Heterogeneous Beam Element for Multiscale Modeling of Non-prismatic Composite Beam-like Structures

Abstract

Anisotropy, heterogeneity, and geometry make full system-level three-dimensional (3D) finite element analysis (FEA) simulation of real composite beam-like structures, such as wind blades, impossible due to limitations on computing resources. A popular approach is to cut the structure into multiple cross-sections, from which the beam properties based on the Euler-Bernoulli or Timoshenko beam models are extracted using two-dimensional (2D) cross-sectional analyses. These properties are then utilized in beam elements for system-level analyses. However, the mechanics behind 2D cross-sectional analyses are based on prismatic beams, limiting the accuracy of this approach on non-prismatic structures, especially in predicting stresses. In this work, we present a new multiscale method based on Mechanics of Structure Genome to analyze beam-like non-prismatic composite structures. A beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with effective beam element stiffness matrices, which are then used as input for one-dimensional (1D) beam analysis using Abaqus User Element subroutine (UEL). Using the macroscopic beam analysis results as input, we can also perform dehomogenization to predict the stresses and strains in the original structure. We use three examples, a prismatic composite beam, an isotropic homogeneous tapered beam, and a composite tapered beam, to demonstrate the capability of HBE and show its advantages over the traditional cross-sectional analysis approach. HBE can capture macroscopic behavior and detailed stresses due to non-prismatic geometry. HBE provides a new concept to model non-prismatic composite beams by modeling heterogeneous beam-like structures as equivalent beam elements rather than beam properties of material points of the reference line.