Implementing Optimization Methods in the Design of IsoTruss Structures in Uniaxial Compression
Publication: Journal of Aerospace Engineering
Volume 35, Issue 5
Abstract
This study examines two techniques to optimize the design of lightweight composite IsoTruss columns subject to uniaxial compression: gradient-based (interior-point with algorithmic differentiation and Latin hypercube sampling) and gradient-free (nonsorting genetic algorithm). Both methods used analytical expressions to minimize mass with respect to the number of bays, number of carbon tows in each longitudinal member, and the outer diameter. The general geometric configuration was based on experimental specimens, tested previously, that were approximately 3 m (10 ft) long and 0.14 kg (0.3 lb). The analytical constraint functions used to predict material failure and buckling were verified by finite-element analysis and validated with experimental data in preceding works. The gradient-based and gradient-free approaches both produced similar results, indicating an optimal design 14%–16% lighter than the experimental configuration used as the initial design criteria. Sensitivity derivatives produced in the gradient-based analysis indicated that (1) increasing any of the design variables increases the mass of the structure; (2) increasing the outer diameter increases the global buckling capacity and decreases the shell-like buckling capacity; (3) increasing the number of bays increases the local buckling capacity with negligible impact on the global buckling capacity; and (4) increasing the number of tows in each longitudinal member increases both the global and local buckling capacities. Although both methods produced similar results and demonstrated satisfactory convergence, the gradient-based framework was selected for a subsequent study to evaluate novel IsoTruss configurations because it provides additional insights to the design space via outputs such as Lagrange multipliers and Jacobian matrices. The gradient-free framework could be augmented and used in future studies to optimize IsoTruss structures for specific applications and design criteria.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the Utah NASA Space Grant Consortium and the Department of Civil Engineering at Brigham Young University.
Disclaimer
The research described in this paper was performed while Dr. David W. Jensen was a full-time Professor of Civil Engineering at Brigham Young University. Dr. Jensen is now Professor Emeritus of Brigham Young University, and a consultant to IsoTruss Inc.
References
Afifi, M. Z., H. M. Mohamed, and B. Benmokrane. 2014. “Strength and axial behavior of circular concrete columns reinforced with CFRP bars and spirals.” J. Compos. Constr. 18 (2): 04013035. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000430.
Belardi, V., P. Fanelli, and F. Vivio. 2018. “Structural analysis and optimization of anisogrid composite lattice cylindrical shells.” Composites, Part B 139 (Apr): 203–215. https://doi.org/10.1016/j.compositesb.2017.11.058.
Buragohain, M., and R. Velmurugan. 2009. “Buckling analysis of composite hexagonal lattice cylindrical shell using smeared stiffener model.” Def. Sci. J. 59 (3): 230–238. https://doi.org/10.14429/dsj.59.1516.
Choi, K.-K., and Y. Xiao. 2010. “Analytical model of circular CFRP confined concrete-filled steel tubular columns under axial compression.” J. Compos. Constr. 14 (1): 125–133. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000056.
Correia, M., F. Nunes, J. Correia, and N. Silvestre. 2013. “Buckling behavior and failure of hybrid fiber-reinforced polymer pultruded short columns.” J. Compos. Constr. 17 (4): 463–475. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000339.
Dmitruk, A., and N. Osmolovskii. 2017. “A general lagrange multipliers theorem.” In 2017 constructive nonsmooth analysis and related topics (dedicated to the memory of V.F. Demyanov) (CNSA), 1–3. Piscataway, NJ: IEEE.
Embley, M. D. 2011. “Damage tolerance of buckling-critical unidirectional carbon, glass, and basalt fiber composites in co-cured aramid sleeves.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
Fitzwilliam, J., and L. A. Bisby. 2010. “Slenderness effects on circular CFRP confined reinforced concrete columns.” J. Compos. Constr. 14 (3): 280–288. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000073.
Grande, E., M. Imbimbo, and V. Tomei. 2018. “Structural optimization of grid shells: Design parameters and combined strategies.” J. Archit. Eng. 24 (1): 04017027. https://doi.org/10.1061/(ASCE)AE.1943-5568.0000286.
Hansen, S. M. 2004. “Influence of consolidation and interweaving on compression behavior of IsoTruss™ structures.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
Jacobson, J. G. 2018. “Investigation of an IsoTruss™ structure as a compliant member used in bending and torsion.” M.S. thesis, Dept. of Mechanical Engineering, Brigham Young Univ.
Jensen, H., D. Kusanovic, M. Valdebenito, and G. Schuëller. 2012. “Reliability-based design optimization of uncertain stochastic systems: Gradient-based scheme.” J. Eng. Mech. 138 (1): 60–70. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000304.
