A method for predicting Mach stem height in steady flows

The prediction of Mach stem height can be important in the design of supersonic intake in supersonic and hypersonic flows. It is also important because of the progress in aircraft and rocket engines. An analytical method of predicting the Mach stem height is necessary in theoretical field of shock reflection and is the basis of the comparable computational fluid dynamics (CFD) method. A method for predicting the Mach stem height in steady flows is performed based on the earlier models. In this article, an analytical model for predicting the Mach stem height is improved based on two main assumptions: one is the calculation of the triple point deflection angle when the Mach stem is an oblique shock and the other is about the shape of the free part of the slip line. Under these assumptions, the relations predicting of Mach stem height in two-dimensional steady flow are derived based on the advanced averaging method of the subsonic flow region. The Mach stem heights are decided solely for the incoming flow Mach numbers and the wedge angles by the improved analytical model. As a result, the Mach stem heights by the model of this article are found to agree well with experimental results at lower Mach numbers, but there are relative errors at higher Mach numbers. The convexity of the slip line is also considered.

Mechanism of Roadway Floor Heave Controlled by Floor Corner Pile in Deep Roadway under High Horizontal Stress

In order to overcome the support difficulty of serious floor heave caused by rock burst, with the floor heave of ventilation roadway in Hegang Xing An Coal Mine as the engineering background, the treatment scheme of the concrete-filled steel tube corner pile and floor grouting is put forward. Based on the solution of the slip line field under plane strain condition, the mechanical model of the slip-type floor heave is established, and the formula for calculating the critical failure depth of the roadway floor and the minimum support depth of the corner pile is derived. Through numerical analysis and similar model tests, the deformation and stress distribution of surrounding rock under the support of the corner piles are studied, and the force law of the pile under high horizontal stress is analyzed. The results show that, compared with the floor corner anchor, the floor corner pile + floor grouting support scheme can significantly improve the mechanical properties of the floor rock mass, and the plastic slip line of the floor plate part can be cut by corner piles, which effectively controls the deformation of the floor plate under high horizontal stress; the length and inclination angle of the corner pile have a great influence on the support effect. In the on-site treatment scheme, 1.1 times the calculated length of pile should be selected. The results of a similar model and field test show that the corner pile is effective in controlling the deformation of roadway floor and two sides.

The numerical calculation of statically admissible slip-line field for plane strain compression of a three-layer symmetric strip between rigid plates

This paper present a method to build up statically admissible slip-line field (the field of characteristics) and, as a result, the field of statically admissible stresses of the compression of a three-layer symmetric strip consisting of two different rigid perfectly plastic materials between rough, parallel, rigid plates (for the case: the shear yield stress of the inner layer is greater than that of the outer layer). Under the conditions of sticking regime at bi-material interfaces and sliding occurs at rigid surfaces with maximum friction, the appropriate singularities on the boundary between the two materials have been assumed, then a standard numerical slip-line technique is supplemented with iterative procedure to calculate characteristic and stress fields that satisfy simultaneously the stress boundary conditions as well as the regime of sticking on the bi-material interfaces

Stress state and power parameters during pulling workpieces through a special die with an inclined working surface

The study of the stress state and power parameters when pulling workpieces in a special die with an inclined working surface at various shapes of the plastic deformation zone and geometric parameters of the special die was conducted. The distinctive feature of the proposed special die and the metal treatment process in the working channel of this die was described. The theoretical provisions and assumptions from the fundamental theory of plasticity and metal forming were used. The influence of the intensity of shear deformations on the stress state and force at the angles of inclination of the working surface of the die within 45–20°, the value of the ratio of the diameter of the workpiece to the length of the inclined surface d/z=1.5–2.0 was investigated. The optimal d/z ratio was determined by the method to a rigid punch indenting a rigid-plastic half-space, as well as by the method of strain energy. The field of slip lines and hodographs of velocities for various shapes of the deformation zone and geometric parameters of a special die were constructed. Based on the constructed slip line fields and velocity hodographs, the mean stress and stress components at the nodal points of the slip line field with the compilation of the equilibrium equations for all forces applied to the plastic zone were calculated. The study of the influence of contact friction between the working surface of the die channel and the workpiece on the stress state and power parameters during pulling was carried out. It was revealed that the optimal ratio d/z=1.5 and the optimal angle of inclination of the working channel of the die α=20°. It was found that for these parameters in the zone of plastic deformation, mainly significant compressive stresses act, which favorably affect the obtaining of a homogeneous and refined microstructure, and also exclude the appearance of anisotropy due to the implementation of maximum shear deformations in the workpiece.