Automatic Control System for Bodies of Revolution Processing

This research is related to metalworking processing of bodies of revolution with the help of universal lathe machines. The technology includes the application of two types of vibrations to the working tool and the processed surface error measurement. To increase the manufacturing accuracy, the workpiece processed surface error is measured while a workpiece is being rotated; this rotation is performed with the workpiece being rigidly fixed in end supports and at the same time being damped in the sections between these supports. Furthermore, the parameters of vibrations applied to the tool working travel are defined by the workpiece form error and the nature of distribution of stresses that appear when the workpiece is fixed; the nature of the workpiece processed surface form error is extrapolated from the data obtained in the workpiece sections between the supports. Before manufacturing, the workpiece is corrected while being fixed in rigid supports, and the correction itself is performed as the function of magnitude and vector of the workpiece maximum deflection plane. The workpiece may be fixed in rigid supports; steady rests with double rollers may be used as such supports. The workpiece dampening in its sections between end supports may be performed using self-centering steady rests.

STRENGTH OF SHIPS’ GRILLAGES UNDER LATERAL LOAD AND IN-PLANE COMPRESSION

The paper deals with strength of a grillage loaded by lateral load and in-plane compression load (in one direction). It consists of a system of prismatic girders crossing under 90°. The compression load is taken by the longitudinal girders that are elastically fixed on rigid supports. The system of aggregated differential equations is derived for solution of the problem using the Lagrange method. It allows for replacement of the system of aggregated differential equations by a system of independent differential equations. These equations for the case of simultaneous action of lateral and longitudinal compression load have the form of differential equations for bending of prismatic girders laying on elastic foundation and loaded with lateral and longitudinal compression forces. When only lateral load exists, the form of these equations coincides with the form of differential equations for bending of girders laying on elastic foundation and loaded with lateral load alone. When only longitudinal compression load exists, the form of these equations coincides with the form of differential equations for buckling of girders laying on elastic foundation. Solutions are given for bending of a grillage (the first two problems). Formulas are derived for calculation of the parameters of longitudinal girders’ bending when girders’ end sections are elastically fixed. Also, formulas are derived for calculation of the reaction forces at cross-points of transverse and longitudinal girders. When only longitudinal compression load exists (third problem), a solution is given for the connection between the coefficient of elastic foundation’s rigidity and the Euler force. Results obtained by using the proposed method are compared with FEA simulations.

Advanced computational technique based on kriging and Polynomial Chaos Expansion for structural stability of mechanical systems with uncertainties

In this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters.

Analysis of Parameters of a Rectified Tank on the Basis of In-Situ Tests

The vertical deflection of building structures is a common problem. However, the rectification of objects is rarely carried out due to the lack of information about the parameters of objects requiring rectification. The subject of the analysis are parameters of rectified water tank 950 m3 in volume, which were investigated due to the stiffness and number of supports built into the structure. During in-situ testing, the stiffnesses of supports were determined. The model of the rectified structure was then defined and it was shown that its parameters can be described by means of three matrices: stiffness, displacement forms of the elevated object and displacement forms of supports. Absolute values of elements of the stiffness matrix increased as the stiffness and number of supports increased. At the same time, values of elements of the matrix of displacement forms of the elevated object increased. The conducted energy analysis demonstrated that the amount of energy required for the vertical displacement of the structure decreased with an increasing stiffness and number of supports. This means that placing a greater number of supports under rectified structures and ensuring more rigid supports is beneficial to the rectification. Results of the conducted analyses were confirmed during in-situ tests.

Vibrations of a Girder on Rigid Supports of Finite Mass Interacting With Soil under Seismic Loads

Transverse vibrations of a single-span girder bridge are considered in the article; the pile part of the bridge interacts with the surrounding soil under seismic action. We assume that the strain of the structure does not go beyond the elastic limit, and the vibrations are linear. The bridge supports are assumed to be immersed in soil and interact with a rigid body under the impact of unsteady dynamic influences. We consider the case when the right and left supports have equal masses and interact with the surrounding soil. Here the symmetry condition is applied, so it is sufficient to consider the equation for the right half of the girder. The problems are solved by the analytical Fourier method under given boundary conditions. The results obtained are analyzed and presented in the form of the distribution of displacements and stresses over the time and length of the bridge structures.

Nonlinear Blast Responses of Thin Shell Roof Over Long Span Structures

This paper adopts both explicit and implicit finite element methods in a specialist package LS-DYNA to investigate the nonlinear, dynamic response of a long span shell roof structure when subjected to blast loading. Parametric studies have been carried out on blast loaded laminated glass plates with reference to experimental results obtained by European researchers. A case study that has been chosen is a light rail station in The Netherlands called The Erasmusline. Following the detonation of 15[Formula: see text]kg TNT charge, explicit analysis showed breakage surrounding the rigid supports along the edge beam where modal vibrations are restrained. An implicit analysis has confirmed the resonances in global eigen-frequencies where most blast damage is localized around the roof canopy hence producing cracking and potential glass detachment from the panels without full structural demolition. This insight from this study will inform structural engineers about the potential modes of failure and preventative strategies to minimize further secondary losses of life or assets from a terrorist attack.

Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

A numerical algorithm for solving initial-boundary value problems with nonlinear boundary conditions was developed and implemented. The algorithm is constructed with reference to modeling of oscillations of an elastically supported deformable rod with limit stops at the ends under the action of a moving variable force. Such a rod is the design scheme of a number of building structures, including the span structure of a floating bridge of continuous system with limiting rigid supports at the ends. Chebyshev's polynomials were used to improve the computational schemes for realizing the practical problems of modeling constructive-nonlinear oscillations of building structures. The solution does not lose stability for large values of the elasticity coefficients of elastic couplings. Using the developed approach, it is possible to perform virtual computing experiments to skip a variety of movable loads on the floating bridge to analyze its deformed state and to make well-grounded design decisions.