S.A. Pimenov, I.J. Palkin

For a wide range of constructions it is difficult to get an analytic form of relation between stress parameters Q and strength R. In such cases the common way is to apply numerical methods. It is a finite elements method as a rule. Using finite elements method construction is considered as a finite elements model with fixed number of definite characteristics (construction parameters). Each parameter is specified by a statistical array (variational series). Solution is made by iterative calculations of finite elements model with each value of every definite parameter out of its variational series. An easy solving method is a loop with nesting level equals to number of construction parameters (n). Number of construction parameters evidently depends on the construction. So the algorithm needs to be transformed to solve the task for any value of n (i.e. for any construction). We suggest a recursive algorithm for computer realization. The main idea of the algorithm follows. While the number of unfixed parameters is more than one the recursive procedure is successively called with each value of the parameter AM out of the variational series. In the other case sequential calculations of the finite elements model are made with each value of the last parameter An out of the variational series. In the case of unconditioned distribution of stress, strength and construction parameters numerical computation of variational series of Qij is made by algorithms described before. Rj, Qij are considered like empirical distributions for finite elements model node. Further calculations are made using method of defining probability of faultless work (reliability) with empirical distributions described in «Reliability in Engineering Design» (K.C. Kapur, L. R, Lamberson).