A novel penalty-based reduced order modelling method for dynamic analysis of joint structures

This work proposes a new reduced order modelling method to improve the computational efficiency for the dynamic simulation of a jointed structures with localized contact friction non-linearities. We reformulate the traditional equation of motion for a joint structure by linearising the non-linear system on the contact interface and augmenting the linearised system by introducing an internal non-linear penalty variable. The internal variable is used to compensate the possible non-linear effects from the contact interface. Three types of reduced basis are selected for the Galerkin projection, namely, the vibration modes (VMs) of the linearised system, static modes (SMs) and also the trial vector derivatives (TVDs) vectors. Using these reduced basis, it would allow the size of the internal variable to change correspondingly with the number of active non-linear DOFs. The size of the new reduced order model therefore can be automatically updated depending on the contact condition during the simulations. This would reduce significantly the model size when most of the contact nodes are in a stuck condition, which is actually often the case when a jointed structure vibrates. A case study using a 2D joint beam model is carried out to demonstrate the concept of the proposed method. The initial results from this case study is then compared to the state of the art reduced order modeling

Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature