A GENERAL DEHOMOGENIZATION METHOD FOR BEAM ANALYSES

Abstract

Traditional multiscale methods homogenize a beam-like structure into a material point in 1D continuum with effective properties computed over a structure gene (SG) in terms of a 2D cross-section or a 3D segment with spanwise periodicity. Such methods lose accuracy when dealing with real beam-like structures usually not uniform or periodic along the spanwise direction. Thus, traditional multiscale methods cannot be rigorously applied to these cases and some refined methods have been proposed to analysis beam structure featuring spanwise heterogeneity. However, those methods usually require specific geometries assumption, assume material to be isotropic and homogeneous, or only predict macroscopic behavior without detailed dehomogenization analysis for local stresses recovery. In our previous work, we proposed Heterogeneous Beam Element (HBE) based on Mechanics of Structure Genome (MSG) to analyze beam-like structures featuring spanwise heterogeneity. Despite more accurate in predicting both macroscopic behavior and local stresses than traditional methods, errors in local stresses predictions on the SG boundary are inevitable due to the invoked assumptions of boundary conditions. In this paper, we propose a general dehomogenization methods for beam modeling (GDMB) based on HBE to better predict local stresses when the macroscopic behavior from other beam models are available. The results show that GDMB improves accuracy of the HBE dehomogenization and provides accurate stresses predictions based on a beam analysis.