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In this work we present interrelations between different finite rotation parametrizations for geometrically exact classical shell models (i.e. models without drilling rotation). In these kind of models the finite rotations are unrestricted in size but constrained in the 3‐d space. In the finite element approximation we use interpolation that restricts the treatment of rotations to the finite element nodes. Mutual relationships between different parametrizations are very clearly established and presented by informative commutative diagrams. The pluses and minuses of different parametrizations are discussed and the finite rotation terms arising in the linearization are given in their explicit forms.

This paper describes a method for the construction of rational polynomial paths that does not require the apriori specification of either vertices or weights. An algebra of rational paths is developed within which paths with positive weights can be generated from more elementary paths with the same property. Case studies demonstrate that the path algebra can provide a simple means of obtaining exact rational representations of paths defined in non‐rational terms.

We consider the gradient method applied to the optimal control of a system for which each simulation is expensive. A method for increasing the number of unknowns, and relying on multilevel ideas is tested for the academic problem of shape optimization of a nozzle in a subsonic or transonic Euler flow.

Observations in a dataset are rarely missing at random. One can control for this non-random selection of the data by introducing fixed effects or other nuisance parameters. This chapter deals with consistent estimation the presence of many nuisance parameters. It derives a new orthogonality concept that gives sufficient conditions for consistent estimation of the parameters of interest. It also shows how this orthogonality concept can be used to derive and compare estimators. The chapter then shows how to use the orthogonality concept to derive estimators for unbalanced panels and incomplete data sets (missing data).

The waste recycling industry increasingly relies on magnetic density separators. These devices generate an upward magnetic force in ferro-fluids allowing to separate the immersed particles according to their mass density. Recently, a new separator design has been proposed that significantly reduces the required amount of permanent magnet material. The purpose of this paper is to alleviate the undesired end-effects in this design by altering the shape of the ferromagnetic covers of the individual poles.

The paper represents the shape of the ferromagnetic pole covers with B-splines and defines a cost functional that measures the non-uniformity of the magnetic field in an area above the poles. The authors apply an iso-geometric shape optimization procedure, which allows us to accurately represent, analyze and optimize the geometry using only a few design variables. The design problem is regularized by imposing constraints that enforce the convexity of the pole cover shapes and is solved by a non-linear optimization procedure. The paper validates the implementation of the algorithm using a simplified variant of the design problem with a known analytical solution. The algorithm is subsequently applied to the problem posed.

The shape optimization attains its target and yields pole cover shapes that give rise to a magnetic field that is uniform over a larger domain.

This increased magnetic field uniformity is obtained at the cost of a pole cover shape that differs per pole. This limitation has negligible impact on the manufacturing of the separator. The new pole cover shapes therefore lead to improved performance of the density separation.

Due to the larger uniformity the generated field, these shapes should enable larger amounts of waste to be processed than the previous design.

This paper treats the shapes optimization of magnetic density separators systematically and presents new shapes for the ferromagnetic poles covers.

The purpose of this paper is to present a method for analysis and optimization of morphing wing. Moreover, a numerical advantage of morphing airfoil wing, typically assessed in simplified two-dimensional analysis is found using higher fidelity methods.

Because of multi-point nature of morphing wing optimization, an approach for optimization by analysis is presented. Starting from naïve parametrization, multi-fidelity aerodynamic data are used to construct response surface model. From the model, many significant information are extracted related to parameters effect on objective; hence, design sensitivity and, ultimately, optimal solution can be found.

The method was tested on benchmark problem, with some easy-to-predict results. All of them were confirmed, along with additional information on morphing trailing edge wings. It was found that wing with morphing trailing edge has around 10 per cent lower drag for the same lift requirement when compared to conventional design.

It is demonstrated that providing a smooth surface on wing gives substantial improvement in multi-purpose aircrafts. Details on how this is achieved are described. The metodology and results presented in current paper can be used in further development of morphing wing.

Most of literature describing morphing airfoil design, optimization or calculations, performs only 2D analysis. Furthermore, the comparison is often based on low-fidelity aerodynamic models. This paper uses 3D, multi-fidelity aerodynamic models. The results confirm that this approach reveals information unavailable with simplified models.

This paper aims to address the issue of designing aerodynamically robust empennage. Aircraft design optimization often narrowed to analysis of cruise conditions does not take into account other flight phases (manoeuvres). These, especially in unmanned air vehicle sector, can be significant part of the whole flight. Empennage is a part of the aircraft, with crucial function for manoeuvres. It is important to consider robustness for highest performance.

