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Design and Analysis of Honeycomb Structures With DESIGN AND ANALYSIS OF HONEYCOMB STRUCTURES WITH ADVANCED CELL WALLS A Dissertation by RUOSHUI WANG Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of Committee, Xinghang Zhang Co-Chair of Committee, Jyhwen Wang Committee Members, Amine Benzerga Karl 'Ted' Hartwig Head of Department, Ibrahim Karaman December 2016 Major Subject: Materials Science and Engineering Copyright 2016 Ruoshui Wang ABSTRACT Honeycomb structures are widely used in engineering applications. This work consists of three parts, in which three modified honeycombs are designed and analyzed. The objectives are to obtain honeycomb structures with improved specific stiffness and specific buckling resistance while considering the manufacturing feasibility. The objective of the first part is to develop analytical models for general case honeycombs with non-linear cell walls. Using spline curve functions, the model can describe a wide range of 2-D periodic structures with nonlinear cell walls. The derived analytical model is verified by comparing model predictions with other existing models, finite element analysis (FEA) and experimental results. Parametric studies are conducted by analytical calculation and finite element modeling to investigate the influences of the spline waviness on the homogenized properties. It is found that, comparing to straight cell walls, spline cell walls have increased out-of-plane buckling resistance per unit weight, and the extent of such improvement depends on the distribution of the spline’s curvature. The second part of this research proposes a honeycomb with laminated composite cell walls, which offer a wide selection of constituent materials and improved specific stiffness. Analytical homogenization is established and verified by FEA comparing the mechanical responses of a full-detailed honeycomb and a solid cuboid assigned with the calculated homogenization properties. The results show that the analytical model is accurate at a small computational cost. Parametric studies reveal nonlinear relationships ii between the ply thickness and the effective properties, based on which suggestions are made for property optimizations. The third part studies honeycomb structures with perforated cell walls. The homogenized properties of this new honeycomb are analytically modeled and investigated by finite element modeling. It is found that comparing to conventional honeycombs, honeycombs with perforated cell walls demonstrate enhanced in-plane stiffness, out-of- plane bending rigidity, out-of-plane compressive buckling stress, approximately the same out-of-plane shear buckling strength, and reduced out-of-plane stiffness. For the future design, empirical formulas, based on finite element results and expressed as functions of the perforation size, are derived for the mechanical properties and verified by mechanical tests conducted on a series of 3D printed perforated honeycomb specimens. iii ACKNOWLEDGEMENTS I would like to thank my committee chair and co-chair, Dr. Zhang and Dr. Wang, and my committee members, Dr. Benzerga, and Dr. Hartwig, for their guidance and support throughout the course of this research. I would also like to thank my colleagues, Cheng-Kang Yang and Ying Zhang, for providing me assists and advice on my research. Thanks also go to my friends and the department faculty and staff for making my time at Texas A&M University a great experience. Finally, I’d like to thank my mother Xiaoli Yang and father Xiaojun Wang for their encouragement and to my wife, Feng Jiang, for her patience and love during the last year of my study. iv TABLE OF CONTENTS Page ABSTRACT .......................................................................................................................ii ACKNOWLEDGEMENTS .............................................................................................. iv TABLE OF CONTENTS ................................................................................................... v LIST OF FIGURES ..........................................................................................................vii LIST OF TABLES ............................................................................................................ xi 1. INTRODUCTION ......................................................................................................... 1 1.1 Literature Review on Honeycomb Materials ....................................................... 2 1.2 Honeycombs with Spline Cell Walls .................................................................. 10 1.3 Honeycombs with Composite Laminated Cell Walls ........................................ 12 1.4 Honeycombs with Perforated Cell Walls ........................................................... 13 1.5 Research Objectives ........................................................................................... 16 2. HONEYCOMBS WITH SPLINE CELL WALLS.......................................................19 2.1 Analytical Modeling ........................................................................................... 19 2.1.1 Bezier Curve Function ................................................................................ 19 2.1.2 In-plane Properties ...................................................................................... 21 2.1.3 Out-of-plane Properties ............................................................................... 24 2.1.4 Boundary Condition: Horizontal Plates ...................................................... 25 2.1.5 Boundary Condition: Bonding Strips .......................................................... 27 2.2 Verification ......................................................................................................... 29 2.2.1 Analytical Verification ................................................................................ 29 2.2.2 Experimental Verification ........................................................................... 32 2.3 Parametric Study and Discussions ..................................................................... 36 2.3.1 FEA Models ................................................................................................ 36 2.3.2 In-plane Stiffness ........................................................................................ 38 2.3.3 Out-of-plane Stability.................................................................................. 39 2.4 Conclusions ........................................................................................................ 42 3. HONEYCOMBS WITH LAMINATED COMPOSITE CELL WALLS .................... 44 3.1 Analytical Modeling ........................................................................................... 44 3.1.1 In-plane Elastic Moduli ............................................................................... 44 v Page 3.1.2 In-plane Shear Modulus .............................................................................. 47 3.1.3 Out-of-plane Elastic Modulus ..................................................................... 47 3.1.4 Out-of-plane Shear Moduli ......................................................................... 48 3.1.5 Poisson’s Ratios .......................................................................................... 49 3.2 Numerical Modeling ........................................................................................... 49 3.3 Result and Discussion ........................................................................................ 52 3.3.1 In-plane Mechanical Behaviors ................................................................... 52 3.3.2 Out-of-plane Mechanical Behaviors ........................................................... 56 3.4 Conclusions ........................................................................................................ 59 4. HONEYCOMBS WITH PERFORATED CELL WALLS .......................................... 61 4.1 Analytical Modeling ........................................................................................... 61 4.1.1 Theoretical Considerations.......................................................................... 61 4.1.2 In-plane Moduli ...........................................................................................62 4.1.3 Out-of-plane Compressive Critical Buckling Stress ...................................70 4.2 Finite Element Modeling and Empirical Formulas ............................................ 73 4.2.1 Methodologies .............................................................................................74 4.2.2 In-plane Elastic Moduli ...............................................................................79 4.2.3 In-plane Shear Modulus .............................................................................. 81 4.2.4 Out-of-plane Elastic Modulus ..................................................................... 83 4.2.5 Out-of-plane Shear Moduli ......................................................................... 85 4.2.6 Out-of-plane Bending Rigidity ................................................................... 88 4.2.7 Out-of-plane Critical Compressive Stress ................................................... 91 4.2.8 Out-of-plane Critical Shear Stress .............................................................. 94 4.3 Experimental Verification .................................................................................
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