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Automated Mixed Dimensional Modelling

Introduction

Dimensional Reduction is an idealisation technique used to simplify a component for analysis. It assumes that plate, shell or beam theory can be used to approximate the behaviour of thin sheets and slender bars within a solid body. Prototype software has been written that automatically extracts 2D-1D mixed dimensional models from the 2D sketches used to generate revolved or swept components. Results from the software are shown below.

The software uses geometric proximity information generated during the creation of the Medial Axis to determine which regions of a surface are slender (have an aspect ratio above a critical value), and which are chunky. The slender regions are approximated using beam elements.

The software splits the 2D sketch into a number of surfaces, each representing either a slender or chunky region. Surfaces that represent a slender surface are removed and replaced with their mid-line.

Examples

The mixed dimensional models for a profile are shown below for a range of Critical Aspect Ratios. Chunky regions are displayed in red and 1D approximations for the slender regions are in green.

Profile/Sketch


Critical Aspect Ratio = 20


Critical Aspect Ratio = 10


Critical Aspect Ratio = 5


Critical Aspect Ratio = 2


The results from this research can be integrated with research into Meshing and Mixed Dimensional Coupling to automate the production of reduced dimensional analysis models.