Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-23-2017 Analysis of Additively Manufactured Lattice Structures Using Finite Element Methods Christopher A. Box Follow this and additional works at: https://scholar.afit.edu/etd Part of the Aerospace Engineering Commons, and the Other Materials Science and Engineering Commons Recommended Citation Box, Christopher A., "Analysis of Additively Manufactured Lattice Structures Using Finite Element Methods" (2017). Theses and Dissertations. 1709. https://scholar.afit.edu/etd/1709 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. ANALYSIS OF ADDITIVELY MANUFACTURED LATTICE STRUCTURES BY FINITE ELEMENT METHODS THESIS Christopher A. Box, Captain, USAF AFIT-ENY-MS-17-M-245 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENY-MS-17-M-245 ANALYSIS OF ADDITIVELY MANUFACTURED LATTICE STRUCTURES BY FINITE ELEMENT METHODS THESIS Presented to the Faculty Department of Astronautical Engineering Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science in Astronautical Engineering Christopher A. Box, B.S.M.E. Captain, USAF March 3, 2017 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT-ENY-MS-17-M-245 ANALYSIS OF ADDITIVELY MANUFACTURED LATTICE STRUCTURES BY FINITE ELEMENT METHODS Christopher A. Box, B.S.M.E. Captain, USAF Committee Membership: Major Ryan O'Hara, PhD Chair Dr. Anthony Palazotto, PhD Member Dr. Eric Swenson, PhD Member AFIT-ENY-MS-17-M-245 Abstract Additive Manufacturing (AM) processes are well known for their ability to fabri- cate parts with complex geometries. Lattice structures leverage this ability to create parts with high strength-to-weight ratio and other desirable structural qualities. This research presents a parameterized modeling tool using common Finite Element Anal- ysis (FEA) and scripting software with which aggregated lattice structures can be analyzed, given different geometric properties and loading conditions. A full facto- rial Design of Experiments is run to explore the effects of various parameters on the strength of lattice structures. Experimental compressive strength results from three Fused Deposition Modeling (FDM)-produced Polylactic Acid (PLA) lattices are dis- cussed and compared to predictions from the Finite Element simulations. iv Acknowledgments I would like to thank my advisor, Maj O'Hara, for the effort and mentorship provided to me throughout the course of this research. You kept me on track in countless weekly meetings. I would like to thank Dr. Philip Flater of AFRL for the collaboration and advice received throughout this endeavor. I'd like to extend my thanks to Matt Lippert and Travis Shelton, whose printer maintenance and printing assistance was invaluable to completion of my work. Thanks goes out to my committee members, Dr. Palazotto and Dr. Swenson, for taking the time to provide feedback on my writing. I'd also like to thank my friends, family, and classmates for withstanding the repeated use of the phrases \working on my thesis" and \crush some lattices." Finally, I'd like to dedicate this paper to my mom, whose love and support for me and my academic (and all other) endeavors was always unwavering. Christopher A. Box v Table of Contents Page Abstract . iv Acknowledgments . .v List of Figures . viii List of Tables . xii List of Acronyms . xiv List of Symbols . .xv I. Introduction . .1 1.1 Chapter Overview . .1 1.2 Objective . .2 1.3 Motivation . .2 1.4 Background . .3 1.5 Assumptions . .4 1.6 Methodology. .4 1.7 Thesis Overview. .5 II. Background . .6 2.1 Chapter Overview . .6 2.2 Cellular and Lattice Structures . .6 2.2.1 Background. .6 2.2.2 Parameters and Definitions . .7 2.3 Bending vs. Stretching Dominated Structures . .8 2.4 Cells to be Studied . 12 2.4.1 Body Centered Cubic (BCC) Cell . 13 2.4.2 Auxetic Re-entrant Cell . 14 2.4.3 Octet-truss . 16 2.5 Additive Manufacturing . 16 2.5.1 History and Background . 16 2.5.2 Manufacturing of Lattices . 18 2.5.3 Applicable Research . 19 2.5.4 Anisotropy . 23 2.6 Finite Element Analysis (FEA) . 24 2.7 Summary . 26 III. Research Methodology . 27 3.1 Chapter Overview . 27 3.2 MATLAB and ANSYS Collaboration . 27 3.2.1 FE Model Inputs . 28 vi Page 3.2.2 FE Model Outputs . 29 3.2.3 Model Operation . 30 3.2.4 Lattice Analysis Tool Features . 38 3.3 Finite Element Analysis Simulations . 45 3.3.1 Main Study - Full Factorial Design of Experiments . 45 3.3.2 Additional Studies . 47 3.4 Experimental Compression Testing . 49 3.4.1 Lattice Selection . 50 3.4.2 Lattice Generation Methods . 51 3.4.3 Lattice Compression Tests . 55 3.4.4 Data Analysis . 56 3.5 Summary . 59 IV. Results . 60 4.1 Chapter Overview . 60 4.2 Simulation Results . 60 4.2.1 Auxetic re-entrant cell angle DOE . 60 4.2.2 Main Study - Full Factorial Design of Experiments . 62 4.2.3 Offset Error DOE . 75 4.2.4 Strut Deletion DOE . 77 4.3 Experimental Compression Testing Results . 78 4.3.1 Data and Results . 78 4.3.2 Discussion . 84 4.4 Summary . 92 V. Conclusions and Recommendations . 93 5.1 Summary of Work . 93 5.2 Future Work . 94 5.3 Conclusion . 96 Bibliography . 97 vii List of Figures Figure Page 1.1 Three unit cell geometries studied in this research. (a) \Body Centered Cubic [BCC]" or \Vertex Centroid" (b) Auxetic \Re-entrant" (c) \Octet truss" (internal struts highlighted red for clarity) . ..