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Discusses the automated shape design of the electrodes supplying an arrangement for high‐voltage test. Obtains results that are feasible for industrial applications by means of an optimisation algorithm able to process discrete‐valued design variables.

In the paper, attention is focused on a class of single‐phase transformers that are employed when a high‐voltage withstand test is required for verifying the quality of the dielectric insulation of a given component. The HV winding of this kind of transformer is made up of several layers, characterized by height that decreases along with the increase of the voltage profile in order to keep the distance between winding and ground within acceptable limits. Therefore, the designer of such devices is mainly concerned with the shaping of the HV winding; starting from a tentative configuration, he has to find the winding shape such that the electric breakdown cannot occur, at the same time keeping the volume of oil and active materials as small as possible. Traditionally, the design is developed by means of a trial‐and‐error approach based on a sequence of field analyses, varying a design variable at a time; the paper shows how the design problem can be solved more efficiently by optimizing the profile of the winding in an automatic way.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.

The power transformer is one of the most important pieces of equipment in a power system. The necessity for the optimum design of a power transformer arises because the design chosen should satisfy all the limitations and restrictions placed on it. This paper presents an improved fast evolutionary programming (IFEP) technique for the optimal design of a three‐phase power transformer.

The optimization of the transformer design problem is formulated as an NLP problem, expressing the objective and constraint functions in terms of the selected independent variables. Here the cost of the transformer is considered as the objective function and is the sum of material cost of stampings and copper windings, cost of cooling tube arrangements, cost of cooling medium, insulation cost and labour cost. A computer program is written from which the optimal design parameters are obtained. For optimization, the classical evolutionary programming (CEP) technique and its variant the IFEP technique are used and the results are compared.

The application of CEP and IFEP for transformer design has been demonstrated on two test cases. It has been observed that this IFEP outperforms the CEP in obtaining the optimum design of transformers of smaller as well as larger ratings in terms of execution time, convergence rate, quality and success rate.

The proposed method results in the economical design of a three‐phase power transformer which can significantly reduce the cost of manufacturing transformers.

The purpose of this paper is to present a methodology based on an optimizer linked with electric finite element method (FEM) for automating the optimized design of power transformer insulation system structures.

The proposed methodology combines two stages to obtain the optimized design of transformer insulation system structures. First, an analytical calculation is carried out with the optimizer to search a candidate solution. Then, the candidate solution is numerically checked in detail to validate its consistency. Otherwise, these two steps are iteratively repeated until the optimizer finds a candidate solution according to the objective function.

The solutions found applying the proposed methodology reduce the inter-electrode distances compared to those insulation designs referenced in the literature for the same value of safety margin.

The proposed methodology explores a wide range of insulation system structures in an automated way which is not possible to do with the classical trial-and-error approach based on personal expertise.

There exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the beam simultaneously; such structures may help fulfil practical design requirements of the future and improve structural efficiency. In this context, the purpose of this paper is to extend the analytical model developed earlier to thick BDFG circular beams by using first-order shear deformation theory which allows for a non-zero shear strain distribution through the thickness of the beam.

Smooth functional variations of the material properties have been assumed along the axis and thickness of the beam simultaneously. The governing equations developed have been solved analytically for some representative determinate circular beams. In order to ascertain the effects of shear deformation in these structures, the total strain energy has been decomposed into its bending and shear components and the effects of the beam thickness and the arch angle on the shear energy component have been studied.

Closed-form exact solutions involving through-the-thickness integrals carried out numerically are presented for the bending of circular beams under the action of a variety of concentrated/distributed loads.

The results clearly indicate the importance of capturing shear deformation in thick BDFG beams and demonstrate the capability of tuning the response of these beams to fit a wide variety of structural requirements.

Seeks to determine the optimal shape design of an induction heating device.

Presents, through a case study, the optimal shape design of a multiple coil inductor for surface heating. Resorts to a procedure of automated optimal design, based on evolutionary optimisation and processing both continuous‐valued and discrete‐valued variables.

Demonstrates that it is possible to solve the design problem routinely using an optimisation tool (OptiNet) that is built to work seamlessly with a coupled electromagnetic‐thermal simulation.

Every design criterion that is likely to be of interest to a designer of industrial applications can be described to the system and optimised in a reasonable time frame.

The purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.

The FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.

A series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.

This paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

In this paper, a superconvergent patch recovery method is proposed for superconvergent solutions of modes in the finite element post-processing stage of variable geometrical Timoshenko beams. The proposed superconvergent patch recovery method improves the solution speed and accuracy of the finite element analysis of a curved beam. The free vibration and natural frequency of the beam were considered for studying forced vibrations and structural resonance. Beam vibration mode analysis was performed for high-precision vibration mode solutions and frequency values. The proposed method can be used to compute beam vibration modes of beams with different shapes and boundary conditions as well as variable cross sections and curvatures. The purpose of this paper is to address these issues.

An adaptive method was proposed to analyse the in-plane and out-of-plane free vibrations of the variable geometrical Timoshenko beams. In the post-processing stage of the displacement-based finite element method, the superconvergent patch recovery method and high-order shape function interpolation technique were used to obtain the superconvergent solution of mode (displacement). The superconvergent solution of mode was used to estimate the error of the finite element solution of mode in the energy form under the current mesh. Furthermore, an adaptive mesh refinement was proposed by mesh subdivision to derive an optimised mesh and accurate finite element solution to meet the preset error tolerance.

The results computed using the proposed algorithm were in good agreement with those computed using other high-precision algorithms, thus validating the accuracy of the proposed algorithm for beam analysis. The numerical analysis of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams helped verify that the solutions of frequencies were consistent with the results obtained using other specially developed methods. The proposed method is well suited for the mesh refinement analysis of a curved beam structure for analysing the changes in high-order vibration mode. The parts where the vibration mode changed significantly were locally densified; a relatively fine mesh division was adopted that validated the reliability of the mesh optimisation processing of the proposed algorithm.

The proposed algorithm can obtain high-precision vibration solutions of variable geometrical Timoshenko beams based on more optimized and reasonable meshes than the conventional finite element method. Furthermore, it can be used for vibration problems of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams. The proposed algorithm can be extended for application in superconvergent computation and adaptive analysis of finite element solutions of general structures and solid deformation fields and used for adaptive analysis of more complex plates, shells and three-dimensional structures. Additionally, this method can analyse the vibration and stability of curved members with crack damage to obtain high-precision vibration modes and instability modes under damage defects.