Modeling complex contact phenomena with nonlinear beamshells

As built-up engineering structures (i.e. structures consisting of many individual pieces connected together) become more complicated and expensive, the need to accurately model their response to dynamic events increases. Take for example electronics mounted to a satellite via a bolted connection. Without the proper understanding of how the electronics will react during launch, the connection will either be over designed, resulting in excess weight, or under designed, resulting in possible damage to the unit. In bolted connections, energy dissipation due to micro-slip (partial slipping of an elastic body in contact that occurs prior to slipping of the entire contact patch) is often the dominating damping mechanism. Capturing this type of nonlinear damping is often challenging within a simulation of large-scale structures. Finite element falls short due to the small element size required to achieve a converged solution in the contact patch. Researchers have been developing reduced order models that capture the micro-slip phenomenon without the numerical penalty associated with finite element analysis. This work shows that nonlinear beamshells could be used as a reduced order model for elastic bodies connected with a frictional connection which exhibits energy dissipation due to micro-slip. In this work we consider the energy dissipated from an elastic shell on a rigid foundation and focus on two unique contact phenomenon: the effect of shear leading iii to load transfer beyond the slip zone, and the effect of compressive material loads that can give rise to receding contact areas. Both phenomenon are investigated using the nonlinear geometrically exact shell theory. It is concluded that edge shearing effects serve to reduce the energy dissipated from the system. This is studied with nonlinear shell theory and validated with finite element analysis. Likewise, it has been postulated that changing contact patch areas during oscillations effects the energy dissipated per load cycle. This work expands on current nonlinear shell theory to account for through thickness compressive stresses as applied to a Cosserat surface. Several examples are solved to show the effects of the expanded nonlinear beamshell theory.

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