An implementation for 2nd-order M-N coupling and geometric stiffness adaptation in tapered beam-column elements. (15th December 2020) - Chiorean, Cosmin G.; Passera, Davide; Ferrari, Rosalba; Rizzi, Egidio
Highlights: Finite Analytic Method (FAM) to handle second-order geometrical effects in tapered beam-column elements. Numerical solution for bending moment/axial force coupling. Consistent flexibility/stiffness matrix adaptation. Examples and comparisons with reference studies, proving the effectiveness of the methodology. Results on critical load evaluation of sample tapered members are delivered. Abstract: The present work outlines a computational approach, based on the so-called Finite Analytic Method (FAM), to deal with second-order effects in the structural analysis of tapered members accounting for geometrical nonlinearity by using only one element per physical member. The proposed modelization considers the equilibrium in the deformed configuration of a "beam-column" element, by addressing the resulting mechanical coupling between bending moment and axial force ( M-N interaction). A flexibility-based method is developed, to derive the force-displacement relations of the finite element, by obtaining its flexibility and stiffness matrices. Through Gauss-Lobatto integration, the stiffness coefficients capturing second-order geometrical effects are consistently evaluated, to achieve the complete stiffness matrix. Examples and comparisons with reference studies are provided, in order to prove the effectiveness of the proposed methodology. Results on the critical load evaluation of sample tapered members are delivered.