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

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 663
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska
Keyword(s):  
Load Capacity ◽  
Element Model ◽  
Critical Discussion ◽  
Bending Stiffness ◽  
Analytical Determination ◽  
Published Data ◽  
Corrugated Board ◽  
Correct Determination ◽  
Corrugated Cardboard

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.

scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3786
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

2021 ◽  
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. That is why numerical analyzes are becoming a common standard in this branch of manufacturing. Such trend causes either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and / or perforation of corrugated board, i.e. processes that undoubtedly weaken the stiffness and strength of the corrugated board locally. However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing, as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

Charge-Transfer Complexes Between Iodine and Substituted Thioureas: Determination of Thermodynamic and Spectroscopic Properties

1996 ◽  
Vol 51 (1-2) ◽  
pp. 116-122 ◽  
Author(s):  
Cornelia Fooken ◽  
Wolfram Baumann
Keyword(s):  
Equilibrium Constants ◽  
Spectroscopic Properties ◽  
Critical Discussion ◽  
Charge Transfer Complexes ◽  
Published Data ◽  
Visible Spectroscopy ◽  
Dichloromethane Solution ◽  
Uv Visible ◽  
Iodine Complexes

Abstract 15 iodine complexes with substituted thioureas were investigated in dichloromethane solution by UV-visible spectroscopy, and their equilibrium constants, reaction enthalpies and molar absorption coefficients were determined. The influence of the substituents on the properties of the charge-trans-fer complexes is examined. A critical discussion of previously published data is given, where comparable data are available.

scholarly journals Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4321
Author(s):  
Tomasz Gajewski ◽  
Tomasz Garbowski ◽  
Natalia Staszak ◽  
Małgorzata Kuca
Keyword(s):  
Load Capacity ◽  
Analytical Techniques ◽  
Shear Stiffness ◽  
Mechanical Tests ◽  
Torsional Stiffness ◽  
Bending Test ◽  
Corrugated Board ◽  
Four Point Bending ◽  
Residual Thickness ◽  
Corrugated Cardboard

As long as non-contact digital printing remains an uncommon standard in the corrugated packaging industry, corrugated board crushing remains a real issue that affects the load capacity of boxes. Crushing mainly occurs during the converting of corrugated board (e.g., analog flexographic printing or laminating) and is a process that cannot be avoided. However, as this study shows, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision of ±10 μm) in the range from 10 to 70% on different laboratory measurements was checked. The typical mechanical tests—i.e., edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc.—were performed on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions. The proposed measurement technique was successfully used to precisely estimate and thus control the crushing of corrugated board, while the proposed numerical and analytical techniques was used to estimate the load capacity of corrugated board packaging. A good correlation between the measured reduced stiffness of the corrugated cardboard and the proposed analytical predictive models was obtained.

scholarly journals Analytical determination of load capacity of the freight wagon wheelset axle with axle journal dimensions ø120×179 mm

Rail Vehicles ◽  
2019 ◽  
pp. 48-59
Author(s):  
Marek Sobaś
Keyword(s):  
Load Capacity ◽  
Analytical Determination

W artykule przedstawiono sposób określenia na drodze analitycznej nośności osi o wymiarach czopa Ø120×179 mm, stosowaną w układach biegowych wagonów towarowych typu 1XTa oraz rodziny Y25 z odmianami. Przedstawiono wyniki obliczeń wytrzymałościowych w poszczególnych sektorach osi wraz z ich oceną i porównaniem do obowiązujących kryteriów, które oparto o aktualnie obowiązujące przepisy europejskie.

Undrained Load Capacity of Torpedo Anchors Embedded in Cohesive Soils

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
José Renato M. de Sousa ◽  
Cristiano S. de Aguiar ◽  
Gilberto B. Ellwanger ◽  
Elisabeth C. Porto ◽  
Diego Foppa ◽  
...  
Keyword(s):  
Large Deformations ◽  
Load Capacity ◽  
Three Dimensional ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Cohesive Soils ◽  
Nonlinear Finite Element Model ◽  
Total Contact Area ◽  
Undrained Shear

This paper presents a numerical based study on the undrained load capacity of a typical torpedo anchor embedded in a purely cohesive isotropic soil using a three-dimensional nonlinear finite element model. In this model, the soil is simulated with solid elements capable of representing its nonlinear physical behavior and the large deformations involved. The torpedo anchor is also modeled with solid elements, and its geometry is represented in detail. Moreover, the anchor-soil interaction is addressed with contact finite elements that allow relative sliding with friction between the surfaces in contact. A number of analyses are conducted in order to understand the response of this type of anchor when different soil undrained shear strengths, load directions, and number and width of flukes are considered. The results obtained indicate two different failure mechanisms: The first one involves significant plastic deformation before collapse and, consequently, mobilizes a great amount of soil; the second is associated with the development of a limited shear zone near the edge of the anchor and mobilizes a small amount of soil. The total contact area of the anchor seems to be an important parameter in the determination of its load capacity, and, consequently, the increase in the undrained shear strength and the number of flukes and/or their width significantly increases the load capacity of the anchor.

scholarly journals Analytical determination of the QCD quark masses

2014 ◽  
Vol 29 (29) ◽  
pp. 1430069 ◽  
Author(s):  
C. A. Dominguez
Keyword(s):  
Recent Progress ◽  
Sum Rules ◽  
Finite Energy ◽  
Critical Discussion ◽  
Current Status ◽  
Analytical Determination ◽  
Qcd Sum Rules ◽  
Quark Masses ◽  
Systematic Uncertainties

The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.

scholarly journals Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Perforations

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1095
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski ◽  
Jakub Krzysztof Grabski
Keyword(s):  
Compressive Strength ◽  
Estimation Error ◽  
Analytical Formula ◽  
Shear Stiffness ◽  
Element Model ◽  
Numerical Approach ◽  
Analytical Framework ◽  
Width Ratio ◽  
Corrugated Board ◽  
Corrugated Cardboard

This paper presents a modified analytical formula for estimating the static top-to-bottom compressive strength of corrugated board packaging with different perforations. The analytical framework is based here on Heimerl’s assumption with an extension from a single panel to a full box, enhanced with a numerically calculated critical load. In the proposed method, the torsional and shear stiffness of corrugated cardboard, as well as the panel depth-to-width ratio is implemented in the finite element model used for buckling analysis. The new approach is compared with the successful though the simplified McKee formula and is also verified with the experimental results of various packaging designs made of corrugated cardboard. The obtained results indicate that for boxes containing specific perforations, simplified methods give much larger estimation error than the analytical–numerical approach proposed in the article. To the best knowledge of the authors, the influence of the perforations has never been considered before in the analytical or analytical–numerical approach for estimation of the compressive strength of boxes made of corrugated paperboard. The novelty of this paper is to adopt the method presented to include perforation influence on the box compressive strength estimation.

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