Recent Advances in the Nonlinear Simulation of Beam-Columns: Mathematical Foundations and OpenSees Implementations

Abstract

A novel computational framework is developed for nonlinear finite element analysis of frames and shells. The proposed framework is shown to furnish a novel geometrically exact frame element that rectifies the lack of objectivity of prior formulations without violating model constraints or compromising symmetry of the tangent stiffness at equilibrium. The proposed framework is consistent with both Petrov-Galerkin and Bubnov-Galerkin formalisms and in both cases is shown to admit an element-independent architecture which resembles the well-known geometric transformation abstraction popularized by the open-source platform OpenSees. Geometrically exact finite elements often provide significantly greater accuracy compared to elements based on truncated strain measures when modeling problems with large displacements. However, very few simulation platforms offer such elements as they often do not fit easily into standard finite element architectures and users may be deterred by their tendency to exhibit alarming properties like path dependence and material frame dependence. The proposed formulation addresses these difficulties and presents the first such implementation in OpenSees.