselage for bioinspired unmanned aerial vehicle based on non-dominated sorting genetic algorithm-II

To achieve an aerodynamically efficient design of fuselage for bioinspired unmanned aerial vehicles (UAV), the development of a systematic method is of paramount need. This work presents a multiobjective optimization study for shape parameterization of a 2D fuselage of foldable flapping wing UAV in low Reynolds number (2e05) flight conditions. The novelty of the research work lies in integrating S1223 airfoil characteristics for predicting the efficient shape design of the fuselage. This paper offers four sections; (i) the validation of the ANSYS Fluent model with experiment, (ii) the exploration of design variables using Design of Experiment (Sparse Grid Initialization), (iii) the implementation of response surface method (Genetic Aggregation) to know about dimensional sensitivity among independent and dependent variables and (iv) the application of multiobjective optimization method i.e. NSGA II to optimize the drag and lift coefficient. To identify the superiority, a comparative study between the original and optimized fuselage is presented considering many parameters like pressure contours, velocity contours, pressure coefficients, and streamlines representations. It is evident from various results that the 2D optimum shape significantly minimizes the drag coefficient and increases the lift coefficient. This work also makes room for 3D shape optimization, which helps in prototype fabrication for real-time flight conditions.

The aerodynamic optimization of hypersonic vehicles with the proper-orthogonal-decomposition-based CST method

The flight performance of traditional hypersonic vehicles is limited to a specified incoming flow condition, their aerodynamic performance significantly deteriorates outside of the design condition. We construct a data-driven design framework for aerodynamic shape optimization of hypersonic vehicles, which can be used to improve the current flexibility of designing hypersonic vehicles based on the existing shockwave shape or flowfield. The framework uses a class function/shape function transformation to set parameters for the control sections of the vehicle, then the dimensions of the parameter matrix are reduced by using the proper orthogonal decomposition, and the surrogate model with improved expectations is combined to carry out the aerodynamic shape optimization of hypersonic vehicles. The hypersonic aerodynamic optimization design of NACA 0012 airfoil is conducted, which verifies the high efficiency of the optimization method. The single-point and multi-point aerodynamic optimization designs for the Hypersonic Technology Vehicle-2 (HTV-2) type are conducted. The correlation analysis to the fundamental modes of control sections and lift-to-drag ratio is performed, which verifies the accuracy of the design. Completed the single-point and multi-point optimized design of the entire vehicle considering 48 design variables and geometry restrictions with volume not less than 95% of the baseline. The single-point optimization increases the lift-to-drag ratio by 10.91%, and the multi-point optimization ensures that the aerodynamic performance is improved at all flight conditions and reduces the drag coefficient by 4.1% at the large angle of attack condition. The vehicle shape change rule that is controlled by the positively correlated and negatively correlated fundamental modes for the three control sections coincides with the optimized trend. The study demonstrated the effectiveness and practicality of the framework in the aerodynamic design of hypersonic vehicles.

Asymptotic properties of an optimal principal Dirichlet eigenvalue arising in population dynamics

We consider a shape optimization problem related to the persistence threshold for a biological species, the unknown shape corresponding to the zone of the habitat which is favorable to the population. Analytically, this translates in the minimization of a weighted eigenvalue of the Dirichlet Laplacian, with respect to a bang-bang indefinite weight. For such problem, we provide a full description of the singularly perturbed regime in which the volume of the favorable zone vanishes, with particular attention to the interplay between its location and shape.First, we show that the optimal favorable zone shrinks to a connected, nearly spherical set, in C1,1 sense, which aims at maximizing its distance from the lethal boundary. Secondly, we show that the spherical asymmetry of the optimal favorable zone decays exponentially, with respect to a negative power of its volume, in the C1,α sense, for every α<1. This latter property is based on sharp quantitative asymmetry estimates for the optimization of a weighted eigenvalue problem on the full space, of independent interest.

Computational Analysis of Concept Autonomous Heavy Vehicle to Reduce Drag Using Shape Optimization Technique and Add-On Devices

Computational Analysis of Concept Autonomous Heavy Vehicle to Reduce Drag Using Shape Optimization Technique and Add-On Devices

Auxiliary Heat System Design and Off-Design Performance Optimization of OTEC Radial Inflow Turbine

In this paper, solar energy is used as the auxiliary heat source of the ocean thermal energy radial inflow turbine, and the thermodynamic model of the circulation system is established. In addition, the ejector is introduced into the ocean thermal power generation system, and the process simulation is carried out using Aspen Plus V12. To address performance attenuation of the radial turbine under varying working conditions, shape optimization of a 30 kW OTEC radial turbine was conducted. Finally, the off-design performance variation in the radial inflow turbine is analyzed in the presence of a solar auxiliary heat source. The results show that the use of an auxiliary heat source can effectively improve the cycle efficiency of the system and is also conducive to the stable operation of the radial turbine. Under the condition of auxiliary heat source, the system cycle efficiency is increased by 2.269%.