Kesler, S. L. 2006. “Consolidation and interweaving of composite members by a continuous manufacturing process.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
Kim, Y., P. Kim, H. Kim, and J. Park. 2018. “An optimization of composite lattice cylinder using the approximate method.” Adv. Compos. Mater. 28 (3): 287–320. https://doi.org/10.1080/09243046.2018.1510590.
Kollar, L. P., and G. S. Springer. 2003. Mechanics of composite structures. Cambridge, UK: Cambridge University Press.
Luo, B., M.-M. Ding, L.-F. Han, and Z.-X. Guo. 2018. “Structural optimization of spoke single-layer cable-net structures based on a genetic algorithm.” J. Aerosp. Eng. 31 (3): 04018012. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000831.
Maji, A. K., M. Harris, D. Garcia, and B. J. deBlonk. 2011. “Feasibility assessment of deployable composite telescope.” J. Aerosp. Eng. 24 (1): 12–19. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000045.
Martins, J., and A. Ning. 2020. Engineering design optimization. Cambridge, UK: Cambridge University Press.
McCune, A. M. 2001. “Tension and compression of carbon/epoxy IsoTruss™ grid structures.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
Opdahl, H. B. 2020. “Investigation of IsoTruss structures in compression using numerical, dimensional, and optimization methods.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
Opdahl, H. B., and D. W. Jensen. 2020. “Validation of a finite element model in ANSYS Work-Bench for IsoTruss structures in uniaxial compression.” In Utah NASA space grant consortium. Logan, UT: Utah State Univ. Digital Commons.
Opdahl, H. B., and D. W. Jensen. 2021a. “Dimensional analysis and optimization of IsoTruss structures with outer longitudinal members in uniaxial compression.” Materials 14 (8): 2079. https://doi.org/10.3390/ma14082079.
Opdahl, H. B., and D. W. Jensen. 2021b. “Dimensional analysis of shell-like buckling in IsoTruss structures using numerical methods.” In AIAA Scitech 2021 forum, 0700. Reston, VA: American Institute of Aeronautics and Astronautics.
Opdahl, H. B., and D. W. Jensen. 2021c. “A mechanics-based derivation of the shell-like buckling load of IsoTruss structures subject to uniaxial compression.” In Proc., 72nd Int. Astronautical Congress. Paris: International Astronautical Federation.
Rackliffe, M. E. 2002. “Development of ultra-lightweight IsoTruss™ grid structures.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
Rackliffe, M. E., D. W. Jensen, and W. K. Lucas. 2006. “Local and global buckling of ultra-lightweight IsoTruss structures.” Compos. Sci. Technol. 66 (2): 283–288. https://doi.org/10.1016/j.compscitech.2005.04.038.
Reif, U. 2020. “AutoDiff_R2016b.” In MATLAB central file exchange. Natick, MA: MathWorks.
Sayad, K. 2010. “Optimization for minimum mass of composite grid stiffened cylindrical shells under axial compressive load based on analytical and graphical methods.” In Proc., 2nd Int. Conf. on Composites: Characterization, Fabrication and Application. Tehran, Iran: Iran Univ. of Science and Technology.
Song, L. 2011. “NGPM: A non-dominated sorting genetic algorithm II (NSGA-II) program in MATLAB.” Accessed August 14, 2021. https://usermanual.wiki/Pdf/NGPM20manual20v14.1073441263/html.
Srivastava, I., T. K. Dey, A. Chakrabarti, and P. Bhargava. 2013. “Structural optimization of FRP web core decks.” J. Compos. Constr. 17 (3): 395–405. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000358.
Sui, Q., H. Fan, and C. Lai. 2015. “Failure analysis of 1D lattice truss composite structure in uniaxial compression.” Compos. Sci. Technol. 118 (Oct): 207–216. https://doi.org/10.1016/j.compscitech.2015.09.003.
Sui, Q., C. Lai, and H. Fan. 2018. “Buckling failure modes of one-dimensional lattice truss composite structures.” Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 232 (13): 2565–2583. https://doi.org/10.1177/0954410017716194.
Thompson, M. D., C. D. Eamon, and M. Rais-Rohani. 2006. “Reliability-based optimization of fiber-reinforced polymer composite bridge deck panels.” J. Struct. Eng. 132 (12): 1898–1906. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:12(1898).
Totaro, G., and Z. Gürdal. 2009. “Optimal design of composite lattice shell structures for aerospace applications.” Aerosp. Sci. Technol. 13 (4–5): 157–164. https://doi.org/10.1016/j.ast.2008.09.001.
Winkel, L. D. 2001. “Parametric investigation of IsoTruss™ geometry using linear finite element analysis.” M.S. thesis, Dept. of Civil and Environmental Engineering, Brigham Young Univ.
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Published In
Journal of Aerospace Engineering
Volume 35 • Issue 5 • September 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 15, 2021
Accepted: Jan 12, 2022
Published online: May 30, 2022
Published in print: Sep 1, 2022
Discussion open until: Oct 30, 2022
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