Theoretical Basics

Responsible professors: Prof. Könke; Prof. Bucher
Cooperating professors: Prof. Gürlebeck, Prof. Freundt
Junior scientists: Dr. Zabel; Dr. Most

The selection of partial models to forecast the response behaviour of engineering structures are carried out on the basis of heuristic experience of the engineer who uses the model. At present, a general methodology for the quantitative assessment of model quality regarding sensitivity and robustness related to special formulations does not exist. The complexity of the problem being considered is increased further when considering the stochastic distribution of input parameters.

To process complex engineering related questions, couplings of several partial models are required. This raises questions concerning the propagation of errors between the partial models in data exchange (quantitative assessment of the model quality) as well as for the assessment of model qualities for the coupling of models based on different analysis techniques (qualitative inconsistency of coupled partial models). On both issues, to the best of our knowledge, there is no documentation in literature regarding these research approaches.

The dissertation topics, which are to be worked on within the framework of core topic I, shall accomplish fundamental orientated research works and apply the results in cooperation with the scientists involved in the core topics II to IV in actual tasks used in constructive civil engineering.

The solution space of the mechanical problem is limited by the choice of approaches in equilibrium, kinematical and material law or different fundamental equations for the description of the respective physical problem. Thus, certain influences in every theory are neglected insignificantly to reduce the problem in its complexity. Inevitably, as a result of abstraction processes, a deviation occurs between the predicted results and the behaviour observed in reality. Different influences which have an effect on the model quality can be distinguished:

• Dimension and scale influences
• Material model influences
• Influences due to consideration or neglect time-variant effect
• Influences due to the consideration or neglect of physical effects
• Influences due to different linearization assumptions

For the assessment of dimension and scale influences, expansion and diminution models shall be examined. Dimension or scale reduced approaches are compared with each other with higher or low approaches in the complete area of the model or in model sections with regard to their energy. Similar procedures can be used for the assessment of model qualities because of different material formulations.

An evaluation of model deviation with regards to time-variant effects is, for example, possible over eigenvalue analysis and the comparison of excitation and structural spectrum. Here too, quantitatively an evaluation on energy content can be conducted

For the assessment of model sensitivity, as a measure for quantitative change in the statements of a model during change of parameter and input quantities, methods to determine the failure probability can be adapted. Under certain circumstances a response function can be produced as a buffer area in the designated parameter space with few result points, e.g. the continuity of respective solution functions.

The derivations of the response surfaces can be understood as a sensitivity calculation of response during fluctuation of input parameters (quantitative evaluation). The size of the parameter space, in which the response surfaces still provides acceptable results with regards to the model robustness as calculation for the capability of a model for parameters and input values within a, for the construction industry typically wide, utility area is permissible. For both questions, in turn different energy measures can be considered for the quantitative assessment.