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5. Conclusions In this study, a detailed analysis of the effect of imperfections in thin-walled asym- metrical sections bent with a constant moment was carried out. The main contribution of this work was the derivation of analytical relationships that accurately describe the phenomenon of the difference in bending stiffness depending on the sign of the moment loading the asymmetric corrugated cardboard sample in machine direction. The paper showed that the applied analytical model satisfactorily reflects the real behavior of bent five- layer corrugated cardboard. The adopted simplifications did not affect the quality of the proposed solution, which was proved by a simple numerical model. Finally, the developed model was compared with the results of experimental research available in the literature. The obtained results are much closer to the experimental results than the results generated by other models available in the literature. Additionally, proposed model is very easy to implement, which makes it possible to use it in practice by cardboard manufacturers. This study also includes the sensitivity analysis, which indicates the most important parameters directly affecting the BS and, therefore, can be very helpful in more conscious design of optimal corrugated board. Author Contributions: Conceptualization, T.G.; methodology, T.G.; software, T.G.; validation, A.K.-P. and T.G.; formal analysis, T.G.; investigation, A.K.-P. and T.G.; resources, A.K.-P.; data curation, A.K.-P.; writing—original draft preparation, T.G. and A.K.-P.; writing—review and editing, A.K.-P. and T.G.; visualization, T.G.; supervision, T.G.; project administration, T.G.; funding acquisition, T.G. and A.K.-P. All authors have read and agreed to the published version of the manuscript. Funding: The APC was funded by the Ministry of Science and Higher Education, Poland, the statu- tory funding at Poznan University of Life Sciences, grant number 506.569.05.00. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conflicts of Interest: The authors declare no conflict of interest.
References 1. Baum, G.A.; Brennan, D.C.; Habeger, C.C. Orthotropic elastic constants of paper. Tappi 1981 , 64 , 97–101. 2. Mann, R.W.; Baum, G.A.; Habeger, C.C. Determination of all nine orthotropic elastic constants for machine-made paper. Tappi 1980 , 63 , 163–166. 3. Frank, B. Corrugated box compression—A literature survey. Packag. Technol. Sci. 2014 , 27 , 105–128. [CrossRef] 4. Zhang, Y.-L.; Chen, J.; Wu, Y.; Sun, J. Analysis of hazard factors of the use of corrugated carton in packaging low-temperature yogurt during logistics. Procedia Environ. Sci. 2011 , 10 , 968–973. [CrossRef] 5. Hung, D.; Nakano, Y.; Tanaka, F.; Hamanaka, D.; Uchino, T. Preserving the strength of corrugated cardboard under high humidity condition using nano-sized mists. Compos. Sci. Technol. 2010 , 70 , 2123–2127. [CrossRef] 6. Gallo, J.; Cort é s, F.; Alberdi, E.; Goti, A. Mechanical behavior modeling of containers and octabins made of corrugated cardboard subjected to vertical stacking loads. Materials 2021 , 14 , 2392. [CrossRef] 7. Böröcz, P.; Moln á r, B. Measurement and analysis of vibration levels in stacked small package shipments in delivery vans as a function of free movement space. Appl. Sci. 2020 , 10 , 7821. [CrossRef] 8. Quesenberry, C.; Horvath, L.; Bouldin, J.; White, M.S. The Effect of pallet top deck stiffness on the compression strength of asymmetrically supported corrugated boxes. Packag. Technol. Sci. 2020 , 33 , 547–558. [CrossRef] 9. Garbowski, T.; Gajewski, T.; Grabski, J.K. Estimation of the compressive strength of corrugated cardboard boxes with various openings. Energies 2021 , 14 , 155. [CrossRef] 10. Garbowski, T.; Gajewski, T.; Grabski, J.K. Estimation of the compressive strength of corrugated cardboard boxes with various perforations. Energies 2021 , 14 , 1095. [CrossRef] 11. Garbowski, T.; Knitter-Pia˛tkowska, A.; Mr ó wczyn´ski, D. Numerical homogenization of multi-layered corrugated cardboard with creasing or perforation. Materials 2021 , 14 , 3786. [CrossRef] 12. Gong, G.; Liu, Y.; Fan, B.; Sun, D. Deformation and compressive strength of corrugated cartons under different indentation shapes: Experimental and simulation study. Packag. Technol. Sci. 2020 , 33 , 215–226. [CrossRef] 13. Fadiji, T.; Coetzee, C.J.; Opara, U.L. Compression strength of ventilated corrugated paperboard packages: Numerical modelling, experimental validation and effects of vent geometric design. Biosyst. Eng. 2016 , 151 , 231–247. [CrossRef]
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