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The present study aims to develop a vortex method capable for solving the complex vortical flows past the moving/deforming bodies.

To achieve such a goal, some innovative work is conducted on the basis of vortex-in-cell (VIC) method that uses the improved semi-Lagrangian scheme. The penalization technique is incorporated with the VIC, which makes the complex boundaries of moving/deforming bodies readily treated. Iterative algorithm is further proposed for the penalization and used to solve the Poisson equation, which enhances the vorticity solution accuracy at the body boundary.

The developed method is used to simulate some distinct flows of different boundaries and features: the impulsively started circular cylinder flow represents the one-way coupling; the falling circular cylinder flow and ellipse leaf flow both represent the two-way coupling of moving boundary; the fish-like body flow represents the two-way fluid-structure interaction of deforming boundary. The vortical physics of the above flows are well revealed, and the developed method is proven capable in dealing with the complex fluid-structure interaction problems.

The penalization technique is incorporated with the semi-Lagrangian VIC method, which makes the complex boundaries of moving/deforming bodies readily treated. An iterative algorithm is further proposed for the penalization and used to solve the Poisson equation, which enhances the vorticity solution accuracy at the body boundary. The complex vortical physics of the moving/deforming body flows are well revealed, and the propulsive mechanism of fish-like swimmer is well illustrated with the present method.

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

Proper platform pose is important for the mobile manipulator to accomplish dexterous manipulation tasks efficiently and safely, and the evaluation criterion to qualify manipulation performance is critical to support the pose decision process. This paper aims to present a comprehensive index to evaluate the manipulator’s operation performance from various aspects.

In this research, a criterion called hybrid manipulability (HM) is proposed to assess the performance of the manipulator’s operation, considering crucial factors such as joint limits, obstacle avoidance and stability. The determination of the optimal platform pose is achieved by selecting the pose that maximizes the HM within the feasible inverse reachability map associated with the target object.

A self-built mobile manipulator is adopted as the experimental platform, and the feasibility of the proposed method is experimentally verified in the context of object-grasping tasks both in simulation and practice.

The proposed HM extends upon the conventional notion of manipulability by incorporating additional factors, including the manipulator’s joint limits, the obstacle avoidance situation during the operation and the manipulation stability when grasping the target object. The manipulator can achieve enhanced stability during grasping when positioned in the pose determined by the HM.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

The purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.

To provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.

In this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.

In this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

The purpose of this paper is to compare between two methods of volume control in the context of topological derivative-based structural optimization of Kirchhoff plates.

The compliance topology optimization of Kirchhoff plates subjected to volume constraint is considered. In order to impose the volume constraint, two methods are presented. The first one is done by means of a linear penalization method. In this case, the penalty parameter is the coefficient of a linear term used to control the amount of material to be removed. The second approach is based on the Augmented Lagrangian method which has both, linear and quadratic terms. The coefficient of the quadratic part controls the Lagrange multiplier update of the linear part. The associated topological sensitivity is used to devise a structural design algorithm based on the topological derivative and a level-set domain representation method. Finally, some numerical experiments are presented allowing for a comparative analysis between the two methods of volume control from a qualitative point of view.

The linear penalization method does not provide direct control over the required volume fraction. In contrast, through the Augmented Lagrangian method it is possible to specify the final amount of material in the optimized structure.

A strictly simple topology design algorithm is devised and used in the context of compliance structural optimization of Kirchhoff plates under volume constraint. The proposed computational framework is quite general and can be applied in different engineering problems.

In this work, the authors deal with topology optimization in electromagnetism using solid isotropic material with penalization (SIMP) method associated with a gradient-based algorithm. The purpose of this study is to propose and investigate the impact of new generalized material interpolation scheme (MIS) used in SIMP approaches.

The variable domains of this kind of electromagnetism design problem are decomposed into small squares which represent a material point (iron here) or void. A least square function where the magnetic field in a target zone has to be as close as possible to a fixed one is minimized. Then the binary optimization problem is relaxed to a continuous one. By using the adjoint variable method, the gradient is provided. By penalizing the objective function using MIS, gradient-based algorithms can then be directly applied to provide efficient solutions close to the binary ones.

In this work, new general MISs are proposed. It is shown on numerous numerical instances that the so-obtained design solutions are more precise to define the zones with or without materials.

Only the linearity of the materials is addressed because the associated adjoint method needs this assumption. However, the new penalization approaches are not dependent directly on this assumption.

The new MISs are efficiently applied to design of a hall effect thruster (HET) magnetic circuits. Furthermore, these schemes are generic and can then be applied to other topology optimization applications in electromagnetism as well as and in mechanism.

The problematic surrounding patients' prioritization decisions are currently at the centre of political leaders' concerns. How to define whom to treat when there are not enough resources to treat everybody is the key question. This exploratory study aims to investigate the views of Bulgarian citizens regarding the relevance of the information concerning eight individual health-related behaviours in priority setting decisions: smoking, excess of alcohol, illegal drug use, overweight/obesity, speed driving, extreme sports practice, unsafe sex and overuse of internet and/or mobile devices.

Data were collected through a questionnaire where 322 respondents faced hypothetical rationing dilemmas comprising option pairs of the eight risky behaviours. Descriptive statistics and non-parametric tests were performed to define the penalization of each of the risky behaviours and to test for the association between this penalization and the respondent's health habits and sociodemographic characteristics.

Most respondents would refuse to grant access to healthcare based on patients' personal responsibility for the disease. Nevertheless, respondents were more willing to consider illegal drug use, excessive alcohol consumption, engagement in unsafe sex behaviours and smoking. Respondent's own interest or advantage seems to be somehow relevant in explaining the penalization of risk behaviours in priority setting.

This study shows that most respondents support the lottery criterion and thus do not want to see lifestyle prioritization in action.

This study is the first attempt to awaken attention to the impact that personal responsibility for health may have on intergenerational access to healthcare in Bulgaria.

Most studies on work–life support at workplaces consider work–life balance to be a women’s issue, either explicitly or implicitly. This chapter analyses how fathers who are involved caregivers are supported or hindered in attaining work–life balance by their workplaces. It explores the following three questions: (1) why fathers value some job adaptations over others compared with mothers; (2) how organizational cultures influence the work–life balance of new fathers and (3) what differences exist across public and private sectors as well as large versus small companies. A qualitative approach with three discussion groups and 22 involved fathers enables us to explore these issues for large companies, public sector workplaces and small businesses. We find that tight time schedules, flextime, telework, schedule control and fully paid nontransferable leaves of absence constitute policies that favor involved fatherhood, while measures without wage replacement generate fear of penalization in the workplace and do not fit the persistent relevance of the provider role. In addition, un-similar supervisors, envy, lack of understanding and gender stereotypes among co-workers and clients constitute cultural barriers at the workplace level. Contrary to our expectations, small businesses may offer a better work–life balance than large companies, while the public sector is not always as family-friendly as assumed.

The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle.

The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field.

The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well.

A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.