Shape Optimization Techniques Research Articles

Foundation Types of Fixed Offshore Wind Turbine

Offshore wind turbines are supported by various foundations, each with its considerations in design and construction. Gravity, monopile, and suction bucket foundations encounter geotechnical issues, while jacket and tripod foundations face fatigue problems. Considering this, a gravity foundation based on a steel skirt was developed, and a monopile foundation was analyzed for Pile-Soil Interaction using the p–y curve and 3D finite element method (3D FEM). In addition, for suction bucket foundations, the effects of lateral and vertical loads were analyzed using 3D FEM and centrifuge tests. Fatigue analysis for jacket and tripod foundations was conducted using a hotspot stress approach. Some hybrid foundations and shape optimization techniques that change the shape to complement the problems of each foundation described above were assessed. Hybrid foundations could increase lateral resistance compared to existing foundations because of the combined appendages, and optimization techniques could reduce costs by maximizing the efficiency of the structure or by reducing costs and weight. This paper presents the characteristics and research directions of the foundation through various studies on the foundation. In addition, the optimal design method is presented by explaining the problems of the foundation and suggesting ways to supplement them.

Reconstruction and stability analysis of potential appearing in time‐fractional subdiffusion

In this work, we establish a local stability estimate for a problem involving the reconstruction of a domain in the time‐fractional diffusion equation with an order of : from the knowledge of a Neumann additional data on a part of the boundary. This problem is motivated by several applications in anomalous diffusion phenomena. The stability estimate is obtained through a straightforward approach utilizing shape optimization techniques. To reconstruct the domain , we formulate the inverse problem as a shape optimization one by minimizing a least‐squares cost function. Using the topological derivative method, we perform a noniterative algorithm for numerically recovering the location and shape of the unknown domain. Finally, we demonstrate the effectiveness of our approach in reconstructing multiple subdomains of varying shapes and sizes, considering noisy data, through numerical experiments.

Optimal actuator placement for control of vibrations induced by pedestrian-bridge interactions

In this paper, an optimal actuator placement problem, with a linear wave equation as the constraint, is considered. In particular, this work presents the framework for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on the shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical tests illustrate the theoretical results.

Design and Analysis of Quad Copter Chassis Using Shape Optimization Technique

Abstract: Unmanned aerial vehicles (UAVs) are replacing many traditional methods ranging from simple play toys to critical defense operations. UAVs or drones that are the little flying machines are used in space, defense, food delivery, pest sprays for agriculture, consumer goods delivery, land-surveillance and the list goes on. However, the physics behind it demands a lesser weight for drone to fly high as lesser the weight, lesser is the power required to operate. In all the components that make up a drone, is the frame that is most important structure which holds and bears everything at place. So the material used for the drone frame plays a very crucial role for it should have a lesser mass but sufficient strength. In this work, frame is modeled taking into consideration, its sturdiness and stress analysis is conducted using Autodesk Fusion 360 software and compared for different materials of frames from plastics to metals and the design is shape optimized to meet the objective

Concurrent shape and build orientation optimization for FDM additive manufacturing using the principal stress lines (PSL)

Additive Manufacturing (AM) with the consisting constantly evolving technologies is a particularly popular research area. Based on the shape forming freedom, size, shape, and topology optimization techniques can be validated by AM produced parts. However, in every manufacturing process, AM also has some adverse inherent properties. One and maybe the most significant optimization problem is the mechanical anisotropy caused by the layered structure. In this paper, a simultaneous build orientation and shape optimization method is presented. Both of the approaches are intended to increase the mechanical performance of the produced parts. Shape optimization was accomplished by varying the cross-section of the beam geometries, based on the angle between a PSL section and the characteristic load direction. To test the efficiency and validate the method 2D structures (with relatively small 3rd dimension) and their tensile properties were tested. Based on the results, we can prove that the PSL method works and help to increase the mechanical performance by 19.2% with only 7.8% size increment.

A new shape optimization approach for fracture propagation

AbstractWithin this work, we present a novel approach to fracture simulations based on shape optimization techniques. Contrary to widely‐used phase‐field approaches in literature the proposed method does not require a specified ‘length‐scale’ parameter defining the diffused interface region of the phase‐field. We provide the formulation and discuss the used solution approach. We conclude with some numerical comparisons with well‐established single‐edge notch tension and shear tests.

