Investigation of Contact Settings on the Result of Topology Optimization to Avoid Contact Stiffness Supports

Abstract

Considering adjacent parts in the finite element analysis (FEA) leads to a contact problem. There are several necessary configuration parameters in computational contact mechanics, like the contact stiffness or discretization. Due to this variety there is a multitude of papers regarding the correct range for contact parameters in terms of FEA.

In topology optimization - especially if the optimization target is set to maximal stiffness - the configuration of the contact problem is much more sophisticated. An overlarge contact stiffness for example leads to a phenomena which is called contact stiffness supports within this paper. This behavior results in a design proposal, which causes major load flow through the contact zone, whereas the rest of the component is removed.

The most difficult part in determining the appropriate range for configuration parameters is comparing different simulations. In topology optimization, it is not sufficient to compare certain stress or displacement values of selected degrees of freedom like it is common in structural mechanic simulations. Instead it is necessary to collate the topology of the resulting design proposals.

For this purpose an evaluation algorithm was designed, which supersedes the necessity of a visual evaluation by describing the similarity of two design proposals by means of a histogram. The result of a simulation with the identical design space but with a matching mesh - thus without contact zone - is used as reference for this computer-aided evaluation. This automated investigation of arbitrary contact configurations shows, that the values of the parameters are usually within the standard values (recommended in literature), but in a notably smaller interval. In general, smaller contact stiffness is required and the examined parameters are more sensitive in topology optimization. The valid intervals for configuration parameters, which were determined by this method, enable a more realistic way of considering the elastic environment in stiffness optimization.