Heterogeneous Beam Element Based on Timoshenko Beam Model

Abstract

Traditional multiscale methods homogenize a beam-like structure into a material point in 1-D continuum with effective properties computed over a structure gene in terms of a cross-section or a 3D segment with spanwise periodicity. Such methods lose accuracy when dealing with real world beam-like structures usually not uniform or periodic along the spanwise direction. Thus, traditional multiscale methods cannot be rigorously applied to these cases. In our previous work, a new multiscale method was proposed based on a novel application of the recently developed Mechanics of Structure Genome (MSG) to analyze beam-like structures. Beam-like structures were homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18 × 18 effective beam element stiffness matrices, which were used as input for one-dimensional beam analyses. However, due to the shape function limitations, HBE could not handle transverse shear loads. In this work, the shape functions and the MSG theory are further modified to enable capabilities of HBE for transverse shear loads. Using the macroscopic behavior of the beam elements as input, dehomogenization can be performed to predict the local stresses and strains in the original structure. Two examples are used (a periodic composite beam and a tapered beam) to demonstrate the capability of this improved HBE.