On lack-of-knowledge theory in structural mechanics

Abstract

Today, the validation of complex structural models – i.e. the assessment of their quality compared to an experimental reference – remains a major issue. Strictly speaking, the validation problem consists in comparing the response of the numerical model (whether deterministic or stochastic) with complete reality. A first answer to this problem, using Lack-Of-Knowledge (LOK) theory, was introduced at LMT-Cachan. This theory is an attempt to “model the unknown” by taking all the sources of uncertainties, including modeling errors, into account through the concept of basic LOKs. In this article, we introduce basic LOKs associated with both the amplitudes and directions of excitations. These basic LOKs are propagated rigorously throughout the mechanical model in order to determine intervals (with stochastic bounds) within which lies a given quantity of interest (stress or displacement). Then, we introduce a strategy for the reduction of lack of knowledge, which we illustrate through an academic example.