Heterogeneous Structural Elements Based on Mechanics of Structure Genome

Rong Chiu, Purdue University

Abstract

The Mechanics of Structural Genome (MSG) is a unified homogenization theory used to find equivalent constitutive models for beam, plate, and solid structures. It has been proven accurate for periodic structures. However, for certain applications such as non-prismatic wind turbine blades and helicopter flexbeams featuring ply drop-off, where there is no repeating structure and the periodic boundary condition cannot be used, MSG’s accuracy is limited. In this work, we aim to extend MSG to find element stiffness matrices directly for aperiodic structures, instead of beam properties or three-dimensional (3D) solid material properties. Two finite elements based on MSG have been developed: Heterogeneous Beam Element (HBE) and Heterogeneous Solid Element (HSE).For beam modeling, the beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18 × 18 effective beam element stiffness matrices. These matrices are used as input for one-dimensional (1D) beam analysis using the 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 MSG cross-sectional analysis approach. HBE can capture macroscopic behavior and detailed stresses due to non-prismatic geometry.The Heterogeneous Solid Element (HSE) is developed based on MSG to model a heterogeneous body as an equivalent solid element using an effective element stiffness matrix. HSE modeling includes homogenization, macroscopic global analysis, and dehomogenization to recover local strains/stresses. HSE avoids the local periodicity assumption for traditional multiscale modeling techniques for composite structures that compute effective material properties instead. Abaqus composite solid element and MSG-based traditional multiscale modeling are used to validate the accuracy of HSE. All example results show that HSE is more accurate in predicting global structural behavior and local strains/stresses.HBE and HSE provide a new concept for modeling aperiodic composite structures by modeling structures into equivalent beam or solid elements instead of beam properties of the reference line in 1D beam analysis or material properties of material points in solid structural analysis.

Degree

Ph.D.

Advisors

Yu, Purdue University.

Subject Area

Mechanics|Genetics|Mathematics

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