Finite element technology-based selective mass scaling for explicit dynamics of thin-walled structures
In numerical simulation methods in the field of structural dynamics, a distinction is made between explicit and implicit methods. Explicit algorithms for time integration are very well suited for strongly nonlinear and nonsmooth problems, since they do not require an iterative solution of the global dynamic equations of motion. In special engineering applications, such as crash or sheet metal forming simulations, they are generally more robust than implicit algorithms. But the conditional stability of explicit algorithms limits the allowed so-called critical time step size, which directly depends on the highest natural frequency of the discrete system. There are several approaches to reduce numerical costs and thus to increase the efficiency of explicit simulations. Here we mention (1) finite element technology to avoid locking effects, (2) adaptive mesh refinement strategies, (3) subcycling or asynchronous time integration, (4) model reduction methods and (5) mass scaling methods. Usually, different approaches are used in combination in practical applications. Especially the combination of the approaches (1) and (5) is obvious and is state of the art in explicit FE programs. So far, however, these two strategies for efficiency improvement have only been applied separately. The theoretical connection and practical combination of efficient methods from FE technology and efficient methods of mass scaling have not been systematically investigated so far. It is precisely this connection that forms the basis for the planned research project. The overall goal of this research project is to increase the accuracy and efficiency of simulations of thin-walled structures in the context of explicit algorithms for time integration. Fundamental improvements are expected for the two most common element types in this context, (I) eight-noded solid or solid-shell elements and (II) four-noded Reissner-Mindlin shell elements. Methodologically, selective mass scaling concepts are developed which are inspired by finite element technology and are characterized by high accuracy. The new mass scaling concepts developed in the preliminary work exhibit accuracies comparable to stiffness-proportional mass scaling methods but with significantly higher efficiency. Furthermore, the newly developed mass scaling concepts exhibit some physically and numerically desirable properties. For example, they are a priori preserving both momentum and angular momentum. The newly developed methods promise a universal applicability of the mass scaling concept, independent of the underlying FE technology to avoid locking, and independent of the mentioned discretization concept (I) or (II).