Large deformations for plates with sliding contacts and friction | CDGudas
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Contact Analysis

Short brief of models, scope and methods

Three aluminium plate, each 10 inches long were used to conduct a series of contact analysis in conditions of large deformations and high plastic stresses/strains.  The plates arranged as in the figure below are fixed at the outer ends with the lower plate resting also on a rigid cylinder (R=0.35 “) located at approx. a quarter of its span. Initially the plates are just touching.
The larger width of the middle plate ensured that under load twisting moments are developed in all parts causing sideways slipping and non-uniform contact and friction stresses.

Two types of loading were used, uniform pressure and end loads on the top plate in three configurations. In the second and third configurations, the top and the top and lower plates joined by one 3/16” Hi-Lok fastener assembly pre-tensioned to 500lbf. prior to loading. A 0.080 inch thick washer was included in the second configuration to ensure that the initial contact between the plate is maintained during fastener installation while, in the third configuration, the washer was removed to allow the external plates to bend freely.

One of the scopes for including the fastener assembly was to develop a reliable method for fasteners (pre-tensioned or not) that have large positional displacements when the parts connected have changes significantly. Using multi-point constraints (MPC) in explicit form or through the BOLT element restricts this types of simulations to assemblies in which the position of the fasteners remains approximately fixed during operation (like the bolts attaching cylinder heads to engine blocks). The video clips in this page show that the approach used enables the fasteners to closely follow a realistic displacements path, maintain pretension and transfer loads without any conflicts with the contact constrains across a large range of deformations.

In the last stage, the load was removed gradually to zero to assess the stress revolutions during this process, the permanent deformations and residual stresses in the components.   Deformations and stress visualisation (von Mises or equivalent non-linear only) for the sliding plates are shown in the video clips listed below.  For the configurations with pensioned fastener, a more detailed review is dedicated to the stress around the holes and near the restraints.  Loading and solution parameters and samples for the iterations histories are included.

Geometrical configuration and loading cases

Click inside border to enlarge

In the models mid plane shell elements were used for the plates and 3D solid elements for the fastener.  The solution was obtained using an implicit nonlinear solver (solution 400 in MSC Nastran).   

In the first configuration the loading applied ensured that the mid plate slides out from between the other two and the sudden increase of the load applied to lower plate is captured and reflected by the solution.  In the case of pressure loading, the two plate were left to wrap around the cylindrical support and the fixed end of the lower plate past the stress level where plastic hinges developed.  For the other two configurations the loading was limited to values which confirmed that the fastener follows the large deformations and the effects of initial pre-tension are maintained throughout the entire loading and unloading cycle.

The convergence criteria requested was on displacements, loads, work and vector component method (UPWV).   Meshing and material details can be seen by clicking in on the figures below.

Meshing details for top plate
Meshing details for lower plate
Materials properties and engineering stress-strain curve for Al