Hencky bar-net model for plate buckling

International Journal of Mechanical Sciences

et al. 2019

Self Cite

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.

Section: A C C E P T E D Mmentioning

confidence: 99%

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

International Journal of Mechanical Sciences

et al. 2019

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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

Applied Mathematical Modelling

et al. 2018

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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.

“…A Hencky bar model is a type of bar-spring structural model that was pioneered by Hencky (1921). Owing to its simple and clear physical representation and great flexibility, it had been recently revisited and expanded to study various static, buckling and dynamic problems of different structural types (Wang et al 2017(Wang et al , 2020Zhang et al 2018cZhang et al , b, a, d, 2019aZhang et al , b, 2022. HBM comprises bars and springs whose stiffnesses may be adjusted to allow for different material property distributions.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

Struct Multidisc Optim

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.