Hencky bar-chain model for optimal circular arches against buckling

Zhang, H.; Wang, Chen

doi:10.1016/j.mechrescom.2018.01.001

Cited by 13 publications

(2 citation statements)

References 26 publications

(35 reference statements)

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“…Axial vibration problem of lattice system comprising mass points multiply connected by lateral springs has been treated by Challamel et al (2018). One-dimensional and twodimensional lattice structures built out of rigid bars connected to each other via elastic rotational springs have also been investigated before via Hencky bar-chain/net model for strings (Zhang et al 2018a), beams (Wang et al 2015;Zhang et al 2016), arches (Zhang and Wang 2018;Zhang et al 2017) and plates (Wang et al 2017b;Zhang et al 2018b;Zhang et al 2018c). However, there is hitherto no rigorous analyses on buckling behaviour of lattice system comprising rigid bars with both direct and indirect neighbouring interactions which will herein be referred to as multiply connected bar-chain (MCB) system.…”

Section: A C C E P T E D Mmentioning

confidence: 99%

Buckling of multiply connected bar-chain and its associated continualized nonlocal model

Zhang

Challamel

Wang

et al. 2019

International Journal of Mechanical Sciences

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights The buckling problem of a multiply connected bar-chain (MCB) system is investigated.  The MCB model has rigid bars connected by both direct and indirect neighbouring rotational springs that simulate the long range interactions between bars.  The buckling loads of the MCB with two-neighbour and N-neighbour interactions are analytically obtained for simply supported and clamped boundary conditions.  A nonlocal continuum model is constructed to predict the buckling behavior of MCB system with short and long range interactions.  The length scale of the nonlocal beam model is calibrated with respect to the rotational spring stiffnesses of MCB.

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Section: A C C E P T E D Mmentioning

confidence: 99%

Buckling of multiply connected bar-chain and its associated continualized nonlocal model

Zhang

Challamel

Wang

et al. 2019

International Journal of Mechanical Sciences

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“…Based on previous studies on FDM for beams [17][18][19][20], columns [21,22], circular arches [23,24] and rectangular plates [25][26][27], there is an equivalent physical structural model which has been named the Hencky bar-chain (for beams and circular arches) or Hencky bar-net (for rectangular plates). The Hencky bar-chain or Henchy bar-net comprises rigid bar segments or rigid arcs (for circular arches) connected to each other by frictionless hinges with elastic rotational springs that allows for the flexibility of the structures.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

Zhang

Wang

Challamel

et al. 2018

Applied Mathematical Modelling

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As there are a few finite difference models in the literature for axisymmetric bending of plates, only one of these models is equivalent to the Hencky bar-net model (HBM) that comprises a finite number of rigid circular arcs and straight radial segments joined by frictionless hinges with elastic rotational springs. This paper is concerned with uncovering the one finite difference model (FDM) that is equivalent to the HBM. Based on the energy formulation, the governing equation for HBM is derived and it will be used to identify the FDM that has the same discrete set of equations. By using this equivalency between the HBM and the identified FDM, the expressions of edge spring stiffnesses of HBM are derived for various boundary conditions. As illustrative examples, the HBM is used to solve the bending problems of circular plates under uniformly and linearly increasing distributed loads. The analytical solutions of HBM avoids the singularity problem faced in FDM at the plate center. This paper also presents some benchmark bending solutions for annular plates with and without an internal ring support for different boundary restraints by using the HBM.

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Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

et al. 2018

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Hencky bar-chain model for optimal circular arches against buckling

Abstract:  Hencky bar-chain model (HBM) is developed for shape optimization of circular arches.  HBM is ease to handle minimum cross-sectional area constraint.  Analytical optimization solutions are obtained via HBM.

Cited by 13 publications

References 26 publications

Buckling of multiply connected bar-chain and its associated continualized nonlocal model

Buckling of multiply connected bar-chain and its associated continualized nonlocal model

Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

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