Geometric non-linearity in a multi-fiber displacement-based finite element beam model – an enhanced local formulation under torsion

Abstract

This paper deals with a geometrically nonlinear finite element formulation for the analysis of torsional behaviour of RC members. Using the corotational framework, the formulation is developed for the inclusion of nonlinear geometry effects in a multi-fiber finite element beam model. The assumption of small strains but large displacements and rotations is adopted. The principle is an element-independent algorithm, where the element formulation is computed in a local reference frame which is uncoupled from the rigid body motions (translations and rotations) of the reference frame. In the corotational based frame, strains and stresses are measured from corotated to current, while base configuration is maintained as reference to measure rigid body motions. Corresponding to the requirement of corotational based, in the local frame, taking into account the torsional effect conducts to nonlinear strain assumption, thus require some specific development using a new kinematic model. Second order strain is accounted in the axial term, however lateral buckling is neglected, therefore this formulation is recommended to use in case of solid cross-section with arbitrarily large finite motions, but small strains and elastic material behaviour, such as slender of long-span reinforced concrete beam-column under flexion-torsional effect following serviceability limit state design. The enhanced formulation is validated in linear and nonlinear material range by several examples concerning beams of rectangular cross-section.