Shape Optimization Research Articles

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.

Optimal Shape and Size of Holes in Hybrid Reinforced Concrete Beams

Optimal Shape and Size of Holes in Hybrid Reinforced Concrete Beams

Merging automatic differentiation and the adjoint method for photonic inverse design

Optimizing the shapes and topology of physical devices is crucial for both scientific and technological advancements, given their wide-ranging implications across numerous industries and research areas. Innovations in shape and topology optimization have been observed across a wide range of fields, notably structural mechanics, fluid mechanics, and more recently, photonics. Gradient-based inverse design techniques have been particularly successful for photonic and optical problems, resulting in integrated, miniaturized hardware that has set new standards in device performance. To calculate the gradients, there are typically two approaches: namely, either by implementing specialized solvers using automatic differentiation (AD) or by deriving analytical solutions for gradient calculation and adjoint sources by hand. In this work, we propose a middle ground and present a hybrid approach that leverages and enables the benefits of AD for handling gradient derivation while using existing, proven but black-box photonic solvers for numerical solutions. Utilizing the adjoint method, we make existing numerical solvers differentiable and seamlessly integrate them into an AD framework. Further, this enables users to integrate the optimization environment seamlessly with other autodifferentiable components such as machine learning, geometry generation, or intricate post-processing which could lead to better photonic design workflows. We illustrate the approach through two distinct photonic optimization problems: optimizing the Purcell factor of a magnetic dipole in the vicinity of an optical nanocavity and enhancing the light extraction efficiency of a µLED.

Stiff morphing composite beams inspired from fish fins.

Morphing materials are typically either very compliant to achieve large shape changes or very stiff but with small shape changes that require large actuation forces. Interestingly, fish fins overcome these limitations: fish fins do not contain muscles, yet they can change the shape of their fins with high precision and speed while producing large hydrodynamic forces without collapsing. Here, we present a 'stiff' morphing beam inspired from the individual rays in natural fish fins. These synthetic rays are made of acrylic (PMMA) outer beams ('hemitrichs') connected with rubber ligaments which are 3-4 orders of magnitude more compliant. Combinations of experiments and models of these synthetic rays show strong nonlinear geometrical effects: the ligaments are 'mechanically invisible' at small deformations, but they delay buckling and improve the stability of the ray at large deformations. We use the models and experiments to explore designs with variable ligament densities, and we generate design guidelines for optimum morphing shape (captured using the first moment of curvature), that capture the trade-offs between morphing compliance (ease of morphing the structure) and flexural stiffness. The design guidelines proposed here can help the development of stiff morphing bioinspired structures for a variety of applications in aerospace, biomedicine or robotics.

Influence of contact characteristics of joint surface on vibration performance of the giant magnetostrictive transducer

The giant magnetostrictive transducer is a transducer device that realizes magneto-mechanical energy conversion. Each mechanical component is connected by the joint surface to realize the transmission of ultrasonic vibration energy. To ensure the efficient transmission of energy, the influence of the contact characteristics of the joint surface on the output stability of the transducer is studied. According to the contact conditions between the mechanical joint surfaces of the giant magnetostrictive ultrasonic transducer (GMUT), the key factors affecting the mechanical vibration performance of the ultrasonic system are obtained by analyzing the vibration transmission characteristics of the joint surfaces. The influence of different joint surface contact characteristics (JSCT) on the amplitude–frequency curve of the transducer is analyzed by the ANSYS software. Simulations and experiments have been conducted to verify the predicted results. As the preload force increases, the natural frequency of the transducer increases, but the growth rate decreases. The natural frequency of the double-rod GMUT with a small joint surface area is slightly higher in the optimal output mode shape, while its amplitude is significantly larger. The optimal prestress for the GMUT with different-sized joint surfaces is 3–5 MPa. This paper acquires the JSCT under a high-frequency vibration condition, reveals the influence of the joint surface on the mechanical output performance of the GMUT, and can provide a theoretical basis for the design and analysis of the rotary ultrasonic vibration processing system.

Optimization of precharge placement in sheet molding compound process

This study aims to provide precise predictions for the compression of reinforced polymers during the sheet Molding Compound (SMC) process, ensuring the attainment of a predefined structure while preventing material overflow during the process. The primary challenge revolves around identifying the optimal initial shape to prevent material rebound during the process. To confront this issue, a numerical model is utilized, faithfully simulating the SMC process and forming the foundation for our investigations. Furthermore, to optimize the pre-fill stage, a surrogate model is proposed to enhance modeling efficiency, and then an inverse analysis method is applied. This approach of minimizing material rebound during the SMC process results in a reliable metamodel to predict an initial mass shape accurately and at a low computational cost, thus ensuring the squeezed material fits the mold shape.

Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

Aero-Structural Comprehensive Nonprobabilistic Reliability-Based Optimization Method for High Aspect Ratio Wings

An aero-structural comprehensive reliability-based optimization method is proposed to construct the optimization framework of designing the high aspect ratio wing. There are three parts included in this method. 1) The ideal cruising shape is obtained by optimizing the geometrical parameters in the cruising conditions, where only the aerodynamic shape optimization is involved and the structural deformation is not considered. 2) The jig-shape optimization method is presented, where the aerodynamic performance of the wing structure with deformation is improved by adjusting the twist angle along the span direction to make sure that the shape with the aeroelastic deformation approaches the ideal cruising shape. 3) A nonprobabilistic reliability-based structural optimization is conducted by updating the thickness of composite layer, where the dispersion of mechanical properties of composite materials is considered and a nonprobabilistic reliability index according to strength and stiffness constraints is established. The global stiffness of the wing structure is changed after jig-shape optimization and structural optimization, and the jig-shape and structural scheme are modified alternately. The previously mentioned process needs to be repeated until the changes in the jig-shape and structural scheme in the iterations can be ignored. Finally, the effectiveness of this method has been verified through the numerical example followed by some conclusions.

Stabilization of SIMPLE-like RANS solvers for computing accurate gradients using the complex-step derivative method

The Reynolds-averaged Navier-Stokes (RANS) approach in Computational Fluid Dynamics (CFD) is increasingly vital for aerodynamic design across wind turbines, gas turbines, aircraft, and rotorcraft. Enhancing the process through CFD-based design optimization requires numerous design variables, favoring gradient-based methods for better scalability than gradient-free methods. This research uses numerical differentiation techniques, particularly the complex-step derivative method, to compute gradients. Challenges arise during aerodynamic shape optimization when unconventional shapes disrupt RANS solver assumptions, causing convergence failures. These failures undermine optimization, prompting the need to enhance solver convergence for robust optimization. The modified-Boostconv method is a residual recombination method bolstering unstable eigenvalues to stabilize convergence of iterative solvers for nonlinear systems of equations. This study extends the modified-Boostconv method to combine it with the complex-step derivative technique, creating robust optimizations via RANS-CFD with accurate gradients, even for these numerically unstable cases. The main issue encountered during the complexification of the modified-Boostconv method is how to correctly ensure that the model reduction leading to the least-squares problem satisfies the complex-step derivative method. We test whether the dot product operation involved in the model reduction should be a Hermitian or non-Hermitian inner product. The problem is first tested for a simple analytical case using the logistic equation in combination with the modified-Boostconv method. It shows that the non-Hermitian inner product should be used. This is also confirmed with a similar study using the RANS solver.

Optimal Uniform Strength Design of Frame and Lattice Structures

This paper provides a procedure to obtain the uniform strength of frame and lattice structures. Uniform strength condition is achieved by performing the shape optimization of all beam elements of the structure. The beam shape which guarantees uniform strength is analytically deduced from the one-dimensional Timoshenko model. The optimization problem presents itself as the search for the zeros of the objective-functions vector, which is a non-linear system of equations representing the kinematic-congruence and forces balance at every node of the structure. The analytical formulation of the optimization problem allows to construct the objective-functions vector without the use of external structural computation, i.e. not recurring to any Finite Element Analysis to accomplish iterations. This latter feature entails a great advantage in terms of computing time required to perform optimization. The proposed analytical formulation allows to directly insert the uniform strength condition into the objective-functions vector, transforming the optimization into an unconstrained problem. Some examples are shown in which the performance of the optimization procedure is discussed in terms of robustness and rate of computational complexity while increasing the degrees of freedom of the structure. The reliability and the quality of the optimization are verified through Finite Element Analysis.

AONN-2: An adjoint-oriented neural network method for PDE-constrained shape optimization

PDE-constrained shape optimization has been playing an important role in a large variety of engineering applications. Traditional mesh-dependent shape optimization methods often encounter challenges due to mesh deformation. To address this issue, we present a new adjoint-oriented neural network method, AONN-2, for PDE-constrained shape optimization problems. This method extends the capabilities of the original AONN method [1], which is developed for efficiently solving parametric optimal control problems. AONN-2 inherits from AONN the direct-adjoint looping (DAL) framework for computing the extremum of an objective functional and the involved neural network methods for solving complicated PDEs. Furthermore, AONN-2 expands the application scope to shape optimization by taking advantage of the shape derivatives to optimize the shape represented by discrete boundary points. AONN-2 is a fully mesh-free shape optimization approach, naturally sidestepping issues related to mesh deformation, with no needs for maintaining mesh quality and additional mesh corrections. A series of experimental results are presented, highlighting the flexibility, robustness, and accuracy of AONN-2.

