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A class of robust and efficient beamforming methods is developed in this paper for the optimised design of realistic microstrip antennas on arbitrarily curved substrates. More specifically, this paper aims to focus on the formulation of an effective and computationally light beamforming algorithm and its implementation on a novel realistic cylindrical-substrate microstrip array antenna with significantly decreased size, wideband operation and enhanced radiation characteristics.

The proposed multi-parametric schemes introduce an efficient null-steering concept, which drastically annihilates the undesired beamformer waveform artefacts, while retaining the real output signal undistorted. In particular, the key objective is the accurate calculation of the appropriate complex feeding weights, required to set nulls along the propagation directions of the unwanted signals and a maximum towards the propagation direction of the desired incoming signal. The featured technique, combined with a modified finite element method, is applied to the design of a new family of cylindrical-substrate microstrip array antennas.

Numerical results, mainly concerning customisable three-dimensional radiation patterns and attributes, certify the merits of the algorithm and its limited system demands. The introduced beamforming algorithms are applied to a variety of different inputs (desired radiation patterns), which indicate that the designed cylindrical-substrate antenna overwhelms existing designs in terms of computational cost for the beamforming algorithm, while retaining acceptable values for radiation characteristics, such as gain, directivity and side-lobe suppression. In this manner, the effectiveness of the prior methodology and the benefits of this newly shaped array antenna are comprehensively revealed and substantiated.

Rigorous beamforming techniques in conjunction with a class of contemporary array antennas are developed for potential use in high-end communication systems, such as 5G configurations. The proposed cylindrical-shaped structures are systematically designed, with an emphasis on space efficiency and wideband radiation effectiveness to offer fully adjustable setups. To this aim, the cylindrical-substrate microstrip antenna, because of its inherent azimuthal symmetry and confined overall dimensions, provides reliable operation and promising performance.

The determination of mode-I fracture toughness of brittle structural materials by means of the notched Brazilian disc configuration is studied. Advantage is taken of a recently introduced analytical solution and, also, of data provided by an experimental protocol with notched marble specimens under diametral compression using the loading device suggested by International Society for Rock Mechanics (ISRM) and also the three-dimensional digital image correlation (3D-DIC) technique.

The analytical solution highlighted the role of geometrical factors, like, for example, the width of the notch, which are usually disregarded. The data of the experimental protocol were comparatively considered with those concerning the response of the specific material under uniaxial tensile load.

This combined study provided interesting data concerning some open issues, as it is the exact crack initiation point and the level of the critical load causing crack initiation. It was definitely indicated that the crack initiation point is not a priori known (even for notched specimens) and, also, that the maximum recorded load does not correspond by default to the critical load responsible for the onset of catastrophic macroscopic fracture.

It was suggested that the load considered critical one for the determination of mode-I fracture toughness K_IC is erroneous. At a load equal to about 70% of the maximum one, a process zone is formed (zone of non-reversible phenomena) around the notch's crown, designating termination of the validity of any linear elastic solution used to determine the normalized stress intensity factors (SIFs). Moreover, at a load level equal to about 95% of the macroscopically observed fracture load, crack propagation has already begun. Therefore, the experimental procedure must be monitored with additional equipment, providing an overview of the displacement field developed during loading.