Reliability analysis for elastoplastic mechanical structures under stochastic uncertainty

Problems from plastic limit load or shakedown analysis and optimal plastic design are based on the convex yield criterion and the linear equilibrium equation for the generic stress (state) vector σ. Having to take into account, in practice, stochastic variations of the vector y = y(ω) of model parameters, e.g. yield stresses, external loadings, cost coefficients, etc., the basic stochastic plastic analysis or optimal plastic design problem must be replaced – in order to get robust optimal designs/load factors – by an appropriate deterministic substitute problem. For this purpose, the existence of a statically admissible (safe) stress state vector is described first by means of an explicit scalar state function s* = s* (y,x) depending on the parameter vector y and the design vector x. The state or performance function s* (y,x) is defined by the minimum value function of a convex or linear program based on the basic safety conditions of plasticity theory: A safe (stress) state exists then if and only if s* < 0, and a safe stress state cannot be guaranteed if and only if s* ≥ 0. Hence, the probability of survival can be represented by ps = P(s* (y(ω),x)