Analytical Determination of the Bending Stiffness of a Five-Layer Corrugated Cardboard with Imperfections

Bending stiffness (BS) is one of the two most important mechanical parameters of corrugated board. The second is edge crush resistance (ECT). Both are used in many analytical formulas to assess the load capacity of corrugated cardboard packaging. Therefore, the correct determination of bending stiffness is crucial in the design of corrugated board structures. This paper focuses on the analytical determination of BS based on the known parameters of the constituent papers and the geometry of the corrugated layers. The work analyzes in detail the dependence of the bending stiffness of an asymmetric, five-layer corrugated cardboard on the sample arrangement. A specimen bent so that the layers on the lower wave side are compressed has approximately 10% higher stiffness value. This is due to imperfections, which are particularly important in the case of compression of very thin liners. The study showed that imperfection at the level of a few microns causes noticeable drops in bending stiffness. The method has also been validated by means of experimental data from the literature and simple numerical finite element model (FEM). The obtained compliance of the computational model with the experimental model is very satisfactory. The work also included a critical discussion of the already published data and observations of other scientists in the field.

Bending stiffness of circular multilayer van der Waals material sheets

We study the bending stiffness of symmetrically bent circular multilayer van der Waals (vdW) material sheets, which corresponds to the non-isometric configuration in bulge tests. Frenkel sinusoidal function is employed to describe the periodic interlayer tractions due to the lattice structure nature and the bending stiffness of sheets is theoretically extracted via an energetic consideration. Our quantitative prediction shows good agreement with recent experimental results, where the bending stiffness of different types of sheets with the comparable thickness could follow a trend opposite to their Young's moduli. Based on our model, we propose that this trend may experience a transition as the thickness decreases. Apart from the apparent effects of Young's modulus and interlayer shear strength, the interlayer distance is also found to have an important impact on the bending stiffness. In addition, according to our analysis on the size effect, the bending stiffness of such symmetrically bent circular sheets can steadily own a relatively large value, in contrast to the cases of isometric deformations.

Simulation of Continuous Tension Stringing Process of Conductor with Bending Stiffness Model

At present, there is no research on the calculation of tension variation of the conductor with bending stiffness model between the continuous span during tension stringing construction. Aiming at the typical terrain with large elevation difference in UHV project, a vector finite element method for calculating the tension of the conductor with bending stiffness model passes through the pulley in the process of tension stringing is proposed. The process of the wire rope under the action of the tractor pulling the conductor passes through the pulley continuously is realized. The variations of tension of tensioner and tractor, reaction force of pulley and envelope angle of the conductor passes through the pulley are obtained by simulation of tension stringing conditions such as 1 pulls 1, 1 pulls 2, etc, which provides reference for equipment selection for the tension stringing construction of mountain terrain with large elevation difference.

Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness – Part II: determination of the spherical part of the couple-stress

The indeterminacy of the spherical part of couple-stress is a well-known drawback of any theoretical formulation stemming from the Cosserat couple-stress theory of elasticity. The relevant theory of finite elastic deformations of solids reinforced by a family of fibres that resist bending is not an exception. The present communication extends and completes that theory in a manner that enables it to measure the spherical part of the couple-stress tensor outside the conventional equilibrium considerations. To achieve this, the present study reconsiders an extra piece of information that has surprisingly emerged already but, so far, has been left unexplained and unexploited; namely, the fact that the energy stored in a fibrous composite elastic solid with fibre-bending stiffness involves a couple-stress generated term that does not influence the relevant couple-stress constitutive equation. The thus resulting new theoretical development complements the theory previously presented without dismissing any of the theoretical results detailed or the conclusions drawn there. Its validity embraces boundary value problems concerning both finite and infinitesimal elastic deformations of polar fibrous composites. In the latter case, its applicability is also tested and verified through the successful determination of the spherical couple-stress of a polar transversely isotropic elastic plate subjected to pure bending.

Methodology for the study and prediction of stiffness characteristics during bending rials for the design of adaptive clothing for people with motor disabilities

The article analyses the existing methods of studying the characteristics of bending stiffness. Topicality of improving the methodology for assessing and predicting bending stiffness in relation to the operating conditions of the studied contingent of consumers is substantiated. The methodology includes two main stages – an experimental study of the stiffness characteristics taking into account the characteristics of the range under study and a stage of forecasting the design solutions of the product. Comprehensive experimen-tal studies of the bending characteristics of modern fabrics of the jacket assortment for adaptive clothing of people with motor disabilities have been carried out. For an objective assessment of wear during use, the proposed method implements an additional forced bending of samples in opposite directions in order to bring the test results closer to real operating conditions. The results of experimental studies can be used at the design stage to predict the bending characteristics of the fabrics of the jacket assortment of clothing for people with motor disabilities.

Study on Mechanical Characteristics of Segmental Joints of a Large-Diameter Shield Tunnel under Ultrahigh Water Pressure

At present, there is no clear design standard for segmental joints of large-diameter shield tunnels under high water pressure. In this paper, a theoretical calculation model for the bending stiffness of segmental joints under high water pressure is proposed. The numerical simulation method is used to investigate the failure and crack formation processes of single-layer and double-layer lining segments under large axial forces. The effects of axial force, bolt strength, and concrete strength on the bending stiffness of joints are then studied using a theoretical calculation model of segmental joints. The results show that under extremely high water pressure, the influence of double lining on joint stiffness is limited. It is more rational and safe to compute the bending stiffness of segmental joints using this theoretical model rather than the numerical simulation method. The parameter analysis reveals that increasing the bolt strength has a minor impact on bending stiffness and deformation, whereas increasing the concrete strength has the opposite effect. The influence of ultimate bearing capacity and deformation decreases non-linearly as the axial force increases.

Numerical and Experimental Study of Five-Layer Non-Symmetrical Paperboard Panel Stiffness

This paper concerns the analysis of five-layer corrugated paperboard subjected to a four-point bending test. The segment of paperboard was tested to determine the bending stiffness. The investigations were conducted experimentally and numerically. The non-damaging tests of bending were carried out in an elastic range of samples. The detailed layers of paperboard were modelled as an orthotropic material. The simulation of flexure was based on a finite element method using Ansys® software. Several material properties and thicknesses of papers in the samples were taken into account to analyse the influence on general stiffness. Two different discrete models based on two geometries of paperboard were considered in this study to validate the experimental stiffness. The present analysis shows the possibility of numerical modelling to achieve a good correlation with experimental results. Moreover, the results of numerical estimations indicate that modelling of the perfect structure gives a lower bending stiffness and some corrections of geometry should be implemented. The discrepancy in stiffness between both methods ranged from 3.04 to 32.88% depending on the analysed variant.