journal article·2024-09-11Open access

Layout Optimisation of Frame Structures with Multiple Constraints and Geometric Complexity Control

Yongpeng He, Paul Shepherd, Jie Wang

Applied Sciences· Volume 14· Issue 18

Abstract

A comprehensive framework for the layout optimisation of rigid-jointed frame structures is proposed, addressing multiple mechanical constraints while effectively managing geometric complexity. The constraints considered include displacement, stress, and both local and global stability. Geometric complexity is controlled by minimising low-stiffness elements and reducing the number of elements in the resulting layouts. Numerical examples demonstrate the effectiveness of the proposed method, showcasing its ability to generate optimal structural layouts with desirable mechanical performance and varying levels of geometric complexity in member connectivity. This innovative optimisation framework offers significant advantages over conventional layout optimisation approaches by ensuring both the optimality and manufacturability of frame structures, thereby facilitating their practical application.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Topology Optimization in Engineering · Innovations in Concrete and Construction Materials · BIM and Construction Integration

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Architecture and Civil Engineering, University of Bath, Claverton Down, Bath BA2 7AY, UK

Funding

Chinese Scholarship Council (CSC) through the CSC-University of Bath Joint Scholarship

References (78)

Show source-provided references
1. LVIII. The limits of economy of material in frame-structures10.1080/14786440409463229 ↗
2. Automatic design of optimal structures
3. GRAND3—Ground structure based topology optimization for arbitrary 3D domains using MATLAB10.1007/s00158-015-1284-2 ↗
4. Including global stability in truss layout optimization for the conceptual design of large-scale applications10.1007/s00158-017-1805-2 ↗
5. Layout optimization of long-span structures subject to self-weight and multiple load-cases10.1007/s00158-022-03242-9 ↗
6. Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization10.1016/j.cma.2020.113157 ↗
7. Uniform thickness control without pre-specifying the length scale target under the level set topology optimization framework10.1016/j.advengsoft.2017.09.013 ↗
8. Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach10.1016/j.cma.2016.08.022 ↗
9. Automatic reconstruction of beam structures from 3D topology optimization results10.1016/j.compstruc.2017.04.018 ↗
10. Image-based truss recognition for density-based topology optimization approach10.1007/s00158-018-2028-x ↗
11. Topologically robust CAD model generation for structural optimisation10.1016/j.cma.2020.113102 ↗
12. Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework10.1007/s00158-014-1157-0 ↗
13. Constructability-based design approach for steel structures: From truss beams to real-world inspired industrial buildings10.1016/j.autcon.2024.105630 ↗
14. Optimization of structures under buckling constraints using frame elements10.1080/0305215X.2018.1444162 ↗
15. Topology optimization of frame structures with stress and stability constraints10.1007/s00158-022-03361-3 ↗
16. On singular topologies in optimum structural design10.1007/BF01836562 ↗
17. Study on topoogy optimization with stress constraints10.1080/03052159208941276 ↗
18. On design-dependent constraints and singular topologies10.1007/s001580050181 ↗
19. ϵ-relaxed approach in structural topology optimization10.1007/BF01197454 ↗
20. A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints10.1007/s00158-001-0156-0 ↗
21. Difficulties in truss topology optimization with stress, local buckling and system stability constraints10.1007/BF01197036 ↗
22. Systematic Control Design by Optimizing a Vector Performance Index10.1016/S1474-6670(17)65584-8 ↗
23. Stress-based topology optimization10.1007/BF01196941 ↗
24. Topology optimization of continuum structures with local and global stress constraints10.1007/s00158-008-0336-2 ↗
25. An enhanced aggregation method for topology optimization with local stress constraints10.1016/j.cma.2012.10.019 ↗
26. Stress-based topology optimization for continua10.1007/s00158-009-0440-y ↗
27. A unified aggregation and relaxation approach for stress-constrained topology optimization10.1007/s00158-016-1524-0 ↗
28. Local stability of trusses in the context of topology optimization Part I: Exact modelling
29. Local stability of trusses in the context of topology optimazation. Part II: A numerical approach
30. Optimum design of truss topology under buckling constraints10.1007/s00158-004-0511-z ↗
31. Resolving issues with member buckling in truss topology optimization using a mixed variable approach10.1007/s00158-014-1095-x ↗
32. Topology optimization of trusses incorporating practical local buckling stability considerations10.1016/j.istruc.2022.05.109 ↗
33. Topology optimization of truss structures considering local buckling stability10.1016/j.compstruc.2024.107273 ↗
