Influence of reinforcing ribs on the deformed state of ellipsoidal shells under distributed load

This paper presents the problem about non-stationary oscillations of reinforced ellipsoidal shells, taking into account the discrete location of the ribs. Problem bases on a geometrically nonlinear variant of the Tymoshenko theory for shells and rods. A numerical method for solving problems of this class has been developed and substantiated. This article focuses on the location of the reinforcing ribs. On the basis of the developed numerical method the deformed state of discretely supported ellipsoidal shells for internal, external and internal-external placement of ribs is investigated. Boundary conditions for rigidly clamped edges of the shell were studied.

Research on the First Breaking Mechanism of the Main Roof of Coal Seam with High Dip Angle

In order to study the mechanism and characteristics of the first breaking of the roof in thick coal seams with high dip angles, a mechanical model of elastic thin plate with four clamped edges of the roof was established, and the expressions of the deflection and stress of the roof were obtained by the energy method. The influence of the change in seam dip angle on the first breaking distance of the roof was presented. Based on the stress solution, the roof breaking criterion was proposed, and the breaking distance of the roof was calculated. Combined with numerical simulation, the stress distribution characteristics of the upper and lower surfaces of the stope roof were analyzed. The results show that the first breaking distance of the roof is inversely proportional to the seam dip angle. Broken morphology of roof in high dip seam is different from the “O-X” morphology of horizontal roof. The roof breaking order of the seam with high dip angle is middle-middle upper-middle lower-upper-lower. These research results have certain theoretical guiding significance for the study of the first breaking mechanism of the main roof of highly inclined working face of coal seams.

Polya Counting Theory Applied to Combination of Edge Conditions for Generally Shaped Isotropic Plates

Structural behaviors of plate components, such as internal stress, deflection, buckling and dynamic response, are important in the structural design of aerospace, mechanical, civil and other industries. These behaviors are known to be affected not only by plate shapes and material properties but also by edge conditions. Any one of the three classical edge conditions in bending, namely free, simply supported and clamped edges, may be used to model the constraint along an edge of plates. Along the entre boundary with plural edges, there exist a wide variety of combinations in the entire plate boundary, each giving different values of structural responses. For counting the total number of possible combinations, the present paper considers Polya counting theory in combinatorial mathematics. For various plate shapes, formulas are derived for counting exact numbers in combination. In some examples, such combinations are confirmed in the figures by a trial and error approach.