Side busking of the cantilever beam with narrow rectangular cross section

The problem of lateral buckling of a cantilever strip with a constant narrow cross section loaded with a concentrated force at the end of the span is considered. In the study of lateral buckling of beam energy method was used. For the case of load application in the center of gravity, the problem is reduced to a generalized secular equation. The relationship between the magnitude of the critical force and the position of the point of application of the load. A comparison of the results obtained by the authors with an analytical solution using infinite series and a numerical iterative method is shown

Calculation of shallow polymer shell taking the creep into account

In this paper, we obtain the equations allowing the calculation of shallow shells taking the creep into account under an arbitrary law of relationship between creep deformations and stresses. We also consider the methodology of calculation of polymeric membranes, the material of which is subject to a nonlinear equation of Maxwell-Gurevich

Calculation of shallow polymer shell taking the creep into account

In this paper, we obtain the equations allowing the calculation of shallow shells taking the creep into account under an arbitrary law of relationship between creep deformations and stresses. We also consider the methodology of calculation of polymeric membranes, the material of which is subject to a nonlinear equation of Maxwell-Gurevich

Determination of physic and mechanical parameters of high-density polyethylene based on relaxation curves due to the presence of hydroxyapatite and ionizing radiation

Relatively low physical and mechanical parameters of polymers negatively affect the possibility of using this material everywhere. There are ways to improve the elastic and rheological characteristics of some varieties of polymers: addition of additives and irradiation with ionizing radiation. However, these methods can lead both to the cross-linking of polymer molecules with the improvement of its parameters, and to its destruction. In this article shown the theoretical definition of physic and mechanical parameters of high-density polyethylene by known stress relaxation curves, and a comparison of the experimental data of high-density polyethylene (HDPE) with the data obtained theoretically, which, in turn, saves material resources and man-hours for the experiment and its subsequent analysis

Determination of physic and mechanical parameters of high-density polyethylene based on relaxation curves due to the presence of hydroxyapatite and ionizing radiation

Relatively low physical and mechanical parameters of polymers negatively affect the possibility of using this material everywhere. There are ways to improve the elastic and rheological characteristics of some varieties of polymers: addition of additives and irradiation with ionizing radiation. However, these methods can lead both to the cross-linking of polymer molecules with the improvement of its parameters, and to its destruction. In this article shown the theoretical definition of physic and mechanical parameters of high-density polyethylene by known stress relaxation curves, and a comparison of the experimental data of high-density polyethylene (HDPE) with the data obtained theoretically, which, in turn, saves material resources and man-hours for the experiment and its subsequent analysis

Stability of E. Reyssner’s plates on the elastic non-winkler foundation

The problem of E. Reyssner’s plate stability lying on an elastic three-dimensional layer with desired elastic constants. The end surfaces of layer are smooth, connection holding. It is assumed that the plate is in a flat stress-strain state of the effects on its cylindrical surface of the self-balanced load, with some numerical parameter characterizing the magnitude of the load at loss of stability of the plate. From the conditions of restraint ties оne obtain a system of equations for determining the numerical parameter. Method is given for calculating the lowest value of the parameter at which the plate’s loss of stability is fixed. As special cases, the results of the classical theory and model of Winkler foundation are present

Stability of E. Reyssner’s plates on the elastic non-winkler foundation

The problem of E. Reyssner’s plate stability lying on an elastic three-dimensional layer with desired elastic constants. The end surfaces of layer are smooth, connection holding. It is assumed that the plate is in a flat stress-strain state of the effects on its cylindrical surface of the self-balanced load, with some numerical parameter characterizing the magnitude of the load at loss of stability of the plate. From the conditions of restraint ties оne obtain a system of equations for determining the numerical parameter. Method is given for calculating the lowest value of the parameter at which the plate’s loss of stability is fixed. As special cases, the results of the classical theory and model of Winkler foundation are present

Optimization of thick-walled spherical shells at thermal and power influences

The problem of optimization for thick-walled shell, experiencing temperature and power feedback. Under the influence of temperature field the properties of material of an object can change. That allows to manage the deflected mode of such objects while achieving a certain law of radial change of physical and mechanical parameters. A centrally symmetric problem of elasticity theory is studied. As a result we received a law of variation of Young's modulus, in which a spherical dome is equally stressed according to the simplified theory of Mohr. The problem was reduced to a Bernoulli differential equation. This equation was solved numerically using Runge-Kutta method of fourth order

Flat bending shape stability of the beams with variable section width

The paper proposes a methodology for calculating lateral buckling of beams of variable rectangular cross section based on the energy approach. The technique is considered on the example of a cantilever beam of variable width with two sections under the action of a concentrated force. The twist angle function was set in the form of a trigonometric series. As a result, the problem is reduced to a generalized secular equation

Calculation of wooden beams on the stability of a flat bending shape enhancement

Flat bending stability problem of constant rectangular cross section wooden beam, loaded by a distributed load is considered. Differential equation is provided for the cases when load is located not in the center of gravity. The solution of the equation is performed numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the Matlab package. A relationship between the value of the critical force and the position of the load application point is obtained. A linear approximating function is selected for this dependence