Improving the performance parameters of metal cylindrical grid shell structures

In this article, to improve the performance of metal cylindrical mesh shells used as roofs for modern construction projects, the sub-aperture diaphragms and the corresponding nodal connections are proposed in the context of the problem of the increased vulnerability of individual sections from actual loads. Finite element models are designed taking into account minimization of production and assembly costs, special features of load perception and structural geometry changes in an acceptable range of overall parameters. The effect of sustaining elements located in the direction of the arc of the circle on the percentage of depletion of the bearing capacity and the maximum value of the deflection of circular mesh surfaces with square and rectangular cells are investigated. An economical design solution of IFI type unit is used to increase the bearing capacity and reduce the deformation of rectangular cylindrical multi-element grids. A joint connection which improves operational characteristics of a structure taking into account the features of the geometric formation and spatial design of the structures has been developed. The force factors and deformation parameters of the basic circuits of a cylindrical mesh surface are checked with conventional and developed joint connections. Increased rigidity and stability of the structure due to the introduction of the diaphragms and the use of units with sustaining elements have been achieved.Keywords: joint connection, grid shell, cylindrical surface, roof diaphragm

Generation a solution to the equations of elasticity theory for a layered strip basing on the principle of compressed mappings

A systematic presentation of the modified classical semi-inverse SaintVenant method as an iterative one is given on the example of generating a solution to the differential equations of elasticity theory for a long layered strip. The firstorder differential equations of the plane problem are reduced to the dimensionless form and replaced by integral equations with respect to the transverse coordinate, just as it is done in the Picard method of simple iterations. In this case, a small parameter appears in the integral equations before the integral sign as a multiplying factor, which is used to ensure convergence of solutions in accordance with the Banach’s principle of compressed mappings. The equations and elasticity relations are converted to a form that enables to calculate the unknowns consecutively, so that the unknowns being calculated in one equation are the inputs for the next equation, and etc. Fulfillment of the boundary conditions at the long edges leads to ordinary differential equations for slowly and rapidly changing singular components of the solution with sixteen effective stiffness coefficients that are defined by integrals from the given ones as a stepped function of Young's moduli for each layer. Integrating of these ordinary differential equations makes it possible to obtain the formulas for all the required unknowns of the problem, including transverse stresses that are not defined in the classical theory of the beam and solutions of the edge effect type, and to fulfill all the boundary conditions for the elasticity theory problem. The solution of three boundary value problems of the strip elasticity theory is provided such as for a two-layer strip with layers of the same thickness and different thicknesses, and a strip with an arbitrary number of layers. Formulas for all unknowns of the problem are obtained

Support Draft Calculation for a Ramp in the Form of Developable Helicoid

The article is about the analytical method of calculation a ramp in the form of developable helicoid on the support draft. The asymptotic method of small parameter is applied to solve the system of three differential equilibrium equations for developable helicoid stressstrain. The numerical results of displacements and bending moments are verified and coincide with engineering practice. The suggested approach can be extended for calculation of torso-helicoids with other boundary conditions. © Published under licence by IOP Publishing Ltd

Analysis of displacements in beam structures and shells with middle developable surfaces

Generally the displacements of the beams are calculated by the traditional methods of structural mechanics with the help of approximate formulas which provide good results for linear tasks. The author shows that the approximate formula is not suitable for analysis in the case of geometrical nonlinearity which occurs during the manufacturing process of bending developable shells. The comparison of results got by methods of structural mechanics and shell theory for the shells with developable middle surfaces is given. © The Authors, published by EDP Sciences, 2017

Preliminary shape design for screws and helical structures

Due to continuous development of additive technologies and perspectives for their practical application in many fields of engineering such as architecture and civil engineering, mechanical engineering, etc., the question of new approaches and requirements for design process is becoming a key point. In this framework the search for the rational or optimal shapes seems reasonable. In the paper, the investigation on the design of several types of helical surfaces which can be applied in different fields of mechanical industry is presented, along with the parametric equations for ruled helicoids which can be useful for further application using additive technologies. Different classifications of ruled helical surfaces are presented and compared from technical and mathematical points of view. There are also some recommendations for usage the proper types of helical structures in accordance with geometry investigation and effective material usage. The paper can be interesting for designers from mechanical and civil engineering, architecture and industry design. © 2020 by the authors

Application and analysis of right helicoidal shells

Drilling machines with drilling elements as helicoid are widely used while making of drilling auger, round section testpit and so on in crust for exploration of geological structure, searching, prospecting, minerals extraction, engineering geological research. Helicoidal shells can be designed as right, inclined, open and wrong-unfolding. There are main thesises of calculation method given by V.G. Rekach for right helicoid

Studying the shape of a helical ramp

The main purpose of this paper is to clarify the classification of helicoids and to introduce several types of hclicoids to engineers in terms of geometry, stress-strain behavior and exploitation parameters for the practical tasks. Mathematically helical ramps are usually designed in the shape of a right helicoid which is well-known among civil engineers and designers, while mechanical engineers also know evolvent and convolute helicoids and use them for screws. The paper mostly focuses on the civil engineering and architectural helical structures such as ramps. It is shown that designers generally do not pay proper attention to the way the surface for a ramp can be formed from mathematical point. However, different types of helicoids (and ramps as final structures) show different stress-strain and buckling behavior. The review of existing classifications, methods of calculation and differences in geometry of all five types of ruled helicoids are presented. The clear classification which can be used by both mathematicians and engineers is shown, along with the most appropriate methods for calculation. The geometry and stress-strain behavior comparison of several types of helicoids is done in order to find forms which are the most rational for application to ramps and screw elements of buildings

Analysis of displacements in beam structures and shells with middle developable surfaces

Generally the displacements of the beams are calculated by the traditional methods of structural mechanics with the help of approximate formulas which provide good results for linear tasks. The author shows that the approximate formula is not suitable for analysis in the case of geometrical nonlinearity which occurs during the manufacturing process of bending developable shells. The comparison of results got by methods of structural mechanics and shell theory for the shells with developable middle surfaces is given. © The Authors, published by EDP Sciences, 2017

Analysis of Thin Walled Wavy Shell of Monge Type Surface with Parabola and Sinusoid Curves by Variational-Difference Method

The paper is about the stress-strain state of the thin shell in the form of Monge surface with parabola generatrix and sinusoid guide. Coordinate system of the Monge surface is a system of coordinate lines of the principal curvatures of the surface. The variational-difference method is used for analysis. Variational-difference method allows using the geometric characteristics of the middle surface of the shell, which is important in the calculation of shells of complex shape. In the finite element method, which is often used in the shells of complex shape analysis, the equation of the middle surface of the shell is used only for finite element mesh. © The Authors, published by EDP Sciences, 2017

generatrix SLOPE ANGlE INFLUENCE ON THE mode of deformation of OPEN HELICOIDAL SHELLS CALCULATED BY ANALYTICAL SMALL PARAMETER METHOD WITH THREE TERMS OF SERIES

There is the analysis of generatrix slope angle influence on the mode of deformation of thin elastic open helicoidal shells which was calculated by the method of small parameter wit