The method of determining the locations of reinforcing elements in a composite orthotropic plate undergoing dynamic impact. Part 2. Calculation algorithm

Abstract

In this investigation, we realize the idea to link reinforcement positions of plane constructions with points of origin of the largest kinematic and dynamic characteristics after impact on the target. It is assumed that the largest dynamic characteristics, e.g. stresses, arise in the intersection points of wave surfaces, which 3542 Alexey A. Loktev et al. have experienced multiple reflections from the boundaries of the target. The origin and propagation of wave surfaces with finite velocities in the proposed model of the deformation of a flat target become possible due to the use of hyperbolic equations of Uflyand-Mindlin-Reissner type describing dynamic displacements of the points of the plate with consideration of the transverse shear deformation and rotational inertia of cross-sections. In this paper, we propose an algorithm taking into account different rheological properties of the interacting bodies, which is based on the analytical method of representation of unknown quantities in the form of expansions in a spatial coordinate and time, initial and boundary conditions, compatibility conditions. The final integro-differential equations are solved using numerical computational schemes. Moreover, the creation of algorithms for calculating impact interactions with a given wave portrait in colliding bodies, as well as their implementation in a software application with a simple and intuitive interface are desirable. In this paper, we developed a computational algorithm and a software system and tested them on the example of a flat target composed of materials with various mechanical characteristics. Furthermore, we provide specific recommendations for locations of reinforcing filaments or rods in the composite material.

Simulation of the railway under dynamic loading. Part 2. Splicing method of the wave and contact solutions

“…For the modeling of the contact the buffer is used, which can be represented as an elastic, visco-elastic and elastoplastic element. For these three elements the dependencies of the arising contact force in the point of interaction on the rail displacement and on mechanic characteristics of applied materials are determined [2,4,5,6] Since the existence of the buffer is a model representation of the contact area between two bodies, the buffer does not loose the stability during the contact process. At the moment of the contact with the rail, the wheelset exhibits a certain velocity, which vertical component is denoted as V0.…”

“…The motion of the wheelset after beginning of the interaction with the construction of the top railway is given by [6]    ,…”

“…This paper deals with the development of the method of matching solutions of the wave and the contact problem on the border of the area of contact of the impactor and target. There is a fairly large class of methods for determining the parameters of the behavior of structures and their elements under dynamic load, taking into account the wave phenomena [1], oscillations [2] and different rheological properties of the target material [3][4][5][6]. There are also analytical [7] and numerical [8] methods allowing to solve problems of contact interaction of solids, taking into account their movement [9], various geometric and mechanical properties [10].…”

Modelling of the dynamic contact between a wheel of a moving railway vehicle and rails with evaluation of defects emerging upon their interaction. Part 1. The defects of the rail and models of contact

“…In this case different contact models can be applied for the analysis, i.e., the quasistatic Hertz model, the linear elastic model, two elastoplastic contact models: the Aleksandrov-Kadomtsev model and the Kilchevsky model, the viscoelastic model with an exponential kernel of relaxation, the aggregated model based on the Hertz model and the unloading curve, and the viscoelastic model with the Riemann-Liouville fractional derivatives [5][6][7][8][9][10]. 2) The linear elastic model [7,9,11]…”

“…Here for a final solution of the described problem and for acquiring graphical or tabular time dependencies of desired characteristics of the railway track's deformation we use the following relations [7,9,11]: 1 21 2 0 0 1 3 5 3 2 1 2 1 0 1 1 4 3 cos 2 cos cos , 2 6 120…”