As is well known, the solution of analytical elastic contact problems [1, 2] is limited to a small number of specific contacts. For this reason, various numerical approaches were proposed to solve contact problems. The use of conventional numerical solving methods is however limited by the large volume of computation due to the use of fine meshing of the assumed area of contact with an important number of nodes. Various methods are proposed in literature to reduce the computing time and power needed to solve contact problems. In order to highlight the dependence between micro-contact parameters and the mechanical properties of the materials in contact, the present paper proposes the numerical modeling of micro-contacts using the Conjugate Gradient and Fast Fourier Transform technique (CG + FFT), [3, 4], and its adaptation to the micro-contact range. Model validation is performed by comparing the obtained results with the classical Hertz model, for various contact body shapes. The obtained results show very good agreement between the numerical and analytical results, thus validating the proposed numerical model.

Surface deformations measured by laser profilometry in a contact model metal punch-sapphire window yield pressure distribution if the contact area is known. This paper advances a new method to assess this area by reflectivity. The contact model possesses higher reflectivity outside the contact area than inside, the step evidencing contact contour. A correction for interference effects is derived. Experimental results on circular Hertz contacts agree well with theoretical predictions.

Important end effects occur in Hertz-like finite length line contacts. If the length of shorter contacting cylinder is bounded by flat surfaces, the pressure tends to infinity at both ends. Many design measures were advanced to reduce or attenuate these pressure riser effects. These imply modification of contact geometry and, in most cases, numerical investigations. Few experiments were performed to check the actual contact between modified surfaces. Applying a previous proposal, contact area between a modified steel roller and a sapphire window is measured by scanning the reflectivity of metallic surface. A typical “dog bone” shape for this area is found. Lateral extensions of contact area, measured experimentally for a roller with rounded edges, agree well with numerical results obtained by a new, refined numerical procedure.

Torsion of bars of various cross-section is of great practical utility in engineering, structural design and mechanical work. It is applied in machine construction, steel bridge or railway construction. Many publications can be found in literature that present the stress-strain analysis in the case of straight rods with constant profiles subjected to torsion. Most of these works were however directed to the case of rods with simple connected domains as cross sections. The present work uses a semi-inverse method which permits to determine general equations for stress-strain analysis in the case of rods having a multiple connected domain as cross section, subjected to torsion. For the present study, the general equations were customized for two particular cases that of an elliptical cross section and that of an elliptical ring.The determined analytical equations were implemented to a specific situation by aid of Mathcad software. This permitted to graphically represent the distribution of torsion stresses and cross-section deflection.

Machine design and electrical contacts involve frequently elastic circular contacts subjected to normal loads. Depending on geometry, these may be Hertzian or surface contacts. Both possess highly nonuniform pressure distributions which diminish contact load carrying capacity. The achievement of a uniform pressure distribution would be ideal to improve the situation, but this violates stress continuity. Instead, the generation of a uniform pressure over most of contact area can be sought. Generally, equivalent punch profile which generates this pressure is found by numerical evaluation of double integrals. This paper simplifies the derivation of punch profile by using an existing correspondence between a polynomial punch surface and elastically generated pressure. First, an improved pressure profile is proposed seeking to avoid high Huber-Mises-Hencky stresses near contact surface. Then, this is approximated by the product between typical Hertz square root and an even polynomial, which yields directly the punch profile. Formulas for normal approach and central pressure are derived.