Stress-Based topology optimization under the stress relaxation effect

References

• Ahmad, Z., T. Sultan, M. Zoppi, M. Abid, and G. J. Park. 2017. Nonlinear response topology optimization using equivalent static loads-case studies. Engineering Optimization 49 (2):252–68. doi:10.1080/0305215X.2016.1187728.
   Web of Science ®Google Scholar
• Allaire, G., and F. Jouve. 2008. Minimum stress optimal design with the level set method. Engineering Analysis with Boundary Elements 32 (11):909–18. doi:10.1016/j.enganabound.2007.05.007.
   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):1125–30. doi:10.1016/S1631-073X(02)02412-3.
   Web of Science ®Google Scholar
• Amir, O. 2017. Stress-constrained continuum topology optimization: a new approach based on elasto-plasticity. Structural and Multidisciplinary Optimization 55 (5):1797–818. doi:10.1007/s00158-016-1618-8.
   Web of Science ®Google Scholar
• Amstutz, S., and A. A. Novotny. 2010. Topological optimization of structures subject to von Mises stress constraints. Structural and Multidisciplinary Optimization 41 (3):407–20. doi:10.1007/s00158-009-0425-x.
   Web of Science ®Google Scholar
• Bendsøe, M. P. 1989. Optimal shape design as a material distribution problem. Structural Optimization 1 (4):193–202. doi:10.1007/BF01650949.
   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.
   Google Scholar
• Bendsoe, M. P., and O. Sigmund. 2013. Topology optimization: Theory, methods, and applications. Berlin; Heidelberg: Springer Science & Business Media.
   Google Scholar
• Betten, J. 2008. Creep mechanics. Berlin; Heidelberg: Springer Science & Business Media.
   Google Scholar
• Bourdin, B. 2001. Filters in topology optimization. International Journal for Numerical Methods in Engineering 50 (9):2143–58. doi:10.1002/nme.116.
   Web of Science ®Google Scholar
• Bruggi, M. 2008. On an alternative approach to stress constraints relaxation in topology optimization. Structural and Multidisciplinary Optimization 36 (2):125–41. doi:10.1007/s00158-007-0203-6.
   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):1413–30. doi:10.1002/nme.783.
   Web of Science ®Google Scholar
• Buhl, T., C. B. Pedersen, and O. Sigmund. 2000. Stiffness design of geometrically nonlinear structures using topology optimization. Structural and Multidisciplinary Optimization 19 (2):93–104. doi:10.1007/s001580050089.
   Web of Science ®Google Scholar
• Capasso, G., J. Morlier, M. Charlotte, and S. Coniglio. 2020. Stress-based topology optimization of compliant mechanisms using nonlinear mechanics. Mechanics & Industry 21 (3):304– 17. doi:10.1051/meca/2020011.
   Web of Science ®Google Scholar
• Chen, W. J., and S. T. Liu. 2014. Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus. Structural and Multidisciplinary Optimization 50 (2):287–96. doi:10.1007/s00158-014-1049-3.
   Web of Science ®Google Scholar
• Cheng, 22 G., and X. Guo. 1997. ε-relaxed approach in structural topology optimization. Structural Optimization 13 (4):258–66. doi:10.1007/BF01197454.
   Web of Science ®Google Scholar
• Chi, H., D. L. Ramos, A. S. Ramos, Jr, and G. H. Paulino. 2019. On structural topology optimization considering material nonlinearity: Plane strain versus plane stress solutions. Advances in Engineering Software 131:217–31. doi:10.1016/j.advengsoft.2018.08.017.
   Web of Science ®Google Scholar
• Chu, S., L. Gao, M. Xiao, Z. Luo, and H. Li. 2018. Stress‐based multi‐material topology optimization of compliant mechanisms. International Journal for Numerical Methods in Engineering 113 (7):1021–44. doi:10.1002/nme.5697.
   Web of Science ®Google Scholar
• Chu, S., L. Gao, M. Xiao, Z. Luo, H. Li, and X. Gui. 2018. A new method based on adaptive volume constraint and stress penalty for stress-constrained topology optimization. Structural and Multidisciplinary Optimization 57 (3):1163–85. doi:10.1007/s00158-017-1803-4.
   Web of Science ®Google Scholar
• da Silva, G. A., 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. doi:10.1016/j.cma.2020.112972.
   Web of Science ®Google Scholar
• Doghri, I. 2013. Mechanics of deformable solids: Linear, nonlinear, analytical and computational aspects. Berlin; Heidelberg: Springer Science & Business Media.
   Google Scholar
• Eschenauer, H. A., and N. Olhoff. 2001. Topology optimization of continuum structures: A review. Applied Mechanics Reviews 54 (4):331–90. doi:10.1115/1.1388075.
   Google Scholar
• Guo, X., G. Cheng, and K. Yamazaki. 2001. A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints. Structural and Multidisciplinary Optimization 22 (5):364–73. doi:10.1007/s00158-001-0156-0.
   Web of Science ®Google Scholar
• Guo, X., W. S. Zhang, M. Y. Wang, and P. Wei. 2011. Stress-related topology optimization via level set approach. Computer Methods in Applied Mechanics and Engineering 200 (47-48):3439–52. doi:10.1016/j.cma.2011.08.016.
   Web of Science ®Google Scholar
• Hassani, B., and E. Hinton. 1998a. A review of homogenization and topology optimization II - analytical and numerical solution of homogenization equations. Computers & Structures 69 (6):719–38. doi:10.1016/S0045-7949(98)00132-1.
   Web of Science ®Google Scholar
• Hassani, B., and E. Hinton. 1998b. A review of homogenization and topology optimization I—homogenization theory for media with periodic structure. Computers & Structures 69 (6):707–17. doi:10.1016/S0045-7949(98)00131-X.
   Web of Science ®Google Scholar
• Hayhurst, D. R. 1972. Creep rupture under multi-axial states of stress. Journal of the Mechanics and Physics of Solids 20 (6):381–2. doi:10.1016/0022-5096(72)90015-4.
   Web of Science ®Google Scholar
• Hetnarski, R. B., M. Reza Eslami, and G. M. L. Gladwell. 2009. Thermal Stresses: advanced Theory and Applications. Vol. 41. Netherlands: Springer.
   Google Scholar
• Holmberg, E., B. Torstenfelt, and A. Klarbring. 2013. Stress constrained topology optimization. Structural and Multidisciplinary Optimization 48 (1):33–47. doi:10.1007/s00158-012-0880-7.
   Web of Science ®Google Scholar
• James, K. A., and H. Waisman. 2015. Topology optimization of viscoelastic structures using a time-dependent adjoint method. Computer Methods in Applied Mechanics and Engineering 285:166–87. doi:10.1016/j.cma.2014.11.012.
   Web of Science ®Google Scholar
• Jung, D., and H. C. Gea. 2004. Topology optimization of nonlinear structures. Finite Elements in Analysis and Design 40 (11):1417–27. doi:10.1016/j.finel.2003.08.011.
   Web of Science ®Google Scholar
• Kawamoto, A. 2009. Stabilization of geometrically nonlinear topology optimization by the Levenberg-Marquardt method. Structural and Multidisciplinary Optimization 37 (4):429–33. doi:10.1007/s00158-008-0236-5.
   Web of Science ®Google Scholar
• Kirsch, U. 1989. Optimal topologies of truss structures. Computer Methods in Applied Mechanics and Engineering 72 (1):15–28. doi:10.1016/0045-7825(89)90119-9.
   Web of Science ®Google Scholar
• Kirsch, U. 1990. On singular topologies in optimum structural design. Structural Optimization 2 (3):133–42. doi:10.1007/BF01836562.
   Web of Science ®Google Scholar
• Kook, J. 2019. Evolutionary topology optimization for acoustic-structure interaction problems using a mixed u/p formulation. Mechanics Based Design of Structures and Machines 47 (3):356–74. doi:10.1080/15397734.2018.1557527.
   Web of Science ®Google Scholar
• Kumar, T., and K. Suresh. 2021. Direct Lagrange multiplier updates in topology optimization revisited. Structural and Multidisciplinary Optimization 63 (3):1563–16. doi:10.1007/s00158-020-02740-y.
   Web of Science ®Google Scholar
• Le, C., J. Norato, T. Bruns, C. Ha, and D. Tortorelli. 2010. Stress-based topology optimization for continua. Structural and Multidisciplinary Optimization 41 (4):605–20. doi:10.1007/s00158-009-0440-y.
   Web of Science ®Google Scholar
• Lee, H.-A., and G.-J. Park. 2012. Topology optimization for structures with nonlinear behavior using the equivalent static loads method. Journal of Mechanical Design 134 (3):031004. doi:10.1115/1.4005600.
   Web of Science ®Google Scholar
• Luo, Q. T., and L. Y. Tong. 2016. An algorithm for eradicating the effects of void elements on structural topology optimization for nonlinear compliance. Structural and Multidisciplinary Optimization 53 (4):695–714. doi:10.1007/s00158-015-1325-x.
   Web of Science ®Google Scholar
• Maute, K., O. Sigmund. 2013. Topology optimization approaches: a comparative review. Structural, and Multidisciplinary Optimization 6: 1031–55.
   Google Scholar
• Michaleris, P., D. A. Tortorelli, and C. A. Vidal. 1994. Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity. International Journal for Numerical Methods in Engineering 37 (14):2471–99. doi:10.1002/nme.1620371408.
   Web of Science ®Google Scholar
• Moon, S. J., and G. H. Yoon. 2013. A newly developed qp-relaxation method for element connectivity parameterization to achieve stress-based topology optimization for geometrically nonlinear structures. Computer Methods in Applied Mechanics and Engineering 265:226–41. doi:10.1016/j.cma.2013.07.001.
