This paper presents a finite element method (FEM)-based fracture risk assessment in patient-specific osteoporotic lumbar vertebra L1. The influence of osteoporosis is defined by variation of parameters such as thickness of the cortical shell, the bone volume–total volume ratio (BV/TV), and the trabecular bone score (TBS). The mechanical behaviour of bone is defined using the Ramberg–Osgood material model. This study involves the static and nonlinear dynamic calculations of von Mises stresses and follows statistical processing of the obtained results in order to develop the patient-specific vertebra reliability. In addition, different scenarios of parameters show that the reliability of the proposed model of human vertebra highly decreases with low levels of BV/TV and is critical due to the thinner cortical bone, suggesting high trauma risk by reason of osteoporosis.

This paper is devoted to investigating numerically, by finite element analysis (FEA), and analytically the influences and effects of laser processing of the surface of thin-plate, low-carbon structural steel. The plate mechanical properties—axial and flexural stiffnesses, force-deflection behavior and cross-section force-strain behavior—are investigated after different laser treatments. An analytical methodology of the estimation of the cross-section area of the laser-processed metal is also proposed in the present article, that can be applied to choosing the reasonable distance between the centers of the laser-processed tracks. The methodology takes into account the width of the laser-processed tracks and the distances between these tracks. The experimental, finite element numerical and analytical analyses showed that the laser treatments of the surface of the steel plate increase the yield point of the laser-processed metal and the axial and flexural stiffnesses of the plate.

In the present article, a version of the lattice or spring network method is proposed to model the mechanical response of elastic particulate composites with a high volume fraction of spherical particles and with a much weaker matrix compared to the stiffness of the particles. The main subject of the article is the determination of the axial stiffnesses of the springs of the cell. A comparison of the mechanical response of a three-dimensional particulate composite cube obtained using the finite element method and the proposed methodology showed that the efficiency of the proposed methodology increases with an increasing volume fraction of the particles.

Modern industrial enterprises require high accuracy and precision feedback systems to fulfil cutting edge requirements of technological processes. As demand for a highly accurate system grows, a thin gap between throughput and quality exists. The conjunction of ultrafast lasers and modern control strategies of mechatronic systems can be taken into account as an effective solution to reach both throughput and tolerances. In the present paper, the dynamic errors of the moving platform of the one degree of freedom stage, based on linear motor and air bearings, have been analyzed. A precision positioning system is investigated as a symmetric system which is based on symmetric linear motor. The goal of the present article is to investigate the controllers of the different architecture and to find the best controller that can ensure a stable and small dynamic error of the displacement of the stage platform at four different constant velocities of the moving platform. The relations between the controller order, velocity and the displacement dynamic error have been investigated. It is determined that higher-order controllers can reduce the dynamic error significantly at low velocities of the moving platforms: 1 and 5 mm/s. On the contrary, the low order controllers of 4th-degree polynomials of the transfer function can also provide small dynamic errors of the displacement of the platform.

The stochastic modelling of the microcracking and the force‐displacement behaviour of the tensile steel reinforced tie using the lattice model is presented in the current article. The three‐dimension problem of the modelling of the tie is reduced to the two‐dimensional so as the main stiffness parameters of the concrete and the reinforcement of the two‐dimensional model would be the same as for the three‐dimensional. The concrete and steel obey the Hook law. All elastic constants, as well as dimensions of the tie, were assumed as the deterministic quantities except for the critical concrete tensile strains which were treated as a two‐dimensional stationary uncorrelated truncated Gaussian random field. The discrete element approach and the explicit integration scheme have been used for the modelling. The estimations of the main parameters of the force‐displacement behaviour stochastic process and other statistical indexes were obtained using 72 realization of the force‐displacement behaviour of a chosen model. Extra two stochastic realizations of the two different models, as well as three deterministic models, were modelled to compare stochastic and deterministic behaviour of the force‐displacement behaviour. The analysis showed that the force‐displacement behaviour of the tie under tensile force cannot be treated as a Gaussian stochastic process when the p value is 0.05 at the small displacements and within the interval when the cracking of the concrete is very intensive. However, at the bigger displacements, when the cracking becomes less intensive, the tensile force can be treated as a Gaussian random variable.