Worst-case Structural Analysis

Qingnan Zhou, Julian Panetta and Denis Zorin

New York University


Direct digital manufacturing is a set of rapidly evolving technologies that provide easy ways to manufacture highly customized and unique products. The development pipeline for such products is radically different from the conventional manufacturing pipeline: 3D geometric models are designed by users often with little or no manufacturing experience and sent directly to the printer. Structural analysis on the user side with conventional tools is often unfeasible as it requires specialized training and software. Trial-and-error, the most common approach, is time-consuming and expensive.

We present a method that would identify structural problems in objects designed for 3D printing based on geometry and material properties only, without specific assumptions on loads and manual load setup. We solve a constrained optimization problem to determine the “worst” load distribution for a shape that will cause high local stress or large deformations. While in its general form this optimization has a prohibitively high computational cost, we demonstrate that an approximate method makes it possible to solve the problem rapidly for a broad range of printed models. We validate our method both computationally and experimentally and demonstrate that it has good predictive power for a number of diverse 3D printed shapes.

Paper: pdf (45M)
Supplementary material: pdf (8M)
Presentation slides: pdf (31M)
Videos: Cow, PowerCog, Turret, Dancer, Flora
Online demo: Link (Input tet mesh should be in MSH format format)
Data: Link
Data and Results

Please check our Drop Test Page for validation against actual 3D printed models.

We are very grateful for the following designers who provide us with their 3D models for testing purposes. If you would like to access the digital models, please contact the designers directly because they hold the copyright. If you would like to 3D print these models, please follow the "3d print" links.

Designer: Improbablecog

Flora earring

3d print
Powercog Pendant

3d print
Blade earring

3d print

Designer: Novastar Design


3d print

3d print

Designer: unellenu


3d print

3d print

Designer: kspaho


3d print

Designer: TerryDiF


3d print

Designer: Julia Boersma

Microscopic trilobyte

3d print

We also want to give thanks to Aim@Shape project for making high quality models freely available.

Source: Aim@Shape

Wood chair

Lastly, the following models are created by the first author (Qingnan Zhou). They are released under GNU General Public License (GPL). Please see download session to get these models.

Designer: Qingnan Zhou

Test 3D 1

3d print
Test 3D 2

3d print

3d print
Star pendant

3d print
Leaf pendant

3d print
Cherry pendant

3d print

3d print
Rocking chair

3d print
Bunny wire (based on Stanford Bunny)

3d print

We are grateful to the authors of [Stava et al. 2012] for sharing their data. We also thank Professor Yu Zhang (NYU Dental School) and Professor Nikhil Gupta (NYU Poly), who allowed us to use their facilities for material testing and Professor Alan T. Zehnder (Cornell) for his helpful discussions regarding these tests. Finally, we thank Shapeways for initiating the project and providing raw materials and the many designers whose shapes we tested (Please see data section)

This work was partially supported by NSF awards IIS-0905502, OCI-1047932, and DMS-0602235.

 author = {Zhou, Qingnan and Panetta, Julian and Zorin, Denis},
 title = {Worst-case structural analysis},
 journal = {ACM Trans. Graph.},
 issue_date = {July 2013},
 volume = {32},
 number = {4},
 month = jul,
 year = {2013},
 issn = {0730-0301},
 pages = {137:1--137:12},
 articleno = {137},
 numpages = {12},