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SLang - the Structural Language : Solving Nonlinear and Stochastic Problems in Structural Mechanics
(1997)

Recent developments in structural mechanics indicate an increasing need of numerical methods to deal with stochasticity. This process started with the modeling of loading uncertainties. More recently, also system uncertainty, such as physical or geometrical imperfections are modeled in probabilistic terms. Clearly, this task requires close connenction of structural modeling with probabilistic modeling. Nonlinear effects are essential for a realistic description of the structural behavior. Since modern structural analysis relies quite heavily on the Finite Element Method, it seems to be quite reasonable to base stochastic structural analysis on this method. Commercially available software packages can cover deterministic structural analysis in a very wide range. However, the applicability of these packages to stochastic problems is rather limited. On the other hand, there is a number of highly specialized programs for probabilistic or reliability problems which can be used only in connection with rather simplistic structural models. In principle, there is the possibility to combine both kinds of software in order to achieve the goal. The major difficulty which then arises in practical computation is to define the most suitable way of transferring data between the programs. In order to circumvent these problems, the software package SLang (Structural Language) has been developed. SLang is a command interpreter which acts on a set of relatively complex commands. Each command takes input from and gives output to simple data structures (data objects), such as vectors and matrices. All commands communicate via these data objects which are stored in memory or on disk. The paper will show applications to structural engineering problems, in particular failure analysis of frames and shell structures with random loads and random imperfections. Both geometrical and physical nonlinearities are taken into account.

In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion.