Investigating the Effect of Perforations on the Load-Bearing Capacity of Cardboard Packaging.

The impact of perforation patterns on the compressive strength of cardboard packaging is a critical concern in the packaging industry, where optimizing material usage without compromising structural integrity is essential. This study aims to investigate how different perforation designs affect the load-bearing capacity of cardboard boxes. Utilizing finite element method (FEM) simulations, we assessed the compressive strength of packaging made of various types of corrugated cardboards, including E, B, C, EB, and BC flutes with different heights. Mechanical testing was conducted to obtain accurate material properties for the simulations. Packaging dimensions were varied to generalize the findings across different sizes. Results showed that perforation patterns significantly influenced the compressive strength, with reductions ranging from 14% to 43%, compared to non-perforated packaging. Notably, perforations on multiple walls resulted in the highest strength reductions. The study concludes that while perforations are necessary for functionality and aesthetics, their design must be carefully considered to minimize negative impacts on structural integrity. These findings provide valuable insights for designing more efficient and sustainable packaging solutions in the industry.

Optimal Design of Bubble Deck Concrete Slabs: Serviceability Limit State.

In engineering practice, one can often encounter issues related to optimization, where the goal is to minimize material consumption and minimize stresses or deflections of the structure. In most cases, these issues are addressed with finite element analysis software and simple optimization algorithms. However, in the case of optimization of certain structures, it is not so straightforward. An example of such constructions are bubble deck ceilings, where, in order to reduce the dead weight, air cavities are used, which are regularly arranged over the entire surface of the ceiling. In the case of these slabs, the flexural stiffness is not constant in all its cross-sections, which means that the use of structural finite elements (plate or shell) for static calculations is not possible, and therefore, the optimization process becomes more difficult. This paper presents a minimization procedure of the weight of bubble deck slabs using numerical homogenization and sequential quadratic programming with constraints. Homogenization allows for determining the effective stiffnesses of the floor, which in the next step are sequentially corrected by changing the geometrical parameters of the floor and voids in order to achieve the assumed deflection. The presented procedure allows for minimizing the use of material in a quick and effective way by automatically determining the optimal parameters describing the geometry of the bubble deck floor cross-section. For the optimal solution, the concrete weight of the bubble deck slab was reduced by about 23% in reference to the initial design, and the serviceability limit state was met.

A Simplified Dynamic Strength Analysis of Cardboard Packaging Subjected to Transport Loads.

The article presents a simplified method for determining the strength of corrugated board packaging subjected to dynamic transport loads. The proposed algorithm consists of several calculation steps: (1) a static analysis of the compressive strength of the package, (2) an analysis of random vibrations in the frequency domain used to determine the resonance frequencies and (3) a dynamic analysis of the package loaded with computed resonant frequencies. For this purpose, numerical models of the static compression test of the packaging before and after the dynamic analysis of the package subjected to general transport loads were developed. In order to validate the model, laboratory packaging compression tests were also performed for samples of boxes using three-layer cardboard. Due to this, it was possible to verify the numerical simulation results of the compression tests for several box geometries. This, in turn, allowed for the development of a method based on dynamic and post-dynamic (static) numerical analyses, permitting a high-accuracy determination of the resistance of the selected packaging to vibrations and dynamic loads. The results of the (experimentally validated) numerical analysis proved the usefulness of the simplified method presented herein for precise estimation of the load capacity of various packages dynamically loaded during transport.

Sensitivity Analysis of Open-Top Cartons in Terms of Compressive Strength Capacity.

Trays in which fruit and vegetables are transported over vast distances are not only stored in extreme climatic conditions but are also subjected to long-term loads. Therefore, it is very important to design them correctly and select the optimal raw material for their production. Geometric parameters that define the shape of the packaging may also be optimized in the design process. In this work, in order to select the most important parameters that affect the load capacity of a tray, sensitivity analysis was used. A sensitivity analysis is often the first step in the process of building artificial-intelligence-based surrogates. In the present work, using the example of a specific tray's geometry, the selection of starting parameters was carried out in the first step, based on the Latin hypercube sampling method. In the next step, local sensitivity analyses were performed at twenty selected starting points of the seventeen-dimensional space of the selected parameters. Based on the obtained results, it was possible to select the parameters that have a significant impact on the load capacity of the tray in the box compression test and whose influence is negligible or insignificant.

Effective Stiffness of Thin-Walled Beams with Local Imperfections.

Thin-walled beams are increasingly used in light engineering structures. They are economical, easy to manufacture and to install, and their load capacity-to-weight ratio is very favorable. However, their walls are prone to local buckling, which leads to a reduction of compressive, as well as flexural and torsional, stiffness. Such imperfections can be included in such components in various ways, e.g., by reducing the cross-sectional area. This article presents a method based on the numerical homogenization of a thin-walled beam model that includes geometric imperfections. The homogenization procedure uses a numerical 3D model of a selected piece of a thin-walled beam section, the so-called representative volume element (RVE). Although the model is based on the finite element method (FEM), no formal analysis is performed. The FE model is only used to build the full stiffness matrix of the model with geometric imperfections. The stiffness matrix is then condensed to the outer nodes of the RVE, and the effective stiffness of the cross-section is calculated by using the principle of the elastic equilibrium of the strain energy. It is clear from the conducted analyses that the introduced imperfections cause the decreases in the calculated stiffnesses in comparison to the model without imperfections.

Parametric Study of the Numerical Model of a Bolted Connection of Steel Structure for Photovoltaic Panels.

