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

Abstract

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.

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

“…employed various size-dependent methods such as the nonlocal elasticity of Eringen, the strain gradient theory, the modified couple stress model, the micromorphic theory, as well as the nonlocal-stress gradient (as a hybrid model) procedure [10][11][12][13][14][15][16][17][18][19][20] to introduce the differences between classical and non-classical models. Many researchers studied the mechanical behavior of micro-/nano-structures based on the non-classical continuum mechanics models induced by different types of loadings including vibration [21][22][23][24][25][26][27][28][29][30][31][32], wave propagation [33][34][35][36][37][38][39][40][41][42][43], and buckling phenomenon [44][45][46][47][48][49][50][51][52][53][54] associated with linear and nonlinear approaches related to the kinematic relations. According to their hypothesis as well as ob...…”

Mechanical behavior of porous solid considering mesoscopic elastic buckling

“…Lattice spring models are based, in principle, on the atomic lattice models originating from condensed matter physics. Due to the explicit representation of local spring‐like interactions between discrete particles, LSM has the natural advantage of simulating the mechanical response of coarse‐grained materials . The classical LSM proposed by Hrennikoff in 1941 had a Poisson's ratio limitation; namely, it could only solve elastic problems at a fixed Poisson's ratio.…”

Exact and nonlocal solutions for vibration of multiply connected bar-chain system with direct and indirect neighbouring interactions

“…This bending model composed of multiply bending short and long range interactions is the bending generalization of the finite generalized axial lattice recently studied by Challamel, et al [10] using both lattice and nonlocal mechanics. Zhang, et al [11] studied the buckling behaviour of such a generalized Hencky bar-chain system with short and long range interactions. This results presented in this paper are based on the same model but now focusing on the vibrational response of this generalized bending lattice.…”