MECHANICAL ANALYSIS OF CYLINDERS BEING UPSET BETWEEN SPHERICAL CONCAVE PLATEN AND CONCAVE SUPPORTING PLATE

Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.

Relection of elastic waves at the elastically supported boundary of a couple stress elastic half-space

The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave（the P wave） and incident transverse wave（the SV wave） are considered.