MS1.8 - Advances in Computational Structural Dynamics

In explicit dynamic simulations, an estimation of the critical time step size is necessary to ensure a stable computation. A direct computation of the critical time step by solving the corresponding eigenvalue problem is too time-consuming and requires the stiffness matrix, which is usually not calculated in explicit dynamics. There are several approaches to estimate the critical time step. Eigenvalue estimates such as Gershgorin’s theorem can be used to find an upper bound for the highest eigenfrequency and heuristic formulas based on geometric considerations exist. They are used to estimate a characteristic length of the element, which is then divided by the wave speed to obtain the critical time step. An example is the estimation of the characteristic length by the element area divided by the longest diagonal for 2d solid elements. The latter approach has the disadvantage that the resulting estimation is not necessarily conservative, which leads to the introduction of a so-called safety factor. In this contribution, we present a data-driven approach to time step estimation. We explain how a representative data set can be generated. Based on this data, we analyze the performance of the estimates mentioned above and propose several improvements. We present a data-driven method to make an existing estimate conservative and develop new time step estimates, which achieve significantly better results than state-of-the-art estimates with only little extra cost.

The Applied Element Method (AEM) has been used extensively through the past decade for doing non-linear analysis of structures subjected to extreme loading conditions like blast, progressive collapse, seismic assessment for new and existing buildings, wind analysis, impact analysis and fire analysis. With the recent advancement in structural health monitoring (SHM) and digital twin (TD) industry, it became essential that SHM and TD need a structural analysis tool that can predict the behavior of different structural components under extreme loads. AEM is a high fidelity numerical dynamic structural analysis method that tracks the structural behavior starting from the elastic stage passing through cracking, crushing, reinforcement yielding, buckling and post buckling up to element separation, debris, and collision. Having an AEM model connected to SHM and TD allows engineers to track in real time the effects of either man-made hazard or natural hazards on the structural behavior. It also allows decision makers to take the appropriate action to repair, strength or demolish the structure before an accident happens that leads to loss of life or assets. In this paper, the authors will present a discussion about the integration of AEM as a tool for digital twinning within an SHM strategy, taking profit of some illustrative numerical case studies. It is concluded that the use of AEM modelling is particularly profitable in association to a static monitoring system in the case of bridges undergoing slow deformation phenomena, for instance resulting from a movement of a foundation due to an active slow landslide, in order to build a digital twin of the deforming bridge useful to predict the remaining useful like of the bridge based on the measurements obtained from either contact or remote sensors. It is also concluded that AEM can be especially useful to setup alert thresholds for static response measurements, such as tilt rotations, and to aid the process of structural strengthening to avoid major accidents.