Session: 04-04-01: (04-04: Advances in Aerospace Structures and Materials & 04-11: Advances in Mechanics, Multiscale Models and Experimental Techniques for Composites)

Paper Number: 94187

94187 - Heterogeneous Beam Element Based on Timoshenko Beam Model 

Beam-like structures have been widely used in various industries such as civil, aerospace, and mechanical systems. Although finite element methods have been widely used to analyze composite beam-like structures, current tools usually assume that the beam-like structures can be approximated as piecewise uniform or periodic along the axial direction, and equivalent properties for a suitable beam model such as the Euler-Bernoulli model or the Timoshenko model are used for the beam analysis. However, some beam-like composite structures have varying cross-sectional geometry along the axial direction and imperfections such as irregular ply-drops or voids. A new method is required to take those factors into consideration for better analysis of the structural behavior.

We present a new multiscale method based on a novel application of the recently developed Mechanics of Structure Genome (MSG) to analyze the beam-like structure. The beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18×18 effective beam element stiffness matrices, instead of a material point with effective properties for 1D continuum in the macroscopic analyses.  We use the term macronodes to describe the 3 nodes of the HBE used in the macroscopic analyses.

The HBE modeling framework can be decouple into three steps: homogenization, macroscopic analysis, and dehomogenization. This decomposition of the original structural analysis using MSG-based HBE can greatly improve the computational efficiency while maintaining the accuracy. The first step of HSE modeling is to identify the different structure genes (SGs) from the original heterogeneous structure. Then, homogenization analyses compute effective element stiffness matrices for different SGs, which are then provided as inputs for the macroscopic analysis via Abaqus User Element subroutine (UEL). After the structural analysis, the structural responses are obtained which are then used for dehomogenization analyses to recover the local displacements, strains and stresses.

To compute effective element stiffness for HBE using MSG, we first express the kinematics of the heterogeneous body in terms of the macronodal displacements of the homogenized element and fluctuating functions. To define the boundary conditions and constraints, the shape functions in finite element formulation must be able to capture Timoshenko shear strains of a beam element precisely at the boundary macronodes. However, for a 3-node beam element, the macroscopic shear strain is only accurate at the integration point based on its shape functions. We need to modify the shape function to express the kinematics correctly.

Then we can use the principle of minimum information loss to solve for the fluctuating functions in order to obtain effective element stiffness matrix. Dehomogenization for computing local displacement, strain, and stress fields with global behaviors from macroscopic analysis would be available with fluctuating function. We have implemented the theory in SwiftComp, a general-purpose multiscale modeling code.

We will show the effectiveness and accuracy of HBE dealing with tension, torsion, bending, and also shear loading by two examples: an 8-layer composite beam and a homogenous tapered beam. We will present examples to show that HBE is more accurate in predicting global structural behavior and local strains/stresses. HBE provides a novel concept for multiscale modeling by homogenizing heterogeneous slender structures into equivalent beam elements rather than material points.

Presenting Author: Rong Chiu Purdue University

Presenting Author Biography: Rong Chiu is a PhD candidate in School of Aeronautics and Astronautics, Purdue University. He received his bachelor degree from Department of Aeronautics and Astronautics, National Cheng Kung University, Taiwan, in 2013. Rong used to intern for Dassault Systèmes in 2019 to explore the new strategies for 3DEXPERIENCE on solving engineering finite element problems. Rong's current research involves developing new multiscale modeling methods by homogenize a heterogenous structures into equivalent solid elements or beam elements, instead of material points. The new methods developed would eliminate the scale separation assumption used in multiscale modeling and improve the accuracy when dealing with irregular shape composite structures with arbitrary imperfections due to manufacturing process. His research also focuses on further improving the beam analyses accuracy for composite wind turbine blades.

Authors:

Rong Chiu Purdue University
Wenbin Yu Purdue University