A rational H∞‐norm–based approach for the optimal design of seismically excited reinforced concrete frames

Venini, Paolo; Ceresa, Paola

doi:10.1002/eqe.3028

Cited by 8 publications

(5 citation statements)

References 24 publications

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“…1 that also shows loads and constraints. By now standard aspects of topology optimization such as the SIMP idealization to handle intermediate materials, the nonlocal filters that are adopted to avoid checkerboarding, the finite elements that are used to derive the discrete version of the problem, not to mention the numerical scheme that is used to solve the optimization problem may be found in [7] among others and are not explicitly described herein.…”

Section: �|𝐺𝐺(𝑖𝑖ω 𝑝𝑝 * )|�mentioning

confidence: 99%

Using multiple singular values in topology optimization of dynamic systems

Venini¹

2023

Theoretical and Applied Mechanics - AIMETA 2022

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Abstract. Within the general framework of frequency-domain topology optimization of Multi Input-Multi Output (MI-MO) dynamic systems, suitable norms of the input/output transfer matrix are introduced as possible merit functions to be minimized. Among them, the by now classical H_∞-norm (i.e. the supremum of the maximum singular value over the whole frequency range), and the so-called nuclear norm (i.e. the sum of all the positive singular values are considered. Heuristic motivations are given that suggest which norm should one choose according to the practical objective to be pursued alongside a few numerical examples on topology optimization of 2D linear-elastic multiload SI-SO and MI-MO dynamic systems.

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Section: �|𝐺𝐺(𝑖𝑖ω 𝑝𝑝 * )|�mentioning

confidence: 99%

Using multiple singular values in topology optimization of dynamic systems

Venini¹

2023

Theoretical and Applied Mechanics - AIMETA 2022

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“…In fact, when, for example, seismic forces are considered, one may show that the matrix B does depend on the design variable vector p (Venini and Ceresa 2018) and that is why the dependence of all the factors in Eq. ( 13) on p should in general be considered.…”

Section: Sensitivity Of the Input/output Transfer Matrixmentioning

confidence: 99%

Static and dynamic topology optimization: an innovative unifying approach

Venini

Pingaro

2023

Struct Multidisc Optim

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This paper presents a topology optimization approach that is innovative with respect to two distinct matters. First of all the proposed formulation is capable to handle static and dynamic topology optimization with virtually no modifications. Secondly, the approach is inherently a multi-input multi-output one, i.e., multiple objectives can be pursued in the presence of multiple loads. The input-to-output transfer matrix, say $${{{\varvec{G}}}}$$ G , is the key ingredient that governs the algebraic mapping between applied loads and structural response. In statics $${{{\varvec{G}}}}$$ G depends on the design variables only, whereas it depends on the frequency variable as well in the dynamic case. The Singular Value Decomposition (SVD) of $${{{\varvec{G}}}}$$ G represents then the core of the proposed approach. Singular values are shown to be the gains of the input/output mapping and are used to compute proper norms of $${{\varvec{G}}}$$ G that represent the goal functions to be minimized. Singular vectors provide at no extra cost the plant directions, i.e., the load combination factors that stress the structure the most. Numerical examples are discussed in much detail and open issues object of ongoing investigations are highlighted. A full Matlab code handling the static topology optimization problem is provided as an online Appendix to the manuscript. Its extension to the dynamic case may be gathered following the formulation proposed in Sect. 5.

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“…Other applications of optimisation in structural concrete design include targeting seismic performance objectives [483][484][485], the optimisation of prestressed concrete members [486], and defining critical concrete structures general topology, from the Optimisation of Continua, as performed by Wu and Wu for bridge pylons [487]. These works will, most certainly, have a contribution also for steel and concrete composite structures.…”

Section: Concrete Structural Designmentioning

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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A rational H_∞‐norm–based approach for the optimal design of seismically excited reinforced concrete frames

Cited by 8 publications

References 24 publications

Using multiple singular values in topology optimization of dynamic systems

Using multiple singular values in topology optimization of dynamic systems

Static and dynamic topology optimization: an innovative unifying approach

Topology Optimisation in Structural Steel Design for Additive Manufacturing

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