A geometrically nonlinear formulation for a 48 degrees-of-freedom (d.0.f.) quadrilateral shell element is presented. Each of the three displacement functions of u, u and w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized rational €3-spline functions which may be linked to the geometric data bases generated by the computer-aided design system. The displacement functions and the 48 d.0.f. are expressed in both curvilinear and Cartesian forms, whereas the strain-displacement equations are expressed in curvilinear co-ordinates. The use of Cartesian displacement functions and degrees-of-freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap-through buckling of a spherical cap and large deflection of a semi-toroidal bellows shell. Results compare well with alternative solutions.

SUMMARYA 48 degrees-of-freedom (d.0.f.) quadrilateral thin elastic shell finite element using variable-order polynomial functions, B-spline functions and rational B-spline functions to model the shell surface is developed. This development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems. The displacement functions are that of bicubic Hermitian polynomials. The displacement functions and d.0.f. are expressed and investigated in both the curvilinear and Cartesian forms. The curvilinear form is simpler and can provide the proper solution for a certain class of shell problems. For certain highly curved shells such as bellows, however, the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions. It is suggested in this study that such difficulty can be circumvented and the rigid body modes can be properly included if a Cartesian form is used for displacement functions. The straindisplacement equations are expressed in curvilinear co-ordinates. Thus, the Cartesian displacement functions require a transformation to curvilinear displacement at each numerical integration point. Examples include a pinched cylinder, a translational shell under central load, a uniformly loaded hypar shell, a pressurized ovel shell, a semi-toroidal bellows and a U-shaped bellows. For the first four examples, geometric modellings consist of polynomials of second-order (subparametric), third-order (isoparametric), and fourth and fifth-order (both superparametric) as well as B-spline functions of fourth-and fifth-order. The geometries of the pinched cylinder, the semi-toroidal bellows, and the U-shaped bellows were modelled exactly using rational B-spline functions. All the results obtained are in good agreement with alternative existing solutions.

This paper reports on experiments and theoretical analyses of heat generation and scuffing failure in rolling contacts. The experiments were conducted with dry contacts, and the theoretical analyses were carried out using a deterministic thermal contact model. The research reveals that heat generated by asperity plastic deformation in the direction normal to the contact can be significant in high-load, high-speed contacts under boundary and mixed lubrication conditions. Under near rolling conditions, heat generated by the plastic deformation largely dominates that by the friction and is the main source leading to contact scuffing. This heat generation is shown to be significant compared to frictional heating even at relatively large slide-to-roll ratios. Parametric studies show that the ratio of asperity-plastic-deformation heating to frictional heating is sensitive to slide-to-roll ratio, hardness and surface finish but insensitive to contact load, rolling velocity and fluid/asperity load sharing.