34. Modeling of global and local stability in optimization of truss-like structures using frame elements10.1007/s00158-014-1203-y ↗
35. Cook, R.D., Malkus, D.S., Plesha, M.E., and Witt, R.J. (2007). Concepts and Applications of Finite Element Analysis, John Wiley & Sons.
36. Generalized topology design of structures with a buckling load criterion10.1007/BF01743533 ↗
37. Bendsøe, M.P., and Sigmund, O. (2004). Topology Optimization, Theory, Method and Applications, Springer.10.1007/978-3-662-05086-6 ↗
38. Topology optimization of continuum structures under buckling constraints10.1016/j.compstruc.2015.05.020 ↗
39. Topology optimization of geometrically nonlinear trusses with spurious eigenmodes control10.1016/j.engstruct.2016.11.001 ↗
40. Topology optimization of steel frame structures with constraints on overall and individual member instabilities10.1016/j.finel.2017.11.003 ↗
41. Finite strain topology optimization with nonlinear stability constraints10.1016/j.cma.2023.116119 ↗
42. Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps10.1007/s00158-007-0101-y ↗
43. Necessary conditions for optimal design of structures with a nonsmooth eigenvalue based criterion10.1007/BF01742645 ↗
44. Multiple eigenvalues in structural optimization problems10.1007/BF01742705 ↗
45. Smooth convex approximation to the maximum eigenvalue function10.1007/s10898-004-8271-2 ↗
46. Structural optimization considering smallest magnitude eigenvalues: A smooth approximation10.1007/s40430-016-0583-x ↗
47. Topology optimization with linearized buckling criteria in 250 lines of Matlab10.1007/s00158-021-02854-x ↗
48. A maximum filter for the ground structure method: An optimization tool to harness multiple structural designs10.1016/j.engstruct.2017.07.064 ↗
49. Joints in optimum frameworks10.1016/0020-7683(75)90044-X ↗
50. Rationalization of trusses generated via layout optimization10.1007/s00158-015-1260-x ↗
51. Incorporating fabrication cost into topology optimization of discrete structures and lattices10.1007/s00158-014-1133-8 ↗
52. Design complexity control in truss optimization10.1007/s00158-016-1403-8 ↗
53. Topology optimization of trusses with stress and local constraints on nodal stability and member intersection10.1007/s00158-004-0480-2 ↗
54. Alternating direction method of multipliers for truss topology optimization with limited number of nodes: A cardinality-constrained second-order cone programming approach10.1007/s11081-017-9372-3 ↗
55. Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints10.1007/s00158-019-02449-7 ↗
56. Adaptive solution of truss layout optimization problems with global stability constraints10.1007/s00158-019-02312-9 ↗
57. Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling10.1007/s00158-003-0294-7 ↗
58. Discrete topology optimization in augmented space: Integrated element removal for minimum size and mesh sensitivity control10.1007/s00158-020-02630-3 ↗
59. Difficulties in truss topology optimization with stress and local buckling constraints10.1007/BF01376857 ↗
60. Reliability based bi-directional evolutionary topology optimization of geometric and material nonlinear analysis with imperfections10.1016/j.compstruc.2023.107120 ↗
61. Advanced elasto-plastic topology optimization of steel beams under elevated temperatures10.1016/j.advengsoft.2024.103596 ↗
62. Design sensitivity analysis and optimization of nonlinear structural response using incremental procedure10.2514/3.9752 ↗
63. Simultaneous analysis and design optimization of nonlinear response10.1007/BF01200177 ↗
64. A unified framework for nonlinear path-dependent sensitivity analysis in topology optimization10.1002/nme.5794 ↗
65. A 99 line topology optimization code written in matlab10.1007/s001580050176 ↗
66. On an alternative approach to stress constraints relaxation in topology optimization10.1007/s00158-007-0203-6 ↗
67. A unified framework for explicit layout/topology optimization of thin-walled structures based on Moving Morphable Components (MMC) method and adaptive ground structure approach10.1016/j.cma.2022.115047 ↗
68. The method of moving asymptotes—A new method for structural optimization10.1002/nme.1620240207 ↗
69. Topology optimization approaches10.1007/s00158-013-0978-6 ↗
70. Benchmarking optimization solvers for structural topology optimization10.1007/s00158-015-1250-z ↗
71. Truss optimization applying finite element limit analysis including global and local stability10.1007/s00158-019-02468-4 ↗
72. Efficient buckling constrained topology optimization using reduced order modeling10.1007/s00158-023-03616-7 ↗
73. Layout optimization of large-scale pin-jointed frames10.1108/02644400310503017 ↗
74. On symmetry and non-uniqueness in exact topology optimization10.1007/s00158-010-0564-0 ↗
75. On projection methods, convergence and robust formulations in topology optimization10.1007/s00158-010-0602-y ↗
76. Revisiting topology optimization with buckling constraints10.1007/s00158-019-02253-3 ↗
77. Truss geometry and topology optimization with global stability constraints10.1007/s00158-020-02634-z ↗
78. GRAND —Ground structure based topology optimization for arbitrary 2D domains using MATLAB10.1007/s00158-014-1085-z ↗