The article deals with the transition from corrugated plates and shells to smooth structures of equivalent rigidity. An expression for the potential deformation energy of an infinitely small element of an equivalent smooth shell and formulas that establish a connection between internal forces and generalized deformations of a corrugated structure are given. A review of the formulas for the equivalent stiffness of the corrugated shell during bending, presented in the works of various authors, is carried out. In order to select the dependencies that provide the smallest error when replacing the corrugated shell with a smooth one, a numerical experiment is performed in the LIRA finite element complex. A corrugated plate hinged around the contour under the action of a uniformly distributed projective load is considered. The calculation of the structurally orthotropic construction is performed numerically by the finite difference method. It is also established that the monograph of S.G. Lekhnitsky contains an incorrect formula for the moment of inertia of a sinusoidal corrugation.
Keywords: corrugated structures, plates and shells, finite element method, finite difference method, orthotropy, equivalent stiffness
The technique of calculating the metal corrugated structures using the finite element method for an axisymmetric load is considered in the article. One-dimensional finite elements in the form of truncated cones are used. Calculations are performed using the program developed by the authors in the Matlab package. An example of calculation of a ground well rigidly clamped in the base under the action of ground pressure is given. The sinusoidal profile of the corrugation is considered. The graphs of changes in bending moments and ring forces are presented. For a smooth shell of the same thickness, the bending moment in the pinch was 30.3% higher compared to the corrugated, and the maximum value of the ring force was 15.7% higher.
Keywords: metal corrugated structures, cylindrical shell, finite element method, axisymmetric problem, soil well, shell theory, edge effect
A constructive solution of the walls of wooden houses from round logs or a profiled beam, which is installed vertically (wooden element) is considered. It is proposed to arrange two longitudinal milled grooves of a rectangular shape located in the diametral plane of the section of the log for the installation of sheet plywood keys, which makes it possible to include in the joint work adjacent contiguous elements when working on bending from the plane of the wall. The variant of the strapping device, it is proposed to use metal rolling profiles of Channel and I-sections, connected with metal tube elements (box section) mounted in the corners of the frame.
Keywords: round log, profiled beam, sheet plywood keys, tubular section elements
We obtained the solution of the optimization problem for the step-parallel beam with constant width of the cross-section. The problem was solved by minimizing the strain energy while the volume of beam is constant. The solution was made for the case of simple support at the ends and evenly distributed along the length load. We introduced the parameter α, which is the ratio of height of the average part to a height of side parts. The optimal value of α was found. At this value the stiffness of the beam is maximum at constant volume. The obtained beam of maximum stiffness is not equal strength.
Keywords: optimization, speed-prismatic beam, the strain energy, variable stiffness, minimum
We solved the problem of optimizing the gable beam by minimizing the strain energy at constant volume. The problem reduced to an integral equation for determining the optimum angle of the beam. This equation was solved numerically by the method of bisection. Integral was calculated using the method of trapezoids. Solution was made in software package Matlab. The optimum angle depends on the width of the cross section b, and the volume of the beam. It was found that with increasing of width of the cross section the optimum tilt angle decreases. Also the volume increases by increasing the width of the beam.
Keywords: optimization, gable beam, strain energy, variable rigidity, minimum volume, method of bisection
The phenomenon of buckling under the creep of concrete arches was investigated. Solution of the problem carried out by means of the finite element method. To analyze the stability we used Newton-Raphson method. It has been established that there is a long-term critical load, beyond which the growth of the deflection has not fading character. As the equation of the relationship between the creep deformation and strains we used viscoelastoplastic hereditary model of aging concrete. To determine the creep strain we used a linear approximation with respect to time. It was found that the long critical load for considered arch was in 1.44 times lower than the instant critical load.
Keywords: reinforced concrete arch, stability, creep, geometric nonlinearity, finite element method, Newton-Raphson method
Experimental and theoretical study of the models of elastic-plastic elements vehicles manufactured from alloys with shape memory effect. Dynamic tests were carried out in the area of deformation (20-30%), which allowed to achieve optimum energy absorption and return to its original position for subsequent deformation. The model proved highly efficient in terms of the one-dimensional dynamic loading, such full-scale, and allow for the absorption from 55.8 to 97.8% of the inputs, depending on the initial geometrical proportions. Evaluation of the effect of the scale factor in the simulation of elastic-plastic elements on the basis of an alloy with shape memory effect showed the possibility of transferring the results of experimental studies on a real model of the car of the future.
Keywords: model, elastic-plastic element, alloy, shape memory effect, the dynamic test, the scale factor, the car of the future
The article is devoted to the stability of the polymer rods variable stiffness with the initial imperfec-tions and the development of creep deformation. The distinctive feature of the paper is a variable stiffness of the cross section and the use of fixing all, "seal-hinge" "seal, seal", "seal-free edge."
Keywords: stability of rods, creep, highly elastic deformation, polymeric materials, coupling equation of Maxwell-Gurevich
This article is related to technological problems of cavities with kamufletnyh explosions, during which the temperature in the cavity greatly exceeds the initial temperature of the array. Often these cavities are created in an array of rock salt. Because the salt even at light loads demonstrate expressive flow properties, it is interesting solution to the problem of creep salt massif with a cavity under the action of a force (pressure inside the cavity and the pressure of the soil), and thermal loads.
Keywords: heterogeneity, creep, highly elastic deformation, hydrochloric array coupling equation, the integral relations