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

Zhang, H.; Wang, Chen; Challamel, Noël; Zhang, Y.P.

doi:10.1016/j.apm.2018.04.019

Cited by 12 publications

(2 citation statements)

References 33 publications

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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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“…The achieved results illustrated the accuracy of the proposed elements to assess the performance of bending plates. In 2018, Zhang et al 12 utilized the finite difference method to improve meshes’ performance in order to measure the behavior of circular plates. Elements were established using energy formulations.…”

Section: Introductionmentioning

confidence: 99%

Representing capabilities of novel semi-analytical triangular plate elements

Pour

Farsangi

2023

The Journal of Strain Analysis for Engineering Design

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Two novel plate-bending elements are developed and investigated in this study. Elements with 13 and 15 degree-of-freedoms are named AT13 and AT15, respectively. These triangular elements are formulated in a semi-analytic way. For this aim, the basic elasticity function is employed with unknown parameters. Subsequently, the trial-and-error procedure is used to determine the unidentified constants. Besides, the achieved results are compared with those obtained by displacement-based triangular elements with the same degrees-of-freedom (TUBA13 and TUBA15). In this research, both stress and displacement responses of diverse structures are assessed. After performing extensive numerical studies, the findings clearly demonstrate the superiorities of the proposed elements.

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Optimal design of functionally graded lattice structures using Hencky bar-grid model and topology optimization

Zhang

Wang

Challamel

et al. 2022

Struct Multidisc Optim

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Presented herein is a novel design framework for obtaining the optimal design of functionally graded lattice (FGL) structures that involve using a physical discrete structural model called the Hencky bar-grid model (HBM) and topology optimization (TO). The continuous FGL structure is discretized by HBM comprising rigid bars, frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. A penalty function is introduced to each of the HBM spring’s stiffnesses to model non-uniform material properties. The gradient-based TO method is applied to find the stiffest structure via minimizing the compliance or elastic strain energy by adjusting the HBM spring stiffnesses subjected to prescribed design constraints. The optimal design of FGL structures is constructed based on the optimal spring stiffnesses of the HBM. The proposed design framework is simple to implement and for obtaining optimal FGL structures as it involves a relatively small number of design variables such as the spring stiffnesses of each grid cell. As illustration of the HBM-TO method, some optimization problems of FGL structures are considered and their optimal solutions obtained. The solutions are shown to converge after a small number of iterations. A Python code is given in the Appendix for interested readers who wish to reproduce the results.

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

Cited by 12 publications

References 33 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

Representing capabilities of novel semi-analytical triangular plate elements

Optimal design of functionally graded lattice structures using Hencky bar-grid model and topology optimization

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