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The paper explores the geometrical structure of electrodynamics using the algebra of differential forms. Stokes' theorem links the local to the global geometrical features of electromagnetic systems. The gauge invariance of the potentials is shown to be linked to the geometry of a circle in the complex plane, which exhibits the inner geometry of electrodynamics. The total geometry of a system is a combination of this inner geometry with the usual space‐time geometry. The application of these geometrical features to computation is explained.

In this paper we present a variational method which fits very well in the wave behaviour of electrodynamics.

The purpose of this paper is to show how the geometrical information of Maxwell's equations is coded into the constitutive equations.

The Maxwell's equations have been written with the tensorial algebra into a three‐dimensional Euclidean space and compared with the usual four‐dimensional relativistic approach.

This simple geometry allows the finding of the relativistic information coded on the electric and magnetic fields, showing that they are not independent as relativity affirm obtaining their transformation for a moving inertial observer.

The main value of the paper is to present a simple mathematical tool which enables the engineers or applied physicists to obtain the relativistic transformations of the fields without using four‐dimensional geometries and the more sophisticated mathematical techniques.

The divergence equations in Maxwell’s theory are Gauss law and the statement that magnetic monopoles do not exist; from this point of view these two equations are fundamental. However, from a practical point of view, it is generally believed that Maxwell’s divergence equations are redundant and may be ignored provided that they are satisfied at some time t‐0. It has been proved recently that this idea is not correct for boundary‐initial value problems. To make mathematical arguments more accessible, we analyse here the role of the divergence equations in the framework of 2D‐electromagnetism.

There are two conflicting views about electromagnetic phenomena. The first is based on the action between stationary and moving particles of electric charge and the second on energy distributions in electric and magnetic fields. The difference between these approaches is seen most clearly in the roles assigned to the potentials. According to the particle view the potentials convey the force from one particle to another, whereas in the field approach the potentials are system parameters related to the field energy. The article compares the two views and concludes that the particle view faces impossible difficulties because it ascribes local significance to quantities which are unobservable and conflicts with the quantum‐mechanical understanding of charge as a statistical distribution.

The purpose of this paper is to examine the current situation in numerical field computation, paying special attention to the role of education in developing new ideas to meet the ever growing demands of industry.

The paper presents a historical review, the state of the art and recent advances in the field of computational electromagnetics at leading universities and research institutes in Poland. Contributions made by Polish scientists to the development of fundamental electromagnetism, as well as to computational methods, are emphasized, and some conclusions are drawn regarding expected future developments.

This paper aims to celebrate the 100th anniversary of Einstein's works, published in 1905.

The paper presents a brief appraisal of Einstein's work.

The paper reminds the reader of the 1905 discoveries, such as photoelectric phenomena, special theory of relativity and Brown's motions.

The paper deals with the problem of how Einstein's concept contradicts or follows the Faraday concept of electromagnetic fields.

This paper aims to study the shape of the concrete arched bridge by particle swarm optimization algorithm.

Finite element model of open-spandrel concrete arch bridges was constructed using a number of parameters. Design variables of optimization problem include height of skewback abutment, height of arch crown, position of crown with respect to global axes and left and right radius of up and down arches. After parametric modeling of bridge geometry and application of multi-objective particle swarm optimization, the shape optimization of bridge arch was determined. The concrete volume used in bridge substructure construction and maximum principal tensile stress of concrete arch body was adopted as two objective functions in this study. The optimization problem aims to minimize the two objective functions. Geometric and stress constraints are also included in the problem.

Based on the results presented in the paper, the Pareto front is generated which helps the decision-maker or designer to pick the compromise solution from among 20 optimum designs according to their subjective preferences or engineering judgment, respectively. Moreover, to help the decision-maker, the two multiple objective decision-making methods were used for selection of the best solution from among nondominated solutions.

This research aims to solve an interesting optimization problem in structural engineering. Optimization of arch bridges structure was done for reducing construction costs and increasing safety for the first time.

The purpose of this study is to enable performing reliability-based design optimisation (RBDO) for a composite component while accounting for several multi-scale uncertainties using a large representative volume element (LRVE). This is achieved using an efficient finite element analysis (FEA)-based multi-scale reliability framework and sequential optimisation strategy.

An efficient FEA-based multi-scale reliability framework used in this study is extended and combined with a proposed sequential optimisation strategy to produce an efficient, flexible and accurate RBDO framework for fibre-reinforced composite laminate components. The proposed RBDO strategy is demonstrated by finding the optimum design solution for a composite component under the effect of multi-scale uncertainties while meeting a specific stiffness reliability requirement. Performing this using the double-loop approach is computationally expensive because of the number of uncertainties and function evaluations required to assess the reliability. Thus, a sequential optimisation concept is proposed, which starts by finding a deterministic optimum solution, then assesses the reliability and shifts the constraint limit to a safer region. This is repeated until the desired level of reliability is reached. This is followed by a final probabilistic optimisation to reduce the mass further and meet the desired level of stiffness reliability. In addition, the proposed framework uses several surrogate models to replace expensive FE function evaluations during optimisation and reliability analysis. The numerical example is also used to investigate the effect of using different sizes of LRVEs, compared with a single RVE. In future work, other problem-dependent surrogates such as Kriging will be used to allow predicting lower probability of failures with high accuracy.

The integration of the developed multi-scale reliability framework with the sequential RBDO optimisation strategy is proven computationally feasible, and it is shown that the use of LRVEs leads to less conservative designs compared with the use of single RVE, i.e. up to 3.5% weight reduction in the case of the 1 × 1 RVE optimised component. This is because the LRVE provides a representation of the spatial variability of uncertainties in a composite material while capturing a wider range of uncertainties at each iteration.

Fibre-reinforced composite laminate components designed using reliability and optimisation have been investigated before. Still, they have not previously been combined in a comprehensive multi-scale RBDO. Therefore, this study combines the probabilistic framework with an optimisation strategy to perform multi-scale RBDO and demonstrates its feasibility and efficiency for an fibre reinforced polymer component design.