The fiber-free approach in the evaluation of the tangent stiffness matrix for elastoplastic uniaxial constitutive laws

It has been shown in a previous paper that the normal stress resultants for an arbitrary polygonal section endowed with a uniaxial elastoplastic law can be computed exactly by means of a general approach; it has been denominated fiber free as no fiber discretization of the section is required. The aim of this paper was to extend the fiber-free approach to the evaluation of the tangent stiffness matrix to allow for the analytical integration of all the basic quantities required by the section state determination occurring in nonlinear frame analysis. The numerical examples showed that the general properties of the fiber-free approach, already discussed with reference to the stress resultants, carry over to the tangent stiffness matrix as well. Namely, independent from the complexity of the constitutive law, the accuracy in the evaluation of the tangent stiffness matrix allowed by the number of fibers adopted in commercial software for nonlinear frame analysis is even worse than that associated with the computation of the stress resultants.