Non-stationary loading of a mechanical system consisting of a hinged beam and additional support installed in the beam span was studied using a model of the beam deformation based on the Timoshenko hypothesis with considering rotatory inertia and shear. The system of partial differential equations describing the beam deformation was solved by expanding the unknown functions in the Fourier series with subsequent application of the integral Laplace transform. The additional support was assumed to be realistic rather than rigid. Thus it has linearly elastic, viscous, and inertial components. This means that the effect of a part of the support vibrating with the beam was considered such that their displacements coincide. The beam and additional support reaction were replaced by an unknown concentrated external force applied to the beam. This unknown reaction was assumed to be time-dependent. The time law was determined by solving the first kind of Volterra integral equation. The methodology of deriving the integral equation for the unknown reaction was explained. Analytic formulae and results of computations for specific numerical parameters were given. The impact of the mass value on the additional viscoelastic support reaction and the beam deflection at arbitrary points were determined. The research results of this paper can be helpful for engineers in designing multi-span bridges.

This paper considers the task to clarify the circumstances of a traffic accident (TA) involving two vehicles as a result of their lateral tangential collision at low angles. The aim of the study is to construct a mathematical model of a tangential collision of vehicles for the reconstruction of TA circumstances. Owing to the combination of the law of conservation of momentum and the theory of impact using the coefficient of recovery, it was possible to construct a mathematical model that describes the development of such an accident and makes it possible to determine the main parameters of the movement of vehicles after and before the collision. An answer is given regarding the possibility of losing the directional stability of the vehicle and its movement in the lateral direction because of a collision. Based on the mathematical model, the basic parameters of vehicles motion after their side collision at angles of 5–15° were analytically determined, when there are no slip marks on the road surface. A numerical experiment was conducted on the example of a specific accident. The findings make it possible to argue about the possibility of losing the directional stability of vehicles and shifting them to the oncoming lane or curb as a result of collision. A comparison of the results of the numerical calculation with the results of software modeling of accidents and the circumstances that were established in the process of studying a real accident was carried out. It was concluded that the results obtained are consistent and make it possible to more accurately assess the parameters of the movement of vehicles after their lateral tangential collision. In general, this produces more objective results of the reconstruction of TA mechanism in cases where there are no traces of slipping and braking on the road surface. The proposed mathematical model could be used in collisions accompanied by minor deformations or damage to vehicles

When manufacturing machine parts using additive 3D technologies, we are faced with the task of choosing a specific manufacturing technology, material, and settings for the 3D printing process. These factors affect the manufacturing time, cost, accuracy, strength and other criteria for the performance of machine parts. Based on this, the purpose of the study is to develop recommendations for optimizing models of machine parts for 3D printing. The study describes the main approaches to optimizing three-dimensional models of machine parts at the design stage. This optimization avoids a number of problems that arise when using various 3D technologies: FDM (fused deposition modeling), SLA (laser stereolithography), etc. Depending on the type of the designed part and the applied additive 3D technology, additional requirements and restrictions are imposed on the models. The issues of optimizing models in terms of 3D printing time, manufacturing cost, geometry (accuracy) of the resulting model are considered, and the issues of the strength of the entire part or its individual elements are also partially investigated. Specific design solutions and recommendations for the manufacture of rotation parts, in particular, shafts and gears, are given. The issues of occurrence of some defects associated with overheating, uneven cooling and plastic shrinkage are considered. The simplest models for studying critical parts for strength are described. Recommendations have been developed for determining the properties of machine parts manufactured using additive 3D technologies for their design. This study will be of interest primarily to developers of 3D models and is designed to eliminate some of the problems that arise during 3D printing at the product design stage.

The problem of identifying the load acting on the elements of structures belongs to the class of inverse problems of the mechanics of a deformable solid, which are often incorrect. Solving such problems is associated with the instability of the calculation results, which requires the development of special methods for their research. This predetermines the relevance of this study. The object of the study is a single-pass cylindrical shell consisting of two rigidly fastened butt-fastened sections made of different materials. Each of the shells is assumed to be elastic isotropic, having a cross-section of medium thickness. The equations of axisymmetric deformation of shells are used within the framework of Timoshenko hypotheses. An approach to solving direct and inverse problems for such discretely heterogeneous objects is proposed, which implies the conditional separation of a discretely heterogeneous cylindrical shell along the length, followed by the addition of functions of fictitious loads. The main analytical relationships for building a system of integral Volterra equations are given, for which an analytic-numerical solution is derived. The final ratios have been obtained, which make it possible to calculate the kinematic and force parameters of the study object in the process of non-stationary deformation. The inverse problem of identifying arbitrary loads acting on a shell that is heterogeneous in length is solved in a general form. An algorithm for the restoration of pulse loads has been developed, which is robust to errors in the initial data (about 5 %). The material related to solving direct and inverse problems for shells that are discretely heterogeneous in length can significantly advance the methodology for identifying pulse loads acting on structural elements