Methodology for robust wing design is presented. Surrogate modelling using kriging is used to reduce the optimization cost for high-fidelity aerodynamic calculations. Analysis of varying flight conditions, angle of attack, is made to assess robustness of design for particular mission. Two cases are compared: global optimization of 11 parameters and optimization divided into two consecutive sub-optimizations.

Surrogate modelling proves its usefulness for cutting computational time. Optimum design found by splitting problem into sub-optimizations finds better design at lower computational cost.

It is demonstrated, how surrogate modelling can be used for analysis of robustness, and why it is important to consider it. Intuitive split of wing design into airfoil and planform sub-optimizations brings promising savings in the optimization cost.

Methodology presented in this paper can be used in various optimization problems, especially those involving expensive computations and requiring top quality design.

In the context of electrical impedance tomography (EIT), this paper aims to evaluate limitations of estimating conductivity or resistivity, as well as the improvements achieved with the use of an alternate description of the solution space, the logarithmic conductivity.

A quantitative analysis is performed, solving the inverse EIT problem by using the Gauss–Newton and non-linear conjugate gradient methods for a numerical phantom of 15 elements. A property of symmetry is studied for the direct EIT problem for a phantom of 385,601 elements.

Solving the inverse EIT problem in logarithmic conductivity is more robust to the initial guess, as solutions are kept within physical bounds (conductivity positiveness). Also, convergence is faster and less dependent on the final values of the estimates.

Logarithmic conductivity provides an advantageous description of the solution space for the EIT inverse problem. Similar estimation problems might be subject to analogous conclusions.

This study provides a novel analysis, quantitatively comparing the effect of different variables to solve the inverse EIT problem.

The purpose of this paper is to determine the magnitude and spatial distribution of the heat transfer coefficient between the workpiece and the backing plate in a friction stir welding process using inverse modelling.

The magnitude and distribution of the heat transfer coefficient are the variables in an optimisation problem. The objective is to minimise the difference between experimentally measured temperatures and temperatures obtained using a 3D finite element model. The optimisation problem is solved using a gradient based optimisation method. This approach yields optimal values for the magnitude and distribution of the heat transfer coefficient.

It is found that the heat transfer coefficient between the workpiece and the backing plate is non-uniform and takes its maximum value in a region below the welding tool. Four different parameterisations of the spatial distribution of the heat transfer coefficient are analysed and a simple, two parameter distribution is found to give good results.

The heat transfer from workpiece to backing plate is important for the temperature field in the workpiece, and in turn the mechanical properties of the welded plate. Accurate modelling of the magnitude and distribution of the heat transfer coefficient is therefore an essential step towards improved models of the process. This is the first study using a gradient based optimisation method and a non-uniform parameterisation of the heat transfer coefficient in an inverse modeling approach to determine the heat transfer coefficient in friction stir welding.

The magnetic characterization of electrical steel is typically examined by measurements under the condition of unidirectional sinusoidal flux density at different magnetization frequencies. A variety of iron loss models were developed and parametrized for these standardized unidirectional iron loss measurements. In the magnetic cross section of rotating electrical machines, the spatial magnetic flux density loci and with them the resulting iron losses vary significantly from these unidirectional cases. For a better recreation of the measured behavior extended iron loss models that consider the effects of rotational magnetization have to be developed and compared to the measured material behavior. The aim of this study is the adaptation, parametrization and validation of an iron loss model considering the spatial flux density loci is presented and validated with measurements of circular and elliptical magnetizations.

The proposed iron loss model allows the calculation and separation of the different iron loss components based on the measured iron loss for different spatial magnetization loci. The separation is performed in analogy to the conventional iron loss calculation approach designed for the recreation of the iron losses measured under unidirectional, one-dimensional measurements. The phenomenological behavior for rotating magnetization loci is considered by the formulation of the different iron loss components as a function of the maximum magnetic flux density B_m, axis ratio f_Ax, angle to the rolling direction (RD) θ and magnetization frequency f.

The proposed formulation for the calculation of rotating iron loss is able to recreate the complicated interdependencies between the different iron loss components and the respective spatial magnetic flux loci. The model can be easily implemented in the finite element analysis of rotating electrical machines, leading to good agreement between the theoretically expected behavior and the actual output of the iron loss calculation at different geometric locations in the magnetic cross section of rotating electrical machines.

Based on conventional one-dimensional iron loss separation approaches and previously performed extensions for rotational magnetization, the terms for the consideration of vectorial unidirectional, elliptical and circular flux density loci are adjusted and compared to the performed rotational measurement. The presented approach for the mathematical formulation of the iron loss model also allows the parametrization of the different iron loss components by unidirectional measurements performed in different directions to the RD on conventional one-dimensional measurement topologies such as the Epstein frames and single sheet testers.