Analysis of the elastic structures strength with stochastic parameters using equivalent strength conditions

The method of constructing approximate solutions for the elasticity stochastic problem is represented in the article. It is shown that the finite element formulation of the elasticity stochastic problem is reduced to a finite set of deterministic discrete problems of elasticity. It is proved that there are infinitely many equivalent strength conditions for random parameters structure. Deterministic approach to find the coefficients of safety factor and operating time for the plastic structures of random mechanical properties is proposed. The procedure of optimal designing the structures having maximum strength properties is shortly considered.