A fidelity equivalence computation method for topology optimization of geometrically nonlinear structures

References

• Alfattani, R., and C. Lusk. 2018. “A Lamina–Emergent Frustum Using a Bistable Collapsible Compliant Mechanism.” Journal of Mechanical Design 140 (12): 125001.
   Web of Science ®Google Scholar
• Allaire G., F. Jouve, and A. M. Toader. 2002. “A Level-Set Method for Shape Optimization.” Comptes Rendus Mathematique 334 (12): 1125–1130.
   Web of Science ®Google Scholar
• Beghini, L. L., A. Beghini, N. Katz, W. F. Baker, and G. H. Paulino. 2014. “Connecting Architecture and Engineering Through Structural Topology Optimization.” Engineering Structures 59: 716–726.
   Web of Science ®Google Scholar
• Bendsoe, M. P., J. M. Guedes, S. Plaxton, and J. E. Taylor. 1995. “Optimization of Structure and Material Properties for Solids Composed of Softening Material.” International Journal of Solids and Structures 33: 1799–1813.
   Web of Science ®Google Scholar
• Bendsoe, M. P., and N. Kikuchi. 1988. “Generating Optimal Topologies in Structural Design Using a Homogenization Method.” Computer Methods in Applied Mechanics and Engineering 71 (2): 197–224.
   Web of Science ®Google Scholar
• Boroomand, B., and A. R. Barekatein. 2009. “On Topology Optimization of Linear and Nonlinear Plate Problems.” Structural and Multidisciplinary Optimization 39 (1): 17–27.
   Web of Science ®Google Scholar
• Bourdin, B. 2001. “Filters in Topology Optimization.” International Journal for Numerical Methods in Engineering 50 (9): 2143–2158.
   Web of Science ®Google Scholar
• Bruns, T. E., and D. A. Tortorelli. 2003. “An Element Removal and Reintroduction Strategy for the Topology Optimization of Structures and Compliant Mechanisms.” International Journal for Numerical Methods in Engineering 57 (10): 1413–1430.
   Web of Science ®Google Scholar
• Buhl, T., C. B. W. Pedersen, and O. Sigmund. 2000. “Stiffness Design of Geometrically Nonlinear Structures Using Topology Optimization.” Structural and Multidisciplinary Optimization 19: 93–104.
   Web of Science ®Google Scholar
• Chang, D. H., K. S. Yoo, J. Y. Park, and S. Y. Han. 2012. “Optimum Design for Nonlinear Problems Using Modified Ant Colony Optimization.” International Conference on Software and Computer Application, Singapore, 41–45.
   Google Scholar
• Chen, Z., K. Long, X. Wang, J. Liu, and N. Saeed. 2021. “A New Geometrically Nonlinear Topology Optimization Formulation for Controlling Maximum Displacement.” Engineering Optimization 53 (8): 1283–1297.
   Web of Science ®Google Scholar
• Chen, Q., X. Zhang, and B. Zhu. 2019. “A 213-Line Topology Optimization Code for Geometrically Nonlinear Structures.” Structural and Multidisciplinary Optimization 59 (5): 1863–1879.
   Web of Science ®Google Scholar
• Eschenauer, H. A., and N. Olhoff. 2001. “Topology Optimization of Continuum Structures: A Review.” Applied Mechanics Reviews 54 (4): 331–389.
   Google Scholar
• Gano, S. E., J. E. Renaud, J. D. Martin, and T. W. Simpson. 2006. “Update Strategies for Kriging Models Used in Variable Fidelity Optimization.” Structural and Multidisciplinary Optimization 32: 287–298.
   Web of Science ®Google Scholar
• Garcez, G. L., R. Picelli, and R. Pavanello. 2022. “Bi-directional Evolutionary Topology Optimization Based on Stress Minimization Under Design-Dependent Surface Loads.” Engineering Optimization 1–21. doi:10.1080/0305215X.2022.2065481.
   Web of Science ®Google Scholar
• Gea, H. C., and J. Luo. 2001. “Topology Optimization of Structures with Geometrical Nonlinearities.” Computers and Structures 79: 1977–1985.
   Google Scholar
• Guo, X., W. S. Zhang, and W. L. Zhong. 2014. “Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework.” Journal of Applied Mechanics 81 (8): 081009.
   Web of Science ®Google Scholar
• Han, Y., B. Xu, and Y. Liu. 2021. “An Efficient 137–Line MATLAB Code for Geometrically Nonlinear Topology Optimization Using Bi-directional Evolutionary Structural Optimization Method.” Structural and Multidisciplinary Optimization 63: 2751–2588.
   Web of Science ®Google Scholar
• Han, Y., B. Xu, Q. Wang, Y. Liu, and Z. Duan. 2021. “Topology Optimization of Material Nonlinear Continuum Structures Under Stress Constraints.” Computer Methods in Applied Mechanics and Engineering 378: 113731.
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2008. “Topology Optimization of Nonlinear Structures Under Displacement Loading.” Engineering Structures 30 (7): 2057–2068.
