A Generalized Optimality Criteria Method for Optimization of Additively Manufactured Multimaterial Lattice Structures

Recent progress in Additive Manufacturing (AM) allows for printing customized products with multiple materials and complex geometries that could form the basis of multi-material designs with high performance and novel functions. Effectively designing such complex products for optimal performance within the confines of additive manufacturing constraints is challenging due to the need to consider fabrication constraints while searching for optimal designs with a large number of variables, which stem from new AM capabilities. In this study, fabrication constraints are addressed through empirically characterizing multiple printed materials’ Young’s modulus and density using a multi-material inkjet-based 3D-printer. Data curves are modeled for the empirical data describing two base printing materials and twelve mixtures of them as inputs for a computational optimization process. An optimality criteria method is developed to search for solutions of multi-material lattices with fixed topology and truss cross-section sizes. Two representative optimization studies are presented and demonstrate higher performance with multi-material approaches in comparison to using a single material. These include the optimization of a cubic lattice structure that must adhere to a fixed displacement constraint and a compliant beam lattice structure that must meet multiple fixed displacement constraints. Results demonstrate the feasibility of the approach as a general synthesis and optimization method for multi-material, lightweight lattice structures that are large-scale and manufacturable on a commercial AM printer directly from the design optimization results.

[1]  David W. Rosen,et al.  A comparison of synthesis methods for cellular structures with application to additive manufacturing , 2010 .

[2]  Donald E. Grierson,et al.  An optimality criteria design method for tall steel buildings , 1993 .

[3]  James W. Rawlins,et al.  Investigation of linear impact energy management and product claims of a novel American football helmet liner component , 2011 .

[4]  Saigopal Nelaturi,et al.  Manufacturability Feedback and Model Correction for Additive Manufacturing , 2015 .

[5]  Frank W. Zok,et al.  Optimal Material Properties for Mitigating Brain Injury During Head Impact , 2014 .

[6]  Ian F. C. Smith,et al.  Improving Full-Scale Transmission Tower Design through Topology and Shape Optimization , 2006 .

[7]  George I. N. Rozvany,et al.  DCOC: An optimality criteria method for large systems Part I: theory , 1992 .

[8]  F. Zok,et al.  Pyramidal Lattice Structures for High Strength and Energy Absorption , 2013 .

[9]  V. B. Venkayya,et al.  Structural optimization: A review and some recommendations , 1978 .

[10]  W Prager,et al.  Optimality criteria in structural design. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Ahmad Barari,et al.  Surface Topography of Additive Manufacturing Parts Using a Finite Difference Approach , 2014 .

[12]  Sergio Pellegrino,et al.  Design of lightweight structural components for direct digital manufacturing , 2012 .

[13]  V. B. Venkayya,et al.  A Compound Scaling Algorithm for Mathematical Optimization , 1989 .

[14]  Jouke Verlinden,et al.  Optimal Design for Additive Manufacturing: Opportunities and Challenges , 2011 .

[15]  Christopher B. Williams,et al.  Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing , 2014 .

[16]  Martin Fischer,et al.  Cifecenter for Integrated Facility Engineering Fully Constrained Design: a Scalable Method for Discrete Member Sizing Optimization of Steel Frame Structures , 2022 .

[17]  David W. Rosen,et al.  The Size Matching and Scaling Method: A Synthesis Method for the Design of Mesoscale Cellular Structures , 2010, 2010 International Conference on Manufacturing Automation.

[18]  V. B. Venkayya,et al.  ENERGY DISTRIBUTION IN AN OPTIMUM STRUCTURAL DESIGN , 1969 .

[19]  Christiane Beyer,et al.  Strategic Implications of Current Trends in Additive Manufacturing , 2014 .

[20]  J. Dvořák,et al.  Is protective equipment useful in preventing concussion? A systematic review of the literature , 2009, British Journal of Sports Medicine.

[21]  L. Berke,et al.  Optimum structural design with stability constraints , 1976 .

[22]  V. B. Venkayya,et al.  Design of Optimum Structures to Impulse Type Loading , 1974 .

[23]  Liang Hou,et al.  Additive manufacturing and its societal impact: a literature review , 2013 .

[24]  Hod Lipson,et al.  Design and analysis of digital materials for physical 3D voxel printing , 2009 .

[25]  Frank W. Liou,et al.  Building Sequence of Boundary Model in Layered Manufacturing , 2005, DAC 2005.

[26]  Aaron M. Dollar,et al.  Hybrid Deposition Manufacturing: Design Strategies for Multimaterial Mechanisms Via Three-Dimensional Printing and Material Deposition , 2015 .

[27]  Caroline Deck,et al.  Angular Impact Mitigation system for bicycle helmets to reduce head acceleration and risk of traumatic brain injury. , 2013, Accident; analysis and prevention.

[28]  Kristina Shea,et al.  Optimization of Additively Manufactured Multi-Material Lattice Structures Using Generalized Optimality Criteria , 2015 .

[29]  Markus H. Gross,et al.  Computational design of actuated deformable characters , 2013, ACM Trans. Graph..

[30]  Frank W. Zok,et al.  Compressive Response of Pyramidal Lattices Embedded in Foams , 2014 .

[31]  Georges M. Fadel,et al.  Design for Manufacturing of 3D Heterogeneous Objects With Processing Time Consideration , 2008 .

[32]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[33]  Georges M. Fadel,et al.  Optimal design for additive manufacturing of heterogeneous objects using ultrasonic consolidation , 2006 .

[34]  N. S. Khot,et al.  ALGORITHMS BASED ON OPTIMALITY CRITERIA TO DESIGN MINIMUM WEIGHT STRUCTURES , 1981 .

[35]  Hod Lipson,et al.  Automatic Design and Manufacture of Soft Robots , 2012, IEEE Transactions on Robotics.

[36]  Brian Mellor,et al.  Multiple material additive manufacturing – Part 1: a review , 2013 .

[37]  V. Venkayya Optimality criteria: A basis for multidisciplinary design optimization , 1989 .