Tracking of fracture‐state displacement data generated by cohesive zone modeling using shape optimization

AbstractMany infrastructure objects made from concrete like bridges are in bad condition. Different types of damage like corrosion and fractures reduce the stiffness and strength significantly. Knowledge of the fracture propagation is essential to predict the remaining life time and to guarantee a safe operation. There are different approaches to solve this problem. On the one hand finite element simulations including cohesive zone modeling are commonly used to determine the current condition and to predict the fracture propagation in a component. In addition, mathematical optimization techniques like shape optimization can be used to predict the fracture growth. In this work, fracture‐state displacement data generated by cohesive zone modeling is tracked using shape optimization techniques, which leads to the imitation of fracture growth. It is shown that the techniques lead to comparable results for the fracture propagation in concrete.

Inverse Design of Linear and Nonlinear Cylindrical Metamaterial Rod

Continuum elastic metamaterials can be used to reduce system-generated 2nd harmonics and they should also pass the fundamental harmonics during nonlinear ultrasonic testing. Linear metamaterials are designed based on the bandgap structure of the periodic layered materials showing contrast in acoustic impedances. Design parameters such as widths of the periodic layered elastic materials are calculated by a parametric sweep by solving eigenvalue problems, and the transfer matrix method. Most of the design studies assume infinitely long periodic elastic layers, but in practice length of metamaterial is limited by the reduction in fundamental amplitude of input short pulse. Though the linear metamaterials are designed for nonlinear ultrasonic applications, considering geometric and material nonlinearity of the layered elastic materials which contributes to harmonic scattering, the sensitivity of widths of layered materials to amplitudes of the 2nd harmonics, along with the linear interference is the most realistic modeling approach. In this study, linear and nonlinear metamaterials are designed using shape optimization techniques by solving transient finite element studies considering realistic geometric and material models. Gradient-free algorithms such as co-ordinate search and Nelder Mead are used during optimization. Effective design approaches are proposed and demonstrated to control longitudinal modes in a cylindrical rod.

Aeroacoustic airfoil shape optimization enhanced by autoencoders

Aeroacoustic noise is a major concern in wind turbine design that can be minimized by optimizing the airfoils that shape the rotating blades. To this end, we present a framework for airfoil shape optimization to reduce the trailing edge noise for the design of wind turbine blades. Far-field noise is evaluated using Amiet’s theory coupled with the TNO-Blake model to calculate the wall pressure spectrum and fast turn-around XFOIL simulations to evaluate the boundary layer parameters. The computational framework is first validated using a NACA0012 airfoil at 0° angle of attack. Particle swarm optimization is used to find the optimized airfoil configuration. The multi-objective optimization minimizes the A-weighted overall sound pressure level at various angles of attack, while ensuring enough lift and minimum drag. Furthermore, traditional shape optimization techniques show difficulties to converge to the optimum, when too many shape parameters are included in the optimization. For this reason, we compare classic parameterization methods to define the airfoil geometry (i.e., CST) to a machine learning method (i.e., a variational autoencoder). We observe that variational autoencoders can represent a wide variety of geometries, with only four encoded variables, leading to efficient optimizations, which result in improved optimal shapes. When compared to the baseline geometry, a NACA0012, the autoencoder-based optimized airfoil reduces by 3% (1.75 dBA) the overall sound pressure level (with decreased noise across the entire frequency range), while maintaining favorable aerodynamic properties in terms of lift and drag.

Shape reconstruction for advection-diffusion problems by shape optimization techniques: The case of constant velocity

Shape reconstruction for advection-diffusion problems by shape optimization techniques: The case of constant velocity

Mixing enhancement of passive type T-mixer through shape optimization

This study looked at optimizing the geometrical shape of a simple T-mixer using Bernstein polynomials-based shape optimization technique to improve the mixing of the T-mixer. Passive micromixers of planar geometry are preferred in a wide range of applications such as lab-on-chips and chemical processing applications, due to their ease of fabrication and low processing costs. Studies conducted on T-mixers have revealed that the performance of T-mixers at low Re (<30) is dismal. At low Reynolds number flows, the mixing is completely dominated by diffusion because of laminar flow conditions. In the present work, an attempt to improve the mixing performance of the T-mixer was made and a nearly three-fold improvement in performance was reported. The adjoint-based shape optimization technique was employed to optimize the wall profile without losing the advantage of the ease of fabrication. The T-mixer boundaries were represented parametrically using Bernstein polynomials that could take any shape within a constrained plane. Different shapes can be generated for different polynomial orders. A limit on the minimum channel thickness (60 microns) was imposed, while the inlet and outlet boundary lengths were fixed. For this particular geometry, the 12th-order polynomial exhibits an optimized shape for maximum mixing performance. The optimized shape of the T-mixer also shows significant improvement in mixing compared to a conventional T-mixer with a reduced channel thickness of 60 microns.

Design and Shape Optimization of Strain Gauge Load Cell for Axial Force Measurement for Test Benches.

