Finite sliding between concentric cylinders—axisymmetric and CAXA models

This example illustrates the use of Abaqus slide line elements and contact surface definitions in an axisymmetric structure that may undergo nonlinear, nonaxisymmetric deformation. This contact problem involves the relative motion of two outer cylinders with respect to one another and with respect to an inner, constrained cylinder. The axisymmetric model is shown in Figure 1, where the three cylinders are identified: the inner cylinder defined by the points $ABHG$, the middle cylinder defined by points $CDLK$, and the outer cylinder defined by points $EFJI$. Two slide lines are used in this model: one along the outer edge of the inner cylinder, from node H through node O, and a second along the outer edge of the middle cylinder, from node L through node D. Axisymmetric contact elements for finite sliding (slide line elements) defined along edge $KC$ of the middle cylinder are associated with the first slide line. Axisymmetric slide line elements defined along edge $IE$ of the outer cylinder are associated with the second slide line.

The structure is subjected to localized pressurization to initiate contact between the surfaces in the three bodies, and then the two outer cylinders are forced to slide down the cylinder. These loading conditions are defined in two separate steps (pressurization followed by sliding). An additional perturbation step is created to test the load case definition.

In the axisymmetric model the inner cylinder is restrained from motion in the z-direction along lines $AB$ and $GH$. In addition, node B is restrained from radial motion. In the first step a pressure of 207 MPa (30 × 10³ lb/in²) is applied to edge $JF$ of the outer cylinder, while nodes L and J are restrained vertically. During the second step the pressure is maintained, and node L is displaced in the negative z-direction by 127 mm (5.0 in), while node J is displaced in the same direction by 114.3 mm (4.5 in).

In the CGAX4 model the same steps and boundary conditions that were applied in the CAX4 model are used. An additional third step is added in which the outermost cylinder is twisted by 0.1 radians about the z-axis while the innermost cylinder is prevented from twisting.

The nonaxisymmetric model is made up of CAXA elements and additional slide line elements at various locations in the $\theta$-direction. The area of integration for the slide line elements and the angular position (measured in degrees) of the slide line elements are defined.

In the CAXA model the boundary conditions that were applied in the axisymmetric model are kept and are extended in the $\theta$-direction. The loading conditions are the same as the axisymmetric model. Any axisymmetric or nonaxisymmetric loading can be applied to the CAXA model after the second step.