Lattice Optimization Analysis by Means of Multiscale Approach Based on Homogenization Technique

This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

Multiscale analysis based on homogenization theory is an important technique that enables to get an-isotropic material properties of non-homogeneous media without real material testing. Examples of non-homogeneous media are porous, metallographic structure, honeycomb and especially composite namely GFRP, CFRP and so on. We have developed this analysis system and embedded in general purpose CAE software which name is ANSYS Workbench by ACT (ANSYS Customization Toolkit). There are roughly 3 functions which are modelling template in order to create complex in-homogeneity automatically, homogenization analysis and localization analysis. Localization analysis makes it possible to observe any result items in micro or meso structure. Homogenization analysis does not only support linear material behavior but also many varieties of nonlinear phenomena including elasto-plastic, creep, hyper-elasticity, visco-elasticity and damage etc. We can perform multiscale analysis by means of these features.

In this presentation, optimization analysis example for lattice structure by multiscale approach is presented. Mesoscopic shape of lattice structure can be flexibly controlled because it is created by additive manufacturing using 3D printer. Lattice structure has an important feature for product designers that the macroscopic material properties are strongly depended on the thickness or angle of lattice columns. In other words, we can create optimized structure which achieve both of high stiffness and lightweight by arranging the lattice columns accordingly. The object of this paper is to decide optimum distribution for thickness and angles of lattice columns in order to achieve highest stiffness during some amount of weight saving. In our suggested approach, some unit cell models as a candidate lattice structure are prepared at first. Each structure has a same thickness but different angles for lattice columns. Macroscopic material properties for each structure are identified by homogenization analysis. And then, structural behaviours of L shaped bracket as macro scale model made by each lattice structure are analyzed. Detailed lattice pattern in macroscopic model is not be modelled and defined as homogenized shape by assigning the equivalent material properties evaluated at homogenization analysis step. It will be shown that the homogenized analysis can reduced analysis costs drastically with maintaining analysis accuracy which is validated by making comparison between analysis results for homogenized model and real structured model as a reference. Optimized lattice angle is decided as results of macroscopic analysis. Finally, the best thickness distribution is decided by means of density based topology optimization. Homogenization analysis is also applied in order to prepare the relationship between equivalent material properties and lattice density.

Document Details

AuthorYamamoto. K
Date 18th June 2019


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