Numerical exploration on snap buckling of a pre-stressed hemispherical gridshell

Motivated by the observations of snap-through phenomena in pre-stressed strips and curved shells, we numerically investigate the snapping of a pre-buckled hemispherical gridshell under apex load indentation. Our experimentally validated numerical framework on elastic gridshell simulation combines two components: (i) Discrete Elastic Rods method, for the geometrically nonlinear description of one dimensional rods; and (ii) a naive penalty-based energy functional, to perform the non-deviation condition between two rods at joint. An initially planar grid of slender rods can be actuated into a three dimensional hemispherical shape by loading its extremities through a prescribed path, known as buckling induced assembly; next, this pre-buckled structure can suddenly change its bending direction at some threshold points when compressing its apex to the other side. We find that the hemispherical gridshell can undergo snap-through buckling through two different paths based on two different apex loading conditions. The first critical snap-through point slightly increases as the number of rods in gridshell structure becomes denser, which emphasizes the mechanically nonlocal property in hollow grids, in contrast to the local response of continuum shells. The findings may bridge the gap among rods, grids, knits, and shells, for a fundamental understanding of a group of thin elastic structures, and inspire the design of novel micro-electro-mechanical systems and functional metamaterials.

NUMERICAL DIFFERENTIATION OF BEND FORMS OF THE LONG ELASTIC RODS

The technique of numerical differentiation of the bend forms of long elastic rods is presented. This technique is based on search for new bend forms of the rod by solving the equations of oscillations with using the time integration method and the polynomial spline-functions that are being described the current bend form. In it, the spline-functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Using the described approximation technique with subsequent numerical differentiation, the dependences of the derivatives on an arbitrary bend form of the rod with a length that is equal to 100 m are shown. To confirm the reliability, the results of numerical differentiation of the bend forms of the elastic rods described by given functions are presented and the numerical results obtained using the proposed method are compared with the results of analytical differentiation of the original functions. The graphs of values derivatives dependence to rod length are drawn and tables with numerical values of differentiation results are shown. It is concluded that the considered technique of numerical differentiation of rods bend forms allows to do the research of dynamics of rod systems. It gives the exact result of differentiation, provides the continuity and smoothness of all four derivatives functions of spline that are being described the bend form with considerable length. Described technique was realized in a computer program with graphic user interface. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation.

Optimization of the main parameters of the support-lump-breaking coil

Agricultural land plays an important role in ensuring food security and employment in rural areas. For many years, the planned economy has forced Uzbekistan to grow water-intensive crops, which has led to declining land productivity and increased crop yields. In a market economy, new innovative technologies are in high demand not only in agriculture but also in other sectors. In order to solve the above-mentioned problems, our research has found it necessary to set goals and objectives. The purpose of the study was to substantiate the parameters of frontal plowing slope, which provides high-quality execution of the technological process in accordance with the agro-technical requirements with minimum energy consumption without furrow plowing, agrotechnical and energy performance of variable frontal forks. The following results were achieved by performing the tasks identified in the study: a – humidity V=16–17 % and load conditions with elastic rods of 3 mm, 4 mm, 5 mm; b – humidity V=13–14 % and the diameter of elastic rods is 3 mm, 4 mm, 5 mm; c – humidity V=9–10 % and the diameter of the elastic rods is 3 mm, 4 mm, 5 mm. The experiments were performed on lumps with different humidity conditions: 9–10 %, 13–14 % and 16–17 %. The speed of the installation was 1.0 m/s. The recommended technology was to destroy soil fragments with a moisture content of 16–17 % at a vertical load of 400 N with 3, 4 and 5 mm elastic rods at 86.6, 81.5, 75.1 %, respectively, and the vertical load equal to 1,000 N – 94.4, 89.2, 81.2 %, respectively

Features for calculating beams with a thin transverse corrugated web plate considering bending-twisting forces

The article describes the features of the work of beams with a thin transverse corrugated web plate. Exponential fractional regression is presented, which allows one to estimate the relative height of web plate sections working together with flanges, obtained by the authors based on an analysis of numerical experiments. Based on the features of the work, a method is proposed for describing the stress state of an arbitrary cross-section of an I-beam with a thin transverse corrugated web plate (the profile of the corrugations is triangular, trapezoidal, sinusoidal) bent in the plane of the web plate and compressed in the longitudinal direction, using the theory of thin-web platted elastic rods by Professor V.Z. Vlasov. The calculations are given for determining the bending-twisting forces (local bending moments and bimoments arising from the action of the main forces) in an arbitrary cross section.