The load cell is an indispensable component of many engineering machinery and industrial automation for measuring and sensing force and torque. This paper describes the design and analysis of the strain gauge load cell, from the conceptional design stage to shape optimization (based on the finite element method (FEM) technique) and calibration, providing ample load capacity with low-cost material (aluminum 6061) and highly accurate force measurement. The amplifier circuit of the half Wheatstone bridge configuration with two strain gauges was implemented experimentally with an actual load cell prototype. The calibration test was conducted to evaluate the load cell characteristics and derive the governing equation for sensing the unknown load depending on the measured output voltage. The measured sensitivity of the load cell is approximately 15 mV/N and 446.8 µV/V at a maximum applied load of 30 kg. The findings are supported by FEM results and experiments with an acceptable percentage of errors, which revealed an overall error of 6% in the worst situation. Therefore, the proposed load cell meets the design considerations for axial force measurement for the laboratory test bench, which has a light weight of 20 g and a maximum axial force capacity of 300 N with good sensor characteristics.

A thinning algorithm based approach to controlling structural complexity in topology optimization

Shape and topology optimization techniques aim to maximize structural performance through material redistribution. Effectively controlling structural complexity during the form-finding process remains a challenging issue. Structural complexity is usually characterized by the number of connected components (e.g., beams and bars), tunnels, and cavities in the structure. Existing structural complexity control approaches often prescribe the number of existing cavities. However, for three-dimensional problems, it is highly desirable to control the number of tunnels during the optimization process. Inspired by the topology-preserving feature of a thinning algorithm, this paper presents a direct approach to controlling the topology of continuum structures under the framework of the bi-directional evolutionary structural optimization (BESO) method. The new approach can explicitly control the number of tunnels and cavities for both two- and three-dimensional problems. In addition to the structural topology, the minimum length scale of structural components can be easily controlled. Numerical results demonstrate that, for a given set of loading and boundary conditions, the proposed methodology may produce multiple high-performance designs with distinct topologies. The techniques developed from this study will be useful for practical applications in architecture and engineering, where the structural complexity usually needs to be controlled to balance the aesthetic, functional, economical, and other considerations. • A structural complexity control approach is proposed for topology optimization. • Efficient designs with controllable topologies can be easily obtained. • This approach is practically useful for creating diverse and competitive designs.

A design study on metal C-ring seals

The seals/gaskets are intended to maintain leak-tightness between the two connecting parts instead of welding or soldering. It is advantageous for a repair or maintenance of a system or equipment. However, there is a risk of losing the sealing effect due to stress relaxation or other unexpected events, especially during long-term operations. This study aims to find a configuration of metal C-rings that maximize elastic energy that affects sealing performance through a shape optimization technique. In addition, contact stress was observed, which is also important for the sealing performance. Unlike O-ring seals, the contact point of the metal C-ring seal varies depending on the compression depth. Thus, the size and position of the contact stress were measured in the various compression depths. Besides, the metal C-ring seals are used in a vacuum as well as in pressure environments. Thus, contact stress was evaluated in such environments. For the optimization study, the genetic algorithm (GA) and B-spline were employed, and the outer boundary of the cross-section of the C-ring was determined to be compatible with the existing standards so that it could replace the typical types.

Shape optimization for the mitigation of coastal erosion via porous shallow water equations

AbstractCoastal erosion describes the displacement of land caused by destructive sea waves, currents, or tides. Major efforts have been made to mitigate these effects using groynes, breakwaters, and various other structures. We address this problem by applying shape optimization techniques on the obstacles. We model the propagation of waves toward the coastline using two‐dimensional porous shallow water equations with artificial viscosity. The obstacle's shape, which is assumed to be permeable, is optimized over an appropriate cost function to minimize the height and velocities of water waves along the shore, without relying on a finite‐dimensional design space, but based on shape calculus.

Microacoustic Metagratings at Ultra‐High Frequencies Fabricated by Two‐Photon Lithography (Adv. Sci. 20/2022)

Microacoustic Metagratings In article number 2200990, Anton Melnikov and co-workers present microacoustic metagratings for passive wavefront manipulation of ultra-high frequency ultrasound. The designs are created with topology and shape optimization techniques by incorporating the thermoviscous effects, and manufactured with two-photon lithography. The successful experimental demonstration of the effectiveness of the designs opens a new route for acoustic metamaterials in ultrasonic applications with high spatial resolution.

