approach

Static stability of thin-walled structures is significantly influenced by random imperfection in their geometric form. The problem should be considered on the level of stochastic approach. Consequently, stochastic version of the FEM should be taken into account. Subsequent solution methods presented in literature are limited as a rule to the first approximation only. It leads to results being more or less in a contradistinction with the energy equilibrium law and with the fact, that the PDF of the response is non-Gaussian and non-symmetric. It seems in general that solution methods based on principles of decomposition into stochastic moments, cumulants and other series are not convenient to solve this problem. The stochastic simulation reveals also non-realistic when taking into account a number of unknown components of the displacement vector. A compromising procedure being based on an application of the Bayes Theorem seems to be promising. Various versions of this approach related with incremental method, arc length method, etc. can be set up. The basic form being based on the incremental method driven by the Bayes algorithm is presented in this paper. Using incremental method combined with Bayes formula, the PDF of node displacements in each loading step can be computed with prescribed accuracy comparing prior and posterior PDF of the response in a particular loading step. Because the posterio