Opportunities to use textile waste for the production of acoustic panels

There are many indoor and outdoor areas where one encounters acoustic discomfort. In this study, the design possibilities of a passive acoustic panel with macro-openings are investigated. An acoustic panel which absorbs a defined frequency of sound can be created when a suitable combination of acoustic absorption affecting parameters is found. These optimum parameters for a panel with macro holes were sought by means of experimental research regarding: the type of raw material suitable for the production of the components of the acoustic panel, the optimal hole shapes, their size and positioning on the panel lid, the possibility of using shredded textile from unsorted textile waste. The experiments in which the influence of the hole size and placement on the acoustic absorption was investigated were verified using a theoretical electrical equivalent circuit model created in the MathCad programming environment. The study found that the commonly used perforated panels made of Plexiglas can be fully replaced by panels made of shredded unsorted textile waste. It has also been shown that the shapes of the holes which can act as a design element can have various combinations, i.e. as long as the same percentage of perforation is maintained, the size of the circular holes or the shape of the slotted holes do not matter, as their acoustic absorption is within approximately the same range. The findings published in the study can help in the design of passive panels for both interiors and exterior use.

NUMERICAL STUDY OF THE RESISTANCE REDUCTION IN HYBRID MINI-SUBMARINE

Hybrid mini-submarine is a single innovative ship combining the concepts of conventional fast ships, hydrofoils, and submarine with the specific mission of safeguarding national sovereignty. This study was conducted to analyze the reduction of resistance in this mini-submarine by examining the positioning and shape of NACA hydrofoils. The process involved adjusting the positions of NACA hydrofoils and incorporating different configurations. This was indicated by the inclusion of nine speed configuration in the hydrofoil mode, eight in the conventional mode, and five in the submarine mode. Moreover, Computational Fluid Dynamics (CFD) simulation was applied for analysis using the Ansys CFX software. The results showed that the positioning of the NACA hydrofoils at close proximity reduced the resistance. The selection of symmetrical and slender configuration was also observed to optimize the reduction of resistance. Moreover, the combination of position and NACA hydrofoil 0012 produced an average resistance reduction of up to 12.52%. The configured model successfully reduced the total ship resistance and also identified the optimal position and shape configuration for the NACA hydrofoils. These findings provided valuable insights into the components and characteristics of total ship resistance and served as a valuable reference for further research on the development of maritime security technology.

Experimental investigation and validation of strength-based topology and fiber path optimization in additively manufactured continuous fiber reinforced composites

Material extrusion-based fused filament fabrication (FFF) is a widely used additive manufacturing (AM) technology that offers design freedom to fabricate intricate, robust, and lightweight parts when used with continuous carbon fiber (CCF) reinforced filaments. FFF is well-suited for optimization methods, as designers can specifically tailor the positioning of CCF filaments, albeit within certain manufacturing limitations. This study integrates experiments and finite element analysis (FEA) to investigate strength-based optimization methods applied to two benchmark structural domains and loading scenarios. Two methods were used to concurrently design the shape or topology and fiber paths: shape optimization using the level-set method, and topology optimization using both density-based solid orthotropic material with penalization (SOMP) and level-set methods. CCF filaments were printed to follow the optimized fiber paths, and a discontinuous fiber reinforced filament was used to fill in the remaining gaps. The parts were then compression molded for full consolidation, followed by testing for their stiffness and failure loads. FEA predicted locations and magnitudes of failure with reasonable accuracy, even in regions with complex stress states and fiber paths. X-ray micro-computed tomography (µCT) examination of failed coupons showed that fiber flow (deviations) during compression molding occurred and impacted parts’ performance. Finally, comparing designs optimized for stiffness versus strength showed premature failures due to stress concentrations in stiffness-optimized designs. This study underscores the critical need for integrating proper optimization strategies with realistic AM constraints and processing-induced defects to enhance the performance and reliability of CCF reinforced AM parts.