Buckling load optimization for 2D continuum models, with alternative formulation for buckling load estimation

Pedersen, Niels Leergaard; Pedersen, Pauli

doi:10.1007/s00158-018-2030-3

Cited by 12 publications

(5 citation statements)

References 9 publications

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“…On the other hand, advances have been made in the last few years on the non-linear buckling of topologically optimized continua [446,447]. Such remarkable achievements employ non-incremental analyses and recursive design.…”

Section: Buckling and Local Instability Phenomenamentioning

confidence: 99%

Topology Optimisation in Structural Steel Design for Additive Manufacturing

2021

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Topology Optimisation is a broad concept deemed to encapsulate different processes for computationally determining structural materials optimal layouts. Among such techniques, Discrete Optimisation has a consistent record in Civil and Structural Engineering. In contrast, the Optimisation of Continua recently emerged as a critical asset for fostering the employment of Additive Manufacturing, as one can observe in several other industrial fields. With the purpose of filling the need for a systematic review both on the Topology Optimisation recent applications in structural steel design and on its emerging advances that can be brought from other industrial fields, this article critically analyses scientific publications from the year 2015 to 2020. Over six hundred documents, including Research, Review and Conference articles, added to Research Projects and Patents, attained from different sources were found significant after eligibility verifications and therefore, herein depicted. The discussion focused on Topology Optimisation recent approaches, methods, and fields of application and deepened the analysis of structural steel design and design for Additive Manufacturing. Significant findings can be found in summarising the state-of-the-art in profuse tables, identifying the recent developments and research trends, as well as discussing the path for disseminating Topology Optimisation in steel construction.

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Section: Buckling and Local Instability Phenomenamentioning

confidence: 99%

Topology Optimisation in Structural Steel Design for Additive Manufacturing

2021

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“…Despite the fact that non-linear analysis provides an accurate description of the buckling phenomenon, the high computational cost hinders its widespread utilization in topology optimization. To improve the computational efficiency of nonlinear analysis, Pedersen and Pedersen (2018) suggested the use of non-incremental analysis and proposed a simple sensitivity analysis along with recursive redesign. In contrast, linear buckling analysis has been commonly employed in topology optimization due to its ease of implementation and acceptable computational cost (Ferrari and Sigmund 2019).…”

Section: Introductionmentioning

confidence: 99%

Bi-directional evolutionary structural optimization with buckling constraints

Lin

Xie

2023

Struct Multidisc Optim

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Buckling is a critical phenomenon in structural members under compression, which could cause catastrophic failure of a structure. To increase the buckling resistance in structural design, a novel topology optimization approach based on the bi-directional evolutionary structural optimization (BESO) method is proposed in this study with the consideration of buckling constraints. The BESO method benefits from using only two discrete statuses (solid and void) for design variables, thereby alleviating numerical issues associated with pseudo buckling modes. The Kreisselmeier-Steinhauser aggregation function is introduced to aggregate multiple buckling constraints into a differentiable one. An augmented Lagrangian multiplier is developed to integrate buckling constraints into the objective function to ensure computational stability. Besides, a modified design variable update scheme is proposed to control the evolutionary rate after the target volume fraction is reached. Four topology optimization design examples are investigated to demonstrate the effectiveness of the buckling-constrained BESO method. The numerical results show that the developed optimization algorithm with buckling constraints can significantly improve structural stability with a slight increase in compliance.

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“…When pre‐buckling displacements are small, and a structural length scale is defined, LBA proves very effective. Outside such assumptions, its limitations become apparent, and the accurate evaluation of structural stability requires explicit modeling of the geometric and material nonlinearities 2,3 . This results in a nonlinear buckling analysis, which, despite its accuracy, is much more time‐consuming 4 and introduces other complications when applied to TO 5,6 .…”

Section: Introductionmentioning

confidence: 99%

A strategy for avoiding spurious localized buckling modes in topology optimization

Ferrari

Sigmund

2023

Numerical Meth Engineering

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SummaryWe introduce a strategy preventing the occurrence of spurious modes in the spectrum computed by linearized buckling analysis in the context of topology optimization. Spurious buckling modes may appear in low density regions, a well‐known and largely discussed phenomenon. However, localized modes may also appear in solid areas, where stress concentrations occur. This second phenomenon, which is due to the inherent limitations of the linearized buckling analysis when used for complex stress states, is hardly addressed in the topology optimization literature. The remedy we propose makes use of elementary operations in the topology optimization framework: filtering and erosion, but now applied to the stress field. We show how this simple strategy helps mitigating the occurrence of spurious modes, in turn regularizing the optimization process towards high performance designs, which are then verified by nonlinear analysis.

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Buckling load optimization for 2D continuum models, with alternative formulation for buckling load estimation

Cited by 12 publications

References 9 publications

Topology Optimisation in Structural Steel Design for Additive Manufacturing

Topology Optimisation in Structural Steel Design for Additive Manufacturing

Bi-directional evolutionary structural optimization with buckling constraints

A strategy for avoiding spurious localized buckling modes in topology optimization

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