Finite elements numerical solution to deep beams based on layerwise displacement field

Abstract

This paper proposes a numerical solution to deep beams using the layerwise displacement theory. Most of the methods for performing structural analyses of deep beams have geometric and boundary conditions limitations, as well as modeling inconveniences. This paper provides a finite element solution for deep beams based on a layerwise displacement field considering the full stress/strain tensors. In this formulation, the cross section is discretized in a pre-defined number of independent virtual layers, with linear interpolation within the thickness direction. To validate the model developed, two numerical examples are analyzed. The first is a reinforced concrete deep beam with two supports, loaded over the top face, validated by finite element analysis based on solid-element ABAQUS™ software. Next, an isotropic deep beam with both ends cantilevered is analyzed and the outcome is compared to the literature. The results of both numerical examples are accurate and can estimate the complete state of stress over all domains of the element. Moreover, the layerwise formulation does not suffer from shear and membrane locking, and it may use fewer computational resources than equivalent 3D finite element analyses.