A novel [[EQUATION]] approach to shape optimisation with Lipschitz domains

This article introduces a novel method for the implementation of shape optimisation with Lipschitz domains. We propose to use the shape derivative to determine deformation fields which represent steepest descent directions of the shape functional in the $W^{1,\infty}-$ topology. The idea of our approach is demonstrated for shape optimisation of $n$-dimensional star-shaped domains, which we represent as functions defined on the unit $(n-1)$-sphere. In this setting we provide the specific form of the shape derivative and prove the existence of solutions to the underlying shape optimisation problem. Moreover, we show the existence of a direction of steepest descent in the $W^{1,\infty}-$ topology. We also note that shape optimisation in this context is closely related to the $\infty-$Laplacian, and to optimal transport, where we highlight the latter in the numerics section. We present several numerical experiments illustrating that our approach seems to be superior over existing Hilbert space methods, in particular in developing optimal shapes with corners.

Research on the Optimization Design of the Acoustic Stealth Shape of a Bottom Object

This paper presents an optimal design method for the acoustic stealth shape for a bottom object with relatively lower echo strength (ES), based on the physical acoustics method (PAM) and genetic algorithm (GA). Specifically, the performance of the PAM was evaluated with acoustic scattering from a Manta-like object, using two-dimensional (2D) axisymmetric calculation method. In the optimization method, GA, the object shape represented by the Bernstein polynomial, grid topology acquired by using the MATLAB-COMSOL module and the scattering calculation are combined into a process. The optimization objective function is given as the weighting function of the ES of the bottom object with different grazing angles and frequencies. Finally, the two optimal shapes of the bottom object under different conditions are given, in which the ES and the angle detection rate after optimization are greatly reduced. This optimal method provides guidance for the lower ES shape design of bottom targets.

Study on airflow and vibraton in a cutting/collection/discharge lawn care system

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

Study on airflow and vibraton in a cutting/collection/discharge lawn care system

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system.Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

Study on airflow and vibraton in a cutting/collection/discharge lawn care system

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system.Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

Study on airflow and vibraton in a cutting/collection/discharge lawn care system

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

Design Optimization of Permanent Magnet Clutch with Ārtap Framework

So far, Permanent Magnet (PM) clutches have been broadly used as torque transmission devices. With the aim of effective utilization of materials and energy in the manufacturing of PM clutches, design optimization has been widely applied. Generally, PM clutches are optimized applying linear dimensions as optimization parameters. On the contrary, optimization of PM clutch shapes has not been done extensively. Therefore, this paper performs optimization of PM clutch shapes with the following objectives: maximum tangential attraction force and minimum volume of utilized materials. To form optimal shapes, the points on the clutch surface are chosen as optimization parameters. The optimization is carried out using Ārtap framework in connection with COMSOL software, where the 3D model of the clutch has been created. After the optimization, the tangential attraction force has increased by 13 % and the volume of the clutch has been reduced by 24 %. Although the obtained shapes appear to be highly intricate, it does not pose an obstacle for modern manufacturing techniques.

Compactness of 𝑀-uniform domains and optimal thermal insulation problems

In this paper, we will consider an optimal shape problem of heat insulation introduced by [D. Bucur, G. Buttazzo and C. Nitsch, Two optimization problems in thermal insulation, Notices Amer. Math. Soc. 64 (2017), 8, 830–835]. We will establish the existence of optimal shapes in the class of 𝑀-uniform domains. We will also show that balls are stable solutions of the optimal heat insulation problem.