Probabilistic FEM for Nonlinear Concrete Structures. I: Theory

Abstract

This is the first part of an investigation on probabilistic finite element methods for nonlinear concrete structures under random loads. The formulation of a method that accounts for both randomness and nonlinearity in material and geometry is proposed. The method is an extension of nonlinear finite element techniques, where: (1) The new quantities required at the element level are the derivatives of the external and internal forces with respect to the basic random variables; (2) the loads are applied in increments until collapse; and (3) the equilibrium at each load level is achieved by using a modified Newton iteration scheme. In contrast to currently available methods the proposed formulation allows for Taylor series expansion of the response about arbitrary reference values of the basic random variables. Furthermore, the collapse load of the system associated with a given combination of reference values of the random variables becomes a result of the analysis. A computer code called PFRAME is developed for the application of the proposed method to concrete frame structures exhibiting geometric and material nonlinear behavior.