Plastic systems reliability by LP and form

Abstract The reliability with respect to plastic collapse of a discretized ideal plastic structure is formulated on the basis of the lower bound theorem of plasticity theory. The reliability is calculated by a first order reliability method (FORM) in which the approximation points on the failure surface in the space of normalized and independent Gaussian variables are found by a suggested directional search procedure. When the yield functions are piecewise linear and the basic variables are normally distributed the approximation is found by use of linear programming (LP), and it is demonstrated how LP and FORM can be combined. In particular, the gradient vector of the failure function for the structure with respect to plastic collapse is needed in the computation, and it is shown how this vector can be calculated. The directional search procedure is applied to two examples.