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2010. “A Further Review of ESO Type Methods for Topology Optimization.” Structural and Multidisciplinary Optimization 41: 671–683.
   Web of Science ®Google Scholar
• Jung, H. S., and S. Cho. 2004. “Reliability-Based Topology Optimization of Geometrically Nonlinear Structures with Loading and Material Uncertainties.” Finite Elements in Analysis and Design 41 (3): 311–331.
   Web of Science ®Google Scholar
• Kambampati, S., H. Chung, and H. A. Kim. 2021. “A Discrete Adjoint Based Level Set Topology Optimization Method for Stress Constraints.” Computer Methods in Applied Mechanics and Engineering 377 (15): 113563.
   Google Scholar
• Kanakasabai, P., and A. K. Dhingra. 2016. “An Efficient Approach for Reliability-Based Topology Optimization.” Engineering Optimization 48 (1): 1–15.
   Web of Science ®Google Scholar
• Kang, Z., and Y. Luo. 2009. “Non-probabilistic Reliability-Based Topology Optimization of Geometrically Nonlinear Structures Using Convex Models.” Computer Methods in Applied Mechanics and Engineering 198: 3228–3238.
   Web of Science ®Google Scholar
• Kawamoto, A. 2009. “Stabilization of Geometrically Nonlinear Topology Optimization by the Levenberg–Marquardt Method.” Structural and Multidisciplinary Optimization 37: 429–433.
   Web of Science ®Google Scholar
• Kim, Y., and G. J. Park. 2010. “Nonlinear Dynamic Response Structural Optimization Using Equivalent Static Loads.” Computer Methods in Applied Mechanics and Engineering 199: 660–676.
   Web of Science ®Google Scholar
• Liang, X., and J. B. Du. 2019. “Concurrent Multi-scale and Multi-material Topological Optimization of Vibro-acoustic Structures.” Computer Methods in Applied Mechanics and Engineering 349 (1): 117–148.
   Google Scholar
• Liu, C., X. Hu, and S. Zhu. 2022. “A Two-Grid Binary Level Set Method for Structural Topology Optimization.” Engineering Optimization 1–18. doi:10.1080/0305215X.2022.2067991.
   Web of Science ®Google Scholar
• Liu, K., and A. Tovar. 2014. “An Efficient 3D Topology Optimization Code Written in Matlab.” Structural and Multidisciplinary Optimization 50 (6): 1175–1196.
   Web of Science ®Google Scholar
• Luo, Y., M. Y. Wang, and Z. Kang. 2015. “Topology Optimization of Geometrically Nonlinear Structures Based on an Additive Hyperelasticity Technique.” Computer Methods in Applied Mechanics and Engineering 286 (1): 422–441.
   Web of Science ®Google Scholar
• Maute, K., S. Schwarz, and E. Ramm. 1998. “Adaptive Topology Optimization of Elastoplastic Structures.” Structural and Multidisciplinary Optimization 15: 81–91.
   Web of Science ®Google Scholar
• Meng, Z., Y. S. Pang, Y. X. Pu, and X. Wang. 2020. “New Hybrid Reliability-Based Topology Optimization Method Combining Fuzzy and Probabilistic Models for Handling Epistemic and Aleatory Uncertainties.” Computer Methods in Applied Mechanics and Engineering 363 (1): 112886.
   Google Scholar
• Meng, Z., Y. Wu, X. Wang, S. H. Ren, and B. Yu. 2021. “Robust Topology Optimization Methodology for Continuum Structures Under Probabilistic and Fuzzy Uncertainties.” International Journal for Numerical Methods in Engineering 122: 2095–2111.
   Web of Science ®Google Scholar
• Nabaki, K., J. Shen, and X. Huang. 2019. “Stress Minimization of Structures Based on Bidirectional Evolutionary Procedure.” Journal of Structural Engineering 145 (2): 04018256.
   Web of Science ®Google Scholar
• Ortigosa, R., D. Ruiz, A. J. Gil, A. Donoso, and J. C. Bellido. 2020. “A Stabilisation Approach for Topology Optimisation of Hyperelastic Structures with the SIMP Method.” Computer Methods in Applied Mechanics and Engineering 364: 112924.
   Web of Science ®Google Scholar
• Park, G. J. 2011. “Technical Overview of the Equivalent Static Loads Method for Non-linear Static Response Structural Optimization.” Structural and Multidisciplinary Optimization 43: 319–337.
   Web of Science ®Google Scholar
• Rozvany, G. I., M. Zhou, and T. Birker. 1992. “Generalized Shape Optimization Without Homogenization.” Structural Optimization 4: 250–252.
   Web of Science ®Google Scholar
• Ryu, Y. S., M. Haririan, C. C. Wu, and J. S. Arora. 1985. “Structural Design Sensitivity Analysis of Nonlinear Response.” Computers and Structures 21: 245–255.
   Google Scholar
• Sethian, J. A., and A. Wiegmann. 2000. “Structural Boundary Design via Level set and Immersed Interface Methods.” Journal of Computational Physics 163: 489–528.
