Investigation of optimal layout of ties in STM developed by topology optimization

Zhou, Linyun; He, Zhi‐Qi; Liu, Zhao

doi:10.1002/suco.201500093

Cited by 10 publications

(7 citation statements)

References 12 publications

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“…As a result, the effect of the reinforcement bars on the load transmission cannot be considered in optimization process 6,30 . In order to detail the layout of struts and ties from the optimal topology, Zhou et al 29 presented two criterions as following:

normalΠ goodbreak= \sum T_{i} l_{i} ε_{i} goodbreak= Minimum

1 / K goodbreak= \sum {\overset{true¯}{F_{i}}}^{2} L_{i} / ((), E_{c} A_{i}) goodbreak= Minimum

where

normalΠ

is the total stain energy in ties;

K

is the stiffness of struts;

E_{c}

is modulus of elasticity of concrete;

T_{i}

l_{i}

, and

ε_{i}

are the force, length and mean strain respectively for tie

i

;

\overset{F_{i}}{true}

L_{i}

, and

A_{i}

are the force, length and mean strain respectively for strut

i

.…”

Section: Modified Optimal Topology Methodsmentioning

confidence: 99%

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Development of strut‐and‐tie models using topology optimization based on modified optimal criterion

Zhou

Wan²

2021

Structural Concrete

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Strut-and-tie models (STMs) have been widely used to design disturbed regions in structural concrete members. Recently, topology optimization methods, based on the principle of minimum strain energy directly and indirectly, have been adopted to generate STMs in reinforced concrete structures. Unfortunately, current topology optimization methods do not work in many typical disturbed regions. The optimization history of the rectangular anchorage zones shows that the principle of minimum strain energy is a necessary condition for STM, not a sufficient condition. Because, it fails to capture the load transfer path properly in structural concrete tensile regions. To address this issue, a modified optimality criterion is proposed to illustrate the load path in tensile regions. And the desired STM is the one with the maximum overall stiffness and minimum strain energy of the tie. The STM of the rectangular anchorage zones and dapped beams have been developed successfully, and verified by the current ACI 318-08 code recommendations and experimental evidence.

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normalΠ goodbreak= \sum T_{i} l_{i} ε_{i} goodbreak= Minimum

1 / K goodbreak= \sum {\overset{true¯}{F_{i}}}^{2} L_{i} / ((), E_{c} A_{i}) goodbreak= Minimum

where

normalΠ

is the total stain energy in ties;

K

is the stiffness of struts;

E_{c}

is modulus of elasticity of concrete;

T_{i}

l_{i}

, and

ε_{i}

are the force, length and mean strain respectively for tie

i

;

\overset{F_{i}}{true}

L_{i}

, and

A_{i}

are the force, length and mean strain respectively for strut

i

.…”

Section: Modified Optimal Topology Methodsmentioning

confidence: 99%

“…As a result, the effect of the reinforcement bars on the load transmission cannot be considered in optimization process. 6,30 In order to detail the layout of struts and ties from the optimal topology, Zhou et al 29 presented two criterions as following:…”

Section: Optimal Layout Of Tiesmentioning

confidence: 99%

Development of strut‐and‐tie models using topology optimization based on modified optimal criterion

Zhou

Wan²

2021

Structural Concrete

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“…More than 120 years after the work by Ritter [476] and Mörsch, as well as over 30 years past Schlaich et al's notorious contribution [477], the Strut-and-Tie Models (STM) still govern the concrete design with remarkable resemblances to what previous generations of structural engineers mastered. That may well be subject to change as new developments in TO are deemed to reshape our understanding of reinforced concrete design, with contributions by Zhou et al's [478], Yang et al's [479], Jewett and Carstensen's [480], and Xia et al's [481]. However, the promise of fundamental innovation beyond the aforesaid applications remains restricted to only a few distinct approaches.…”

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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“…The stress distribution is nonlinear in this region, and Bernoulli's Hypothesis is not applicable. The strut-and-tie models (STMs) are an effective method to analyze the D-region and has been accepted worldwide by many researchers, [1][2][3][4][5][6] which was first proposed by Schlaich et al [7][8][9][10] to analyze concrete beams.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the strut‐and‐tie model of a two‐plane cable‐stayed bridge tower under vertical component of the cable force

Hong

Huang

et al. 2021

Structural Concrete

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The geometry and mechanical behavior of concrete bridge towers are complex.Hence, it is important to generate a rational mechanical analysis model for structural design. The method of strut-and-tie models (STMs) is an effective way to analyze disturbed regions (D-regions) such as the anchorage zones of cables in bridge towers. This paper provides a detailed analysis of the elastic stress distribution on the bridge tower of a cable-stayed bridge with two cable planes. The vertical component of the stay cable force was considered for the analysis. Additionally, two different STMs of the bridge tower were developed with the load path method using different horizontal spacings of the stay cables. Based on the minimum energy principle, the optimal STMs of the two different STMs were generated. A detailed calculation method for the configuration of the optimal STMs is presented. In the paper, computational expressions of the internal force for the tie members in the two STMs are also proposed. Overall, this study demonstrated the strong applicability of the proposed STMs for a bridge tower in a cable-stayed bridge with two cable planes. This can be considered an effective simplified method in the structural design of bridge towers. Furthermore, the study established that the influence of the horizontal distance between stay cables on the mechanical response-behavior of the structure should be considered in the design of concrete bridge towers. K E Y W O R D Scable-stayed bridge, concrete bridge tower, load path method, minimum energy principle, optimal STM, strut-and-tie model (STM)

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Investigation of optimal layout of ties in STM developed by topology optimization

Cited by 10 publications

References 12 publications

Development of strut‐and‐tie models using topology optimization based on modified optimal criterion

Development of strut‐and‐tie models using topology optimization based on modified optimal criterion

Topology Optimisation in Structural Steel Design for Additive Manufacturing

Investigation of the strut‐and‐tie model of a two‐plane cable‐stayed bridge tower under vertical component of the cable force

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