In the paper, parametric equations of right conoidal surfaces with an orthogonal coordinate system with different guiding curves are obtained for the first time. Parametric equations for conoids with guide curves sine, cosine and parabola are presented. In the MathCad system, the constructions of right conoids with selected guide curves with various initial geometric parameters are visually performed and presented in the paper for the possibility of expanding their use in architectural design, construction and other industries.

Keywords: conoid, orthogonal coordinate system, sine, cosine, parabola, parametric equation, MathCad system

The paper deals with the problem of choosing the most rational form of spatial metallic cross-barrel coating. Mathematical models of flat structural coating, elliptical paraboloid and hyperbolic paraboloid coatings in SCAD software package based on finite element method are analyzed. Nodal connections of rod elements of coatings are taken according to the system “Kislovodsk”. The obtained parameters of stress-strain state of three different structural coverings allow us to speak about practically identical operation of the structures.

Keywords: structural covering, spatial covering, cross-bar covering, stress-strain state, “Kislovodsk” system, SCAD program complex, finite element method, hyperbolic paraboloid, elliptic paraboloid