Title: Topology Optimization of Coupled Thermomechanical Analysis for Additive Manufacturing
Authors: Jack S. Ramsey and Dr. Douglas E. Smith
Abstract: Topology optimization methods have been developed over the past three decades to optimize the structural design of composite parts. It is now possible to fabricate complex structures generated from topology optimization with additive manufacturing techniques such as large-scale polymer composite deposition. However, large-scale polymer composite deposition produces strutures with anisotropic material properties. This directional orienation affects the structural response of the part and the structure’s behavior during the printing process where thermal stress can led to unacceptable distortion. This paper presents a topology optimization approach that considers the structural response of the product during its use and the printing process employed in its manufacturing. A finite element-based topology optimization algorithm is developed to model structures under weakly coupled thermomechanical loads and anisotropic material properties. Design derivatives are evaluated using the adjoint variable method for the weakly coupled thermal-mechanical system. An optimality criterion-based algorithm maximizes the stiffness of a two-dimensional design space over material density and direction. We consider a steady-state thermal response where the resulting thermal stresses are included in the mechanical optimization. This weakly coupled thermal analysis and material direction optimization includes the anisotropic Young’s modulus and thermal stresses present in large-scale polymer deposition and extends topology optimization to weakly coupled thermomechanical systems with design-dependent temperature fields. Examples are given to demonstrate our proposed weakly coupled system topology optimization.
References: 1. Bendsoe, Martin Philip, Kikuchi, Noboru. “Generating Optimal Topologies in Structural Design Using a Homogenization Method.” Computer Methods in Applied Mechanics and Engineering (1988): 197-224. DOI: 10.1016/0045-7825(88)90086-2 2. Svanberg, Krister. “The Method of Moving Asymptotes – a New Method for Structural Optimization.” International Journal for Numerical Methods in Engineering (1987): 359-373. doi:10.1002/nme.1620240207 3. Sigmund, O. “A 99 Line Topology Optimization Code Written in Matlab.” Structural and Multidisciplinary Optimization (2001): 120-127. DOI: 10.1007/s001580050176 4. Wang, Michael Yu, Wang, Xiaoming, Guo, Dongming. “A Level Set Method for Structural Topology Optimization.” Computer Methods in Applied Mechanics and Engineering (2003): 227-246. DOI: 10.1016/S0045-7825(02)00559-5 5. Bendsoe, M. P., Sigmund, O. Topology Optimization Theory, Methods, and Applications. Germany: Springer-Verlag Berlin Heidelberg 2003 6. Hoglund, Robert. “An Anisotropic Topology Optimization Method For Carbon Fiber-Reinforced Fused Filament Fabrication.” Masters Thesis, Baylor University. 7. Jiang, Dale. “Three Dimensional Topology Optimization with Orthotropic Material Orientation Design for Additive Manufacturing Structures.” Masters Thesis, Baylor University. 8. Jiang, Delin, Hoglund, Robert, Smith, Douglas E. “Continuous Fiber Angle Topology Optimization for Polymer Composite Deposition Additive Manufacturing Applications.” Fibers (2019): DOI: 10.3390/fib7020014 9. Luo, J. H., Gea, H. C. “Optimal Orientation of Orthotropic Materials Using an Energy Based Method.” Structural Optimization (1998): 230-236. DOI: 10.1007/BF01203536 10. Deaton, Joshua. “Design of Thermal Structures Using Topology Optimization.” Dissertation for Doctor of Philosophy, Wright State University 2009. 11. Pederson, Pauli, Pederson, Niels. “Strength Optimized Designs of Thermoelastic Structures.” Structural and Multidisciplinary Optimization (2010): 681-691. DOI: 10.1007/s00158-010-0535-5 12. Zhang, Weihong, Yang, Jungang, Xu, Yingjie, Gao, Tong. “Topology Optimization of Thermoelastic Structures: Mean Compliance Minimization or Elastic Strain Energy Minimization.” Structural and Multidisciplinary Optimization (2014): 417-429. DOI: 10.1007/s00158-013-0991-9 13. Neiford, David John, Grandhi, Ramana V., Deaton, Joshua D., Beran, Philip S. “Level-Set Topology Optimization of Thermoelastic Structures – a Comparison of Compliance, Strain Energy, and Stress Objectives.” 2018 Multidisciplinary Analysis and Optimization Conference. Atlanta, Georgia, June 25-29 2018. AIAA Aviation Forum. DOI: 10 2514/6 2018-3577 14. Kunc, Vlastimil, Compton, Brett, Simunovic, Srdjan, Duty, Chad, Love, Lonnie, Post, Brian, Blue, Craig, Talagani, Farid, Dutton, Renly, Godines, Cody, DorMohammadi, Saber, Baid, Harsh, Abdi, Frank. “Modeling of Large Scale Reinforced Polymer Additive Manufacturing.” ANTEC. Orlando, Florida, March 23-25 2015. Society of Plastics Engineers. 15. Compton, Brett G., Post, Brian K., Duty, Chad E., Love, Lonnie, Kunc, Vlastimil. “Thermal Analysis of Additive Manufacturing of Large-Scale Thermoplastic Polymer Composites.” Additive Manufacturing (2017): 77-86. DOI: 10.1016/j.addma.2017.07.006
Conference: SAMPE 2019 - Charlotte, NC
Publication Date: 2019/05/20
Price: FREEGet This Paper