REVIEW AND ASSESSMENT OF MODEL UPDATING FOR NON-LINEAR, TRANSIENT DYNAMICS

The purpose of this publication is to motivate the need of validating numerical models based on time-domain data for non-linear, transient, structural dynamics and to discuss some of the challenges faced by this technology. Our approach is two-fold. First, several numerical and experimental testbeds are presented that span a wide variety of applications (from non-linear vibrations to shock response) and difficulty [from a single-degree-of-freedom (sdof) system with localised non-linearity to a three-dimensional (3-D), multiple-component assembly featuring non-linear material response and contact mechanics]. These testbeds have been developed at Los Alamos National Laboratory in support of the Advanced Strategic Computing Initiative and our code validation and verification program. Conventional, modal-based updating techniques are shown to produce erroneous models although the discrepancy between test and analysis modal responses can be bridged. This conclusion offers a clear justification that metrics based on modal parameters are not well suited to the resolution of inverse, non-linear problems. In the second part of this work, the state-of-the-art in the area of model updating for non-linear, transient dynamics is reviewed. The techniques identified as the most promising are assessed using data from our numerical or experimental testbeds. Several difficulties of formulating and solving inverse problems for non-linear structural dynamics are identified. Among them, we cite the formulation of adequate metrics based on time series and the need to propagate variability throughout the optimisation of the model's parameters. Another important issue is the necessity to satisfy continuity of the response when several finite element optimisations are successively carried out. An illustration of how this problem can be resolved based on the theory of optimal control is provided using numerical data from a non-linear Duffing oscillator. The publication concludes with a brief description of current research directions in inverse problem solving for structural dynamics.