Shape Optimization Research Articles

Flow induced form: Shape optimization of bridge piers using CFD analyses and adjoint method

This study investigates the optimization of cylindrical bridge pier geometry using a relatively new technique involving Computational Fluid Dynamics (CFD) and adjoint shape optimization methods. Initially, Reynolds Averaged Navier-Stokes (RANS) equations were used in CFD models, integrated with an adjoint algorithm to reshape the pier and reduce bed shear stress. This approach is hereinafter called the “Flow induced Form”, FiF, aiming to minimize shear stress on the bed while maintaining the pier's cross-sectional and projected areas in the flow direction. Subsequently, Large Eddy Simulation (LES) transient analyses assessed the performance of the optimized geometry. Results show a reduction of approximately 5% in the time average of maximum shear stresses on the bed and a reduction of around 50% in instantaneous maximum values compared to the original pier design. These improvements were achieved with minimal changes to the cross-sectional area and projected area of the original geometry (∼2%), considering that the load-bearing capacity of the bridge pier.

Shape optimization of a non-uniform piezoelectric bending beam for human knee energy harvester

Abstract Scavenging energy from the human body to provide a sustainable source for electronic devices has gained significant attention. Recently, scientists have focused on harnessing biomechanical energy from human motion. This study was dedicated to developing and optimizing a non-uniform piezoelectric bending beam-based human knee energy harvester. The bimorph non-uniform piezoelectric bending beam consisted of a non-uniform carbon fiber substrate and piezoelectric macro fiber composites. Compared to the uniform piezoelectric bending beam, the non-uniform piezoelectric beam can optimize the shape to improve the average strain, thus improving the energy harvesting efficiency. In this study, eight shape functions, including ellipse, sin, tanh, exponential function, parabola, trigonometric line, and bell curves, were investigated and optimized. The bell curve bending beam was selected and fabricated due to its good performance. Then, a benchmark platform was developed to test the deflection curve and reaction force when the nonuniform bending beam was compressed. Finally, to validate the design, experimental testing on three subjects was conducted when they were equipped with the harvester and walked on a treadmill. Testing results indicated that the non-uniform bending beam-based energy harvester can improve the energy harvesting efficiency by 28.57% compared to the uniform beam-based energy harvester. The output power can reach 18.94 mW when walking at 7.0 km h−1.

Deep Reinforcement Learning for Fluid Mechanics: Control, Optimization, and Automation

A comprehensive review of recent advancements in applying deep reinforcement learning (DRL) to fluid dynamics problems is presented. Applications in flow control and shape optimization, the primary fields where DRL is currently utilized, are thoroughly examined. Moreover, the review introduces emerging research trends in automation within computational fluid dynamics, a promising field for enhancing the efficiency and reliability of numerical analysis. Emphasis is placed on strategies developed to overcome challenges in applying DRL to complex, real-world engineering problems, such as data efficiency, turbulence, and partial observability. Specifically, the implementations of transfer learning, multi-agent reinforcement learning, and the partially observable Markov decision process are discussed, illustrating how these techniques can provide solutions to such issues. Finally, future research directions that could further advance the integration of DRL in fluid dynamics research are highlighted.

An experimental acoustofluidic system for analyzing boundary-driven acoustic streaming generated by flat and curved walls

While boundary-driven acoustic streaming in fluids surrounded by flat walls has been extensively studied in the literature, theoretical studies on boundary-driven acoustic streaming generated by curved walls have recently emerged. This paper aims to present a quantitative analysis of acoustic streaming fields driven by forces induced by both flat and curved walls. A semi-circular channel made of stainless steel was designed to serve as a model channel with both flat and curved boundaries. A multi-layered glass-steel-glass device, actuated by a piezoelectric transducer, was assembled for experimental characterization of boundary-driven acoustic streaming in such scenarios. First, the various standing acoustic modes in the semi-circular channel were measured through the acoustophoretic patterning of 20 µm polystyrene particles. Next, the acoustic radiation force fields and boundary-driven acoustic streaming patterns under various resonant acoustic modes were characterized through micro-particle-image-velocimetry measurements of the motion of 20 µm and 1 µm polystyrene particles, respectively. Finally, the experimental results were explained using efficient finite element simulations of acoustofluidics and acoustophoresis in a semi-circular reduced-fluid model, with a focus on analyzing the streaming velocities driven by the flat and curved walls. Both experimental and numerical results demonstrated that the ratio of streaming velocities induced by the flat wall and the curved wall in this semi-circular channel depends on the resonant acoustic modes. This research highlights the diverse boundary-driven acoustic streaming patterns that arise in irregular channels and provides a theoretical foundation for choosing strategies for shape optimization to suppress acoustic streaming in acoustofluidic devices.

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.

Concurrent and sequential coupled optimization design of a transonic compressor blade with axial slot casing treatment

This paper explores the optimization of the interaction between the rotor and axial slot casing treatment (ASCT) to enhance both efficiency and stability margins. Previous studies primarily focused on rotor tip optimization, often compromising flow in non-tip regions and reducing overall rotor performance. To address these limitations, this study introduces a new optimization framework integrating full-span 3D blade design with a semicircular axial slot, utilizing both sequential and concurrent optimization strategies. The sequential approach first optimizes blade geometries, followed by ASCT adjustments, while the concurrent approach treats the blade and ASCT as a unified aerodynamic system. Compared to prior studies focusing exclusively on tip-only 3D shape optimization, results indicate that sequential coupled optimization improves the stall margin by 13.32% and efficiency by 0.05%, whereas the concurrent strategy further enhances performance, shaping the blades into an inverse S form, reducing efficiency losses from 0.12% to 0.02%, and increasing the stall margin increment from 14.88% to 21.83%. These findings demonstrate the significant performance gains achievable through coordinated rotor and ASCT design.

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.

Simplified Procedure for the Design and Optimisation of Oval Tensile Spoke Wheels for Roof Structures

This paper presents a simplified procedure for the design and shape optimisation of oval tensile spoke wheels to be used in roof structures for grandstands in sports stadiums. This procedure combines graphical methods with simple numerical methods to obtain the geometrical definition of an oval wheel and to estimate the prestressing forces. It also allows for the compression forces in the outer ring to be estimated and compared with those in a circular wheel. This makes it easy to make small geometrical adjustments for optimisation. Application examples are given for each step of the procedure. Several wheel designs are defined, showing how the shape of the inscribing oval determines the magnitude of the forces in the outer ring.

Optimization of probabilistic and geometrical shaping in RoF system based on overlapping labels

We used a hybrid probabilistic geometric shaping scheme that uses a probabilistic shaping method with labels and a pairwise optimization (PO) algorithm to transmit signals in a 2 × 2 MIMO Photon-assisted millimeter wave (MMW) radio-over-fiber (RoF) system in the D-band. This scheme has low complexity and a simple recovery method. This scheme optimizes 16-ary quadrature amplitude modulation (16QAM) to probabilistically shaped 9-ary quadrature amplitude modulation (PS-9QAM) by adding labels, and optimizes it to hybrid probabilistically and geometrically shaped 9-ary quadrature amplitude modulation (PGS-9QAM) by geometric shaping using the PO algorithm. The experimental results prove the optimization effect of this scheme. Under the bit error rate threshold of 0.0038, when the net bit rate is the same, compared with 16QAM, PS-9QAM and PGS-9QAM, the optical power at the transmitter can be reduced by 0.8 dB and 1.45 dB respectively. When the transmission power is the same, compared with 16QAM, the net rates of PS-9QAM and PGS-9QAM can be increased by 7.5Gbit/s and 9Gbit/s respectively.

Minimization of detent force in PMLSM by end magnetic regulating module with free topologies

In this paper, a novel method for suppressing the detent force of permanent magnet linear synchronous motors is proposed. First, the end force is adjusted to offset the cogging force while the cogging force remains unchanged. On the other hand, the proposed method can arbitrarily change the shape of the end magnetic regulating module (EMRM), thus allowing the end force to obtain a wider adjustment range, which is different from the conventional limited shape optimization. More interestingly, compared to the traditional approach for suppressing the end force, which is to suppress the end force to the lowest level, the proposed method does not necessarily suppress the end force to the lowest level, but rather adjusts it to a reasonable level, so that it can offset the cogging force. This leads to the fact that the optimized end magnetic regulating module is effective in adjusting the end force and may even increase the end force, which is different from the conventional idea of suppressing the detent force. Next, the optimal EMRM's topologies are solved using the optimization algorithm, which replaces the traditional low-dimensional single-direction optimization and performs multi-direction global search. Finally, the prototype with optimal EMRM's topology and the testing platform are established and the experimental results validate the effectiveness of the proposed method.

CFD-based shape optimization of flashing converging-diverging nozzles in pelton turbines for domestic carbon dioxide heat pumps including off-design conditions

A path to enhance the coefficient of performance (COP) of domestic heat pumps is to replace the throttling valve with a turboexpander. Designing this component requires addressing supersonic flashing flows localized within the nozzle. In particular, two-phase flows prevent the application of the method of characteristics to design efficient converging–diverging shapes. To overcome this issue, we propose a shape optimization combined with a homogeneous equilibrium flow model as a design tool. Kriging models are used as surrogates of the objective function and constraint to reduce the overall computational burden associated with shape optimization. The infilling criterion to improve surrogate accuracy involves the maximization of the constrained expected improvement. A multi-point optimization is formulated, including design and off-design conditions in both objective and constraint, for a total of four relevant operating conditions. The off-design conditions are derived from system analysis, accounting for variations in the evaporator temperature and outlet gas-cooler temperature. The optimized nozzle results in a COP improvement of 7.6%, compared to a 6.6% increase when replacing the throttling valve with a baseline geometry designed as recommended by the literature. The adoption of a multi-point optimization strategy ensures that this enhancement in design conditions is not offset by off-design performance decay, which is 0.3 percentage points over the three off-design conditions. Overall, replacing the throttling valve with the optimized expander leads to an average COP improvement of 8.6%.

Artificial neural network infused quasi oppositional learning partial reinforcement algorithm for structural design optimization of vehicle suspension components

Abstract This paper introduces and investigates an enhanced Partial Reinforcement Optimization Algorithm (E-PROA), a novel evolutionary algorithm inspired by partial reinforcement theory to efficiently solve complex engineering optimization problems. The proposed algorithm combines the Partial Reinforcement Optimization Algorithm (PROA) with a quasi-oppositional learning approach to improve the performance of the pure PROA. The E-PROA was applied to five distinct engineering design components: speed reducer design, step-cone pulley weight optimization, economic optimization of cantilever beams, coupling with bolted rim optimization, and vehicle suspension arm optimization problems. An artificial neural network as a metamodeling approach is used to obtain equations for shape optimization. Comparative analyses with other benchmark algorithms, such as the ship rescue optimization algorithm, mountain gazelle optimizer, and cheetah optimization algorithm, demonstrated the superior performance of E-PROA in terms of convergence rate, solution quality, and computational efficiency. The results indicate that E-PROA holds excellent promise as a technique for addressing complex engineering optimization problems.

Analysis and optimal design of forging preforming for I-shaped forgings

Abstract The optimal design of forging preforming is the key to improving forging quality and productivity. Taking an I-shaped forging as a research object, an approach to optimize two-dimensional preform shape is employed. The mathematical model of multi-objective optimization in forging forming simulation is established, and the forming load and die wear are used as the objective functions to optimize the design. Two forms of straight line and circular arc are designed for the shape of the deformation area of the preforming die. With the aid of the finite element simulation software, the process of preforming and finishing forging by using the preformed die with different design variables and different parameters is simulated. Simulation results show that the best optimization results can be achieved when the linear angle is 53.5° and the circular arc radius is 66 mm. After optimization, the load drops by about 36 percent by adopting the circular arc shape, and by about 76 percent by adopting the straight-line shape. The die wear depth decreases and the wear zones become more balanced after optimization. Numerical results prove that this approach is effective in designing the optimal preform shape in forging.

Design and Validation of a Modular, Backdrivable Ankle Exoskeleton.

Partial-assist ankle exoskeletons have been limited by inherent trade-offs between favorable characteristics including high torque capacity, high control bandwidth, back-drivability, compliance, and low mass. Emerging quasi-direct drive actuators have a rigid transmission with a low gear ratio, enabling inherent backdrivability and compliance with accurate torque and position control. Our existing modular, backdrivable exoskeleton system (M-BLUE) uses quasi-direct drive actuators at the hip and/or knee to deliver high assistive torques alongside low dynamic backdrive torques, enabling natural interaction with users with remnant voluntary motion. This paper extends our modular system with the design and validation of a back-drivable ankle exoskeleton module to assist both plantarflexion and dorsiflexion. The bi-directional torque capabilities enable the study of control methods and gait outcomes for able-bodied users and users with gait impairments. Benchtop tests of the actuator performance and control bandwidth indicate that the position, voltage, and current control modes can provide assistance to the ankle joint across activities of daily living (ADLs). We also implement an optimal task-agnostic energy shaping controller for an experiment with a single human subject to validate the ability of the ankle exoskeleton to provide biomimetic torque assistance across a circuit of ADLs.