   Web of Science ®Google Scholar
• Nakshatrala, P. B., D. A. Tortorelli, and K. B. Nakshatrala. 2013. Nonlinear structural design using multiscale topology optimization. Part I: Static formulation. Computer Methods in Applied Mechanics and Engineering 261-262:167–76. doi:10.1016/j.cma.2012.12.018.
   Web of Science ®Google Scholar
• Penny, R. K., and D. L. Marriott. 2012. Design for creep. Netherlands: Springer Science & Business Media.
   Google Scholar
• Rozvany, G. I. N. 2001. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Structural and Multidisciplinary Optimization 21 (2):90–108. doi:10.1007/s001580050174.
   Web of Science ®Google Scholar
• Rozvany, G. I., M. Zhou, and T. Birker. 1992. Generalized shape optimization without homogenization. Structural Optimization 4 (3-4):250–2. doi:10.1007/BF01742754.
   Web of Science ®Google Scholar
• Sigmund, O. 1997. On the design of compliant mechanisms using topology optimization. Mechanics of Structures and Machines 25 (4):493–524. doi:10.1080/08905459708945415.
   Web of Science ®Google Scholar
• Sigmund, O. 2007. Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33 (4-5):401–24. doi:10.1007/s00158-006-0087-x.
   Web of Science ®Google Scholar
• Suresh, K., and M. Takalloozadeh. 2013. Stress-constrained topology optimization: A topological level-set approach. Structural and Multidisciplinary Optimization 48 (2):295–309. doi:10.1007/s00158-013-0899-4.
   Web of Science ®Google Scholar
• Swan, C. C., and I. Kosaka. 1997. Voigt-Reuss topology optimization for structures with linear elastic material behaviours. International Journal for Numerical Methods in Engineering 40 (16):3033–57. doi:10.1002/(SICI)1097-0207(19970830)40:16<3033::AID-NME196>3.0.CO;2-Z.
   Web of Science ®Google Scholar
• Takalloozadeh, M., and G. H. Yoon. 2019. Topology Optimization Under Stress Relaxation Effect Using Internal Element Connectivity Parameterization. Journal of Computational and Nonlinear Dynamics 14 (2):021006. doi:10.1115/1.4041578.
   Web of Science ®Google Scholar
• Tegart, W. M., and O. D. Sherby. 1958. Activation energies for high temperature creep of polycrstalline zinc. Philosophical Magazine 3 (35):1287–96. doi:10.1080/14786435808233311.
   Web of Science ®Google Scholar
• van Dijk, N. P., K. Maute, M. Langelaar, and F. van Keulen. 2013. Level-set methods for structural topology optimization: A review. Structural and Multidisciplinary Optimization 48 (3):437–72. doi:10.1007/s00158-013-0912-y.
   Web of Science ®Google Scholar
• Wang, S., E. d Sturler, and G. H. Paulino. 2007. Large‐scale topology optimization using preconditioned Krylov subspace methods with recycling. International Journal for Numerical Methods in Engineering 69 (12):2441–68. doi:10.1002/nme.1798.
   Web of Science ®Google Scholar
• Weertman, J. 1955. Theory of steady‐state creep based on dislocation climb. Journal of Applied Physics 26 (10):1213–7. doi:10.1063/1.1721875.
   Web of Science ®Google Scholar
• Xia, L., and P. Breitkopf. 2014. A reduced multiscale model for nonlinear structural topology optimization. Computer Methods in Applied Mechanics and Engineering 280:117–34. doi:10.1016/j.cma.2014.07.024.
   Web of Science ®Google Scholar
• Xia, L., and P. Breitkopf. 2016. Recent advances on topology optimization of multiscale nonlinear structures. Archives of Computational Methods in Engineering 2 (24):227–49.
   Google Scholar
• Xu, B., Y. Han, and L. Zhao. 2020. Bi-directional evolutionary topology optimization of geometrically nonlinear continuum structures with stress constraints. Applied Mathematical Modelling 80:771–91. doi:10.1016/j.apm.2019.12.009.
   Web of Science ®Google Scholar
• Yang, R. J., and C. J. Chen. 1996. Stress-based topology optimization. Structural Optimization 12 (2-3):98–105. doi:10.1007/BF01196941.
   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. doi:10.1016/j.ijsolstr.2004.09.005.
   Web of Science ®Google Scholar
• Yoon, G. H., and Y. Y. Kim. 2007. Topology optimization of material‐nonlinear continuum structures by the element connectivity parameterization. International Journal for Numerical Methods in Engineering 69 (10):2196–218. doi:10.1002/nme.1843.
   Web of Science ®Google Scholar
• Zhang, X., A. S. Ramos, and G. H. Paulino. 2017. Material nonlinear topology optimization using the ground structure method with a discrete filtering scheme. Structural and Multidisciplinary Optimization 55 (6):2045–72. doi:10.1007/s00158-016-1627-7.
   Web of Science ®Google Scholar