   Web of Science ®Google Scholar
• Shin, M. K., K. J. Park, and G. J. Park. 2007. “Optimization of Structures with Nonlinear Behavior Using Equivalent Loads.” Computer Methods in Applied Mechanics and Engineering 196: 1154–1167.
   Web of Science ®Google Scholar
• Sigmund, O. 2007. “Morphology-Based Black and White Filters for Topology Optimization.” Structural and Multidisciplinary Optimization 33: 401–424.
   Web of Science ®Google Scholar
• Sigmund, O., and K. Maute. 2013. “Topology Optimization Approaches.” Structural and Multidisciplinary Optimization 48: 1031–1055.
   Web of Science ®Google Scholar
• Silva, G., A. T. Beck, and O. Sigmund. 2020. “Topology Optimization of Compliant Mechanisms Considering Stress Constraints, Manufacturing Uncertainty and Geometric Nonlinearity.” Computer Methods in Applied Mechanics and Engineering 365: 112972.
   Web of Science ®Google Scholar
• Soto, C. A. 2001. “Optimal Structural Topology Design for Energy Absorption: A Heuristic Approach.” International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 80234: 1087–1092.
   Google Scholar
• Svanberg, K. 1987. “The Method of Moving Asymptotes—A New Method for Structural Optimization.” International Journal for Numerical Methods in Engineering 24: 359–373.
   Web of Science ®Google Scholar
• Truong, Q. D., N. D. K. Tran, and D. A. Wang. 2017. “Design and Characterization of a Mouse Trap Based on a Bistable Mechanism.” Sensors and Actuators A: Physical 267: 360–375.
   Web of Science ®Google Scholar
• Vantyghem, G., V. Boel, W. D. E. Corte, and M. Steeman. 2019. “Compliance, Stress-Based and Multi-physics Topology Optimization for 3D-Printed Concrete Structures.” RILEM International Conference on Concrete and Digital Fabrication 19: 323–332.
   Google Scholar
• Wang, M. Y., X. Wang, and D. Guo. 2003. “A Level Set Method for Structural Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 192: 227–246.
   Web of Science ®Google Scholar
• Wen, G., J. Liu, Z. Chen, W. Peng, K. Long, H. Wang, J. Rong, and Y. Xie. 2022. “A Survey of Nonlinear Continuum Topology Optimization Methods.” Chinese Journal of Theoretical and Applied Mechanics 54: 1–17.
   Google Scholar
• Xia, L., L. Zhang, Q. Xia, and T. Shi. 2018. “Stress-Based Topology Optimization Using Bi-directional Evolutionary Structural Optimization Method.” Computer Methods in Applied Mechanics and Engineering 333 (1): 356–370.
   Google Scholar
• Yan, J., Q. Xu, Z. Fan, D. Geng, B. Niu, and Z. Duan. 2022. “A Study on Topology Optimization of Heat Dissipation Structures with Different Objective Functions Based on an Explicit Moving Morphable Components Method.” Engineering Optimization 1–16. doi:10.1080/0305215X.2022.2086236.
   Web of Science ®Google Scholar
• Yoon, G. H., and Y. Y. Kim. 2005. “Element Connectivity Parameterization for Topology Optimization of Geometrically Nonlinear Structures.” International Journal of Solids and Structures 42 (7): 1983–2009.
   Web of Science ®Google Scholar
• Zhang, W. S., J. Yuan, J. Zhang, and X. Guo. 2016. “A new Topology Optimization Approach Based on Moving Morphable Components (MMC) and the Ersatz Material Model.” Structural and Multidisciplinary Optimization 53: 1243–1260.
   Web of Science ®Google Scholar
• Zhong, Y., W. Yu, H. Feng, H. Wang, and R. Wang. 2022. “Research on an Effective Bionic Topology Optimization Method for Engineering Applications.” Engineering Optimization. doi:10.1080/0305215X.2022.2137877.
   Web of Science ®Google Scholar
• Zhu, J., Y. Li, F. Wang, and W. Zhang. 2020. “Shape Preserving Design of Thermo-Elastic Structures Considering Geometrical Nonlinearity.” Structural and Multidisciplinary Optimization 61: 1787–1804.
   Web of Science ®Google Scholar
• Zhu, B. L., R. X. Wang, H. C. Zhang, H. Li, J. W. Liang, X. M. Zhang, H. Li, and S. Nishiwaki. 2022. “An Approach for Geometrically Nonlinear Topology Optimization Using Moving Wide-Bézier Components with Constrained Ends.” Journal of Mechanical Design 144: 011704.
   Web of Science ®Google Scholar
• Zhu, B. L., X. M. Zhang, H. Li, J. W. Liang, R. X. Wang, H. Li, and S. Nishiwaki. 2021. “An 89-Line Code for Geometrically Nonlinear Topology Optimization Written in FreeFEM.” Structural and Multidisciplinary Optimization 63: 1015–1027.
   Web of Science ®Google Scholar
• Zirbel, S. A., K. A. Tolman, B. P. Trease, and L. L. Howell. 2016. “Bistable Mechanisms for Space Applications.” PloS One 11: e0168218.
   PubMed Web of Science ®Google Scholar