Numerical design of distributive mixing elements

This paper presents a novel shape-optimization technique for the design of mixing elements in single-screw extruders. Extruders enable the continuous production of constant-cross-section profiles. Equipped with one or several screw-shaped rotors, extruders transport polymer particles towards the outlet. Due to shear heating, melting is induced and a melt stream is created, which can be further processed. While many variants of multi-screw extruders exist, a significant share of all extrusion machines is made up of single-screw extruders due to their comparatively low operating costs and complexity. While the reduced complexity yields economic benefits, single-screw extruders' mixing capabilities, i.e., their ability to produce a melt with a homogeneous material and temperature distribution, suffer compared to multi-screw extruders. To compensate for this shortcoming, so-called mixing elements are added to the screw to enhance mixing by recurring flow reorientations. In view of the largely unintuitive flow characteristics of polymer melts, we present an optimization framework that allows designing these mixing elements numerically based on finite-element simulations of the melt flow. To reduce the computational demand required by shape optimization of a complete mixing section, we only focus on the shape optimization of a single mixing element. This paper presents advances in three aspects of numerical design: (1) A combination of free-form deformation and surface splines is presented, allowing to parameterize the mixing element's shape by very few variables. (2) The combination of this concept with a linear-elasticity-based mesh update method to deform the computational domain without the need for remeshing is demonstrated. (3) A simple yet robust and sensitive objective formulation to assess distributive mixing in laminar flows based on a measure for the interfacial area is proposed.

Applying the phononic crystal concept to the intake muffler of a refrigeration compressor

Many previous works explore the creation of wave stop bands (bandgaps) using periodic structures. Aiming at improving the transmission loss of a muffler used in a refrigerant compressor, this work proposes the redesign of an existing intake muffler using the concept of wave attenuation bands caused by Bragg scattering. The challenge consists in designing a phononic crystal (PnC) with bandgaps in the audio frequency range with the size constraints of a practical muffler application. The first part of the research focuses on the development and validation of numerical and experimental techniques to provide guidelines for periodic muffler design. The second part consists in applying the developed concepts and tools to a real compressor muffler following the constraints of the product specifications. A shape optimization technique is used to enlarge the bandgap while keeping the unit cell length in the order of tens of millimeters. Two designs were 3D-printed and tested on the real compressor, reaching 7 dB reduction on the sound power level (SPL) in the aimed frequency band and 4 dB reduction on the overall compressor noise level.

Microacoustic Metagratings at Ultra-High Frequencies Fabricated by Two-Photon Lithography.

The recently proposed bianisotropic acoustic metagratings offer promising opportunities for passive acoustic wavefront manipulation, which is of particular interest in flat acoustic lenses and ultrasound imaging at ultra‐high frequency ultrasound. Despite this fact, acoustic metagratings have never been scaled to MHz frequencies that are common in ultrasound imaging. One of the greatest challenges is the production of complex microscopic structures. Owing to two‐photon polymerization, a novel fabrication technique from the view of acoustic metamaterials, it is now possible to precisely manufacture sub‐wavelength structures in this frequency range. However, shrinking in size poses another challenge; the increasing thermoviscous effects lead to a drop in efficiency and a frequency downshift of the transmission peak and must therefore be taken into account in the design. In this work three microacoustic metagrating designs refracting a normally incident wave toward −35° at 2 MHz are proposed. In order to develop meta‐atoms insensitive to thermoviscous effects shape optimization techniques incorporating the linearized Navier–Stokes equations discretized with finite element method are used. The authors report for the first time microscopic acoustic metamaterials manufactured using two‐photon polymerization and, subsequently, experimentally verify their effectiveness using an optical microphone as a detector in a range from 1.8 to 2.2 MHz.

Inverse design of non-periodic nonlinear metamaterials for nonlinear ultrasonics

Previous work by the author gives an idea about the effective design of linear and phononic “periodic” metamaterial using shape optimization to suppress the system-generated 2nd harmonics of a longitudinal wave during nonlinear ultrasonic testing [Ghodake, J. Acoust. Soc. Am. 150, A149 (2021)]. That work considers only the geometric nonlinearity of the layered materials and sinusoidal waves as an input short pulse. The present work implements a shape optimization technique to obtain the optimal design parameters of the “non-periodic” metamaterial by considering both material and geometric nonlinearities of the layered materials present in the phononic crystal as this assumption is close to the real experimental situations. Gaussian short input pulses are considered in this study with two different objectives such as only reducing the amplitude of the 2nd harmonics and reducing the amplitude of 2nd harmonics, maximizing the amplitude of 1st harmonics as well as maintaining the Gaussian shape of the output pulse which makes this inverse problem challenging. This study demonstrates the applicability of the non-periodic metamaterial in practical situations and the importance of the proposed inverse design approach in linear and nonlinear elastic wave propagation applications such as ultrasonic waves and seismic waves.