APPLICATIONS OF RANDOM FIELD MODELS. IN STOCHASTIC STRUCTURAL MECHANICS

Christian Bucher

Institute of Structural Mechanics,
Bauhaus-University Weimar, Germany

Abstract

Stochastic structural mechanics deals with the analysis of random phenomena occurring in structural systems or components. There are two major categories of structural uncertainties which involve spatial correlation and which consequently require the treatment as random fields. These are:

• Material properties such as modulus of elasticity or strength,

• Geometrical properties such as shape or thickness

of structural components. The outcome of the stochastic structural analyses is significantly affected
by the appropriate treatment of the random properties in the context of the Finite Element method.

The paper will provide an overview of random field representation as appropriate for the stochastic finite element method (cf. Matthies and Bucher, 1999). This includes integral representation models as well a point representation models. In addition, conditional random fields as required in the presence of pointwise deterministic information (e. g. from measurements) are introduced.

Example applications illustrate these concepts and discuss the numerical implications of random field modeling. These applications involve static and dynamic problems which arise in system iden­tification (Macke and Bucher, 2000; Bucher et al., 2003) as well as dynamic stability issues due to geometrical imperfections of shells (Most et al., 2004).