PDE parametric modeling with a two-stage MLP for aerodynamic shape optimization of high-speed train heads

PDE parametric modeling with a two-stage MLP for aerodynamic shape optimization of high-speed train heads

Shape optimization for nonlocal anisotropic energies

In this paper we consider shape optimization problems for sets of prescribed mass, where the driving energy functional is nonlocal and anisotropic. More precisely, we deal with the case of attractive/repulsive interactions in two and three dimensions, where the attraction is quadratic and the repulsion is given by an anisotropic variant of the Coulomb potential. Under the sole assumption of strict positivity of the Fourier transform of the interaction potential, we show the existence of a threshold value for the mass above which the minimizer is an ellipsoid, and below which the minimizer does not exist. If, instead, the Fourier transform of the interaction potential is only non-negative, we show the emergence of a dichotomy: either there exists a threshold value for the mass as in the case above, or the minimizer is an ellipsoid for any positive value of the mass.

Design of Steel-Cu composites for enhancing thermal properties of plastic processing tools by using a numerical model of the microstructure

Limitationsof conventional materials used for plastic processing tools, particularly related to thermal conductivity, significantly influence production efficiency, with the cooling time of moulded parts appearing as one of the key factors. Therefore, this study focuses on designing Steel-Cu composites with the aid of a numerical model of the composite's microstructure for enhancing their overall thermal properties. We present a novel procedure for designing such composites, which facilitates the identification of the optimal shape for the phases to improve overall thermal conductivity. We have developed a data-driven homogenization model to aid the optimization process and ensure time-efficient solutions. The data has been generated through numerical homogenization based on the finite element method. The proposed shape optimization procedure has been applied to determine the optimal shape of the Cu phase across various volume fractions. We found out that the optimal shape of the Cu phase is not constant but depends on its volume fraction. Emphasizing the practical utility of the proposed procedure, it is noteworthy that once the data-driven model is established, it enables a time-efficient optimization of the Cu phase shape for arbitrary volume fractions of phases. Consequently, this may expedite the decision-making process for material manufacturers.

Twice-topology optimized heat sinks for enhanced heat transfer performance: Numerical and experimental investigation

Since the heat dissipation problem is always confusing and hindering the computing power improvement of electronic chip, an effective thermal management strategy is critical to relieve these problems. In this work, a new twice topology optimization design method combining topology optimization and image processing to design heat sinks is presented, which extends topology optimization from 2Dimention (2D) to 3Dimention(3D). Firstly, on the horizontal design domain, the conventional topology optimization is conducted for the minimization of average temperature/standard deviation. Then the optimal shape of liquid domain is converted into 1D flow routine by thinning algorithm. After that, another topology optimization is performed on the flow channel cross-section plane to get the best cross-section shape of channels. The liquid domain of the final heat sink is then obtained by scanning the optimized flow channel cross-section along the 1 Dimension (1D) flow routine and solving the interference by introducing cylinder joints. Finally, two kinds of twice topology optimized heat sinks including TTOHS-1 with minimized temperature variation as optimal goal and TTOHS-2 with minimized average temperature as optimal goal are generated by combining the liquid domain and a cuboid using Boolean Operation. The performance of heat sinks is numerically investigated, and the results indicate that the thermal performance of TTOHS-1 and TTOHS-2 are much better than that of the traditional heat sink with straight channels (TSCHS). When Re = 689, the average temperature and the maximum temperature of the heat source surface of TTOHS-1 are decreased by 4.99 % and 6.29 % respectively, compared to the TSCHS. The Nusselt number is increased by 46.16 % while the thermal resistance is reduced by 33.13 %. At last, the thermal and flow performance of the TTOHS-1 is studied by conducting experiments, showing that the numerical results agree well with that of the experiment.

Analysis of Resonance Efficiency According to Length and Entrance Depth of Channel Resonance Part of Multi-Resonance Wave Energy Converter

Multi-resonance wave energy converter can generate efficient power generation by complexly utilizing the resonance phenomenon of waves even when waves propagate normally. As the wave is amplified by resonance, the power generation efficiency of the multi-resonance wave energy converter increases, and the shape of the resonance part needs to be optimized to maximize power generation efficiency. The multi-resonance wave energy converter amplifies waves in the seiche resonance part and the channel resonance part. In this study, CFD numerical experiments were performed under various conditions such as the length and location of the channel resonance part to analyze the sensitivity for each condition and derve the optimal shape of the channel resonance part.

Low-loss and compact arbitrary-order silicon mode converter based on hybrid shape optimization

Low-loss and compact arbitrary-order silicon mode converter based on hybrid shape optimization