Extension of the Lack Of Knowledge (LOK) theory to force uncertainties

This paper deals with the structural modeling of a family of similar, real structures taking into account uncertainties and modeling errors. The concept of Lack Of Knowledge (LOK), first introduced in [1,2], consists in globalizing the various sources of errors by means of internal variables, called the LOK variables, defined over an interval whose upper and lower bounds follow probabilistic laws. From these basic LOKs, one can derive for the whole structure the effective LOK for a quantity of interest α, resulting in an interval with stochastic bounds that one can compare with experimental values. Thus, structural modeling with LOKs is a new type of description of the solution: the model does not lead to a single value of the quantity of interest, but to an envelope of the actual values of this quantity of interest. Initially, errors on the ”structural stiffness” alone were considered [1−3]. Here, using the same mathematical framework, we go a step further and extend the concept of LOK to modeling errors on applied forces.