An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations

An electromagnetic shape optimisation for perfectly electric conductors by the time-domain boundary integral equations

Optimizing Capacitive Pressure Sensor Geometry: A Design of Experiments Approach with a Computer-Generated Model.

This study presents a comprehensive investigation into the design and optimization of capacitive pressure sensors (CPSs) for their integration into capacitive touch buttons in electronic applications. Using the Finite Element Method (FEM), various geometries of dielectric layers were meticulously modeled and analyzed for their capacitive and sensitivity parameters. The flexible elastomer polydimethylsiloxane (PDMS) is used as a diaphragm, and polyvinylidene fluoride (PVDF) is a flexible material that acts as a dielectric medium. The Design of Experiment (DoE) techniques, aided by statistical analysis, were employed to identify the optimal geometric shapes of the CPS model. From the prediction using the DoE approach, it is observed that the cylindrical-shaped dielectric medium has better sensitivity. Using this optimal configuration, the CPS was further examined across a range of dielectric layer thicknesses to determine the capacitance, stored electrical energy, displacement, and stress levels at uniform pressures ranging from 0 to 200 kPa. Employing a 0.1 mm dielectric layer thickness yields heightened sensitivity and capacitance values, which is consistent with theoretical efforts. At a pressure of 200 kPa, the sensor achieves a maximum capacitance of 33.3 pF, with a total stored electric energy of 15.9 × 10-12 J and 0.468 pF/Pa of sensitivity for 0.1 dielectric thickness. These findings underscore the efficacy of the proposed CPS model for integration into capacitive touch buttons in electronic devices and e-skin applications, thereby offering promising advancements in sensor technology.

Robust shape optimization of the FDA blood pump

Robust shape optimization of the FDA blood pump

Periodic driving shape controls energy transmission.

In the early 2000s, Geniet and Leon [Phys. Rev. Lett. 89, 134102 (2002)0031-900710.1103/PhysRevLett.89.134102] discovered the nonlinear supratransmission (NST) in a medium with a forbidden frequency band gap. It is a process in which nonlinear structures are created by a sinusoidal harmonic boundary condition imposed at a frequency in the band gap. The present study extends this concept and shows that an optimal shape of a periodic nonsinusoidal excitation may induce (or inhibit) energy flow through the lattice below (or above) the NST threshold, demonstrating that nonlinear supratransmission is reliant not only on the driving amplitude but also on its shape. This is evidenced through numerical simulations and mathematical calculations varying the excitation signal shape in the Fermi-Pasta-Ulam case study. Setting the shape parameter to zero recovers the results of the literature in relation to the sinusoidal signal.

Optimizing the Shape of the Spinning Electrode for Needleless Coaxial Electrospinning

This work deals with designing the optimal shape of the spinning electrode to optimize the distribution of the electric field and suppress the formation of corona discharges on the surface of the electrode during electrospinning using direct current (DC). Some of the solutions used for electrospinning are solved in flammable solvents, such as PVB; therefore, corona discharges are hazardous, as they cause sparks that can cause fires and explosions. The shape optimization was carried out on a plate weir electrode, which uses the principle of free surface spinning. Using the electric field simulation, an analysis of the plate weir spinner was carried out, and its optimization was aimed at minimizing the occurrence of corona discharges, which negatively affect the spinning process. Based on the simulations’ results, the spinning electrode design parameters were adjusted so that an even distribution of the electric field over the entire active surface of the electrode was ensured, and the incidence of corona discharges was prevented. A laboratory experiment was used to validate the function of the design changes in the spinning electrode.

Reimagining Antitrust Institutions: A (Modest?) Proposal

Abstract It is always an appropriate time to reevaluate, reexamine, and question the optimal scope and shape of antitrust institutions. In this article we ask whether the complex current distribution of competition functions in the U.S. can be improved by some reorganization or other reform. We answer in the affirmative and propose a number of improvements – perhaps the most significant being consolidating the competition functions of the FTC into the Antitrust Division and stripping the FCC of authority independently to review mergers, as it did in view of the similarly poor performance of the DOT when reviewing airline mergers. Our more general proposal with the authority of sectoral regulators over competition should not be overlooked, however; it would do much good with little or no downside.

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

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

Three-dimensional Darcy’s reduced-order isogeometric shape optimization for cooling channels

Three-dimensional Darcy’s reduced-order isogeometric shape optimization for cooling channels