Enhanced Strain Beam Formulation Resolving Several Issues of Displacement-Based Elements for Nonlinear Analysis

Abstract

This paper presents an enhanced-strain beam formulation for the analysis of frame structures with material and geometric nonlinearities. The focus is on slender members, for which the Euler–Bernoulli beam theory can be adopted. The generalized strain enhancement vector, which only includes an axial strain component, is introduced in an element for which the sectional response is evaluated at the two end points. When combined with a modified integration rule, the enhanced-strain formulation resolves inherent problems of displacement-based elements caused by the weak satisfaction of equilibrium, while ensuring a simpler and more robust element state determination algorithm compared to those of mixed and force-based elements. The accuracy of the proposed formulation is validated through a series of analyses.