Nonlinear analysis of frame structural systems based on closed form solutions of thin beam-columns with multiple strong axial and rotation embedded discontinuities

Abstract

A new thin beam-column element with capability to model multiple embedded discontinuities is developed, in which the mechanical failure process is simulated, leading to nonlinear analysis of frame structural systems. The physical and mathematical principles are based on a Lagrangian variational formulation of the mechanical behavior of thin beam-columns with multiple strong axial and rotation embedded discontinuities adapted to represent strain localization. These strong embedded discontinuities represent the material failure process as hinges for beams and cracking or crushing for bars. The developed variational formulation is derived from a decomposed continuous incremental plasticity model with hardening, softening and elastoplastic behavior, from which the strong embedded discontinuities, that represent the strain concentration at non-predetermined localization zone, are naturally obtained. The boundary value problem, which is valid throughout the domain of the structural member, is obtained. Closed form solutions for bars and thin beams with multiple strong embedded discontinuities for any boundary condition are obtained by solving the proposed variational formulation. Closed form solutions are particularized to a basic system without rigid-body displacement modes, which naturally leads to a symmetric flexibility matrix and thus a symmetric stiffness matrix of the thin beam-column element with capability to model multiple embedded discontinuities with arbitrary locations. This matrix is more efficient than those developed with the finite element method, since it is naturally condensed, its coefficients are defined values, not in terms of integrals, and any type of loads are modelled. Representative examples of beams and frames validate the capability of the formulated thin beam-column element for modelling damage. In these examples, the load-displacement curves are in agreement with those reported in the literature.