In the face of the reality that unexpectedly mobilized the governments of most central European countries (including Poland), the development of renewable energy sources (RES) seems to be an important direction. Therefore, both wind parks and solar farms will be constructed at double speed for energetic independence. This urgency makes the market of producers of structures for mounting solar panels also need to adapt quickly to the new situation. New constructions adapted to quick assembly with the use of nutless screw connections seem to be one of the best solutions. These structures must not only be easy and quick to install but also durable, which makes the connections resistant to cyclical loads. The speed of assembly of the substructure can be achieved precisely with the help of nutless connections, but their durability should be carefully analyzed. This article presents parametric analyses of the numerical model of this type of connection. The selection of appropriate numerical models for simulation is of key importance in the fatigue strength analysis of bolted connections. This article investigates two different models used in numerical fatigue analyses performed in the Abaqus FEA and FE-Safe program, namely, traditional bolt with nut and innovative self-tapping nutless bolt. Extended parametric analyses of both numerical models were carried out, which ultimately allowed optimization of the fatigue capacity of the connection.

Influence of Analog and Digital Crease Lines on Mechanical Parameters of Corrugated Board and Packaging.

When producing packaging from corrugated board, material weakening often occurs both during the die-cutting process and during printing. While the analog lamination and/or printing processes that degrade material can be easily replaced with a digital approach, the die-cutting process remains overwhelmingly analog. Recently, new innovative technologies have emerged that have begun to replace or at least supplement old techniques. This paper presents the results of laboratory tests on corrugated board and packaging made using both analog and digital technologies. Cardboard samples with digital and analog creases are subject to various mechanical tests, which allows for an assessment of the impact of creases on the mechanical properties of the cardboard itself, as well as on the behavior of the packaging. It is proven that digital technology is not only more repeatable, but also weakens the structure of corrugated board to a much lesser extent than analog. An updated numerical model of boxes in compression tests is also discussed. The effect of the crushing of the material in the vicinity of the crease lines in the packaging arising during the analog and digital finishing processes is taken into account. The obtained enhanced computer simulation results closely reflect the experimental observations, which prove that the correct numerical analysis of corrugated cardboard packaging should be performed with the model taking into account the crushing.

Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing.

The production of thin-walled beams with various cross-sections is increasingly automated and digitized. This allows producing complicated cross-section shapes with a very high precision. Thus, a new opportunity has appeared to optimize these types of products. The optimized parameters are not only the lengths of the individual sections of the cross section, but also the bending angles and openings along the beam length. The simultaneous maximization of the compressive, bending and shear stiffness as well as the minimization of the production cost or the weight of the element makes the problem a multi-criteria issue. The paper proposes a complete procedure for optimizing various open sections of thin-walled beam with different openings along its length. The procedure is based on the developed algorithms for traditional and soft computing optimization as well as the original numerical homogenization method. Although the work uses the finite element method (FEM), no computational stress analyses are required, i.e., solving the system of equations, except for building a full stiffness matrix of the optimized element. The shell-to-beam homogenization procedure used is based on equivalence strain energy between the full 3D representative volume element (RVE) and its beam representation. The proposed procedure allows for quick optimization of any open sections of thin-walled beams in a few simple steps. The procedure can be easily implemented in any development environment, for instance in MATLAB, as it was done in this paper.

Shell-to-Beam Numerical Homogenization of 3D Thin-Walled Perforated Beams.

Determining the geometric characteristics of even complex cross-sections of steel beams is not a major challenge nowadays. The problem arises when openings of various shapes and sizes appear at more or less regular intervals along the length of the beam. Such alternations cause the beam to have different stiffnesses along its length. It has different bending and shear stiffnesses at the opening point and in the full section. In this paper, we present a very convenient and easy-to-implement method of determining the equivalent stiffness of a beam with any cross-section (open or closed) and with any system of holes along its length. The presented method uses the principles of the finite element method (FEM), but does not require any formal analysis, i.e., solving the system of equations. All that is needed is a global stiffness matrix of the representative volumetric element (RVE) of the 3D representation of a beam modeled with shell finite elements. The proposed shell-to-beam homogenization procedure is based on the strain energy equivalence, and allows for precise and quick determination of all equivalent stiffnesses of a beam (flexural and shear). The results of the numerical homogenization procedure were compared with the existing analytical solution and experimental results of various sections. It has been shown that the results obtained are comparable with the reference results.

Identification of Aluminium Powder Properties for Modelling Free Air Explosions.

Aluminium is a component in many energetic formulations. Therefore, its combustion is one of the main thermochemical processes that govern the output from the energetics. Modelling aluminium combustion is a challenging task because the process is highly complex and difficult to measure. Here, tests of aluminium powder were conducted in an effort to isolate the burning of the aluminium and to determine an adequate representation of this process. Charges of 100 g and 500 g were tested, and the size of the Al/air cloud and the ratio of components in the Al/air mixture were determined, which has not been published previously. This information was used to assess the validity of the assumption that the detonation of the mixture was representative of the event. Parameters for the Jones-Wilkins-Lee equation of state for the explosive mixture and detonation products were defined. Simulations of the tests were performed, and the results were consistent with the field test data, indicating that detonation occurred when there was a mixture of 70-75% Al and 25-30% air by mass.

Determination of Transverse Shear Stiffness of Sandwich Panels with a Corrugated Core by Numerical Homogenization.

Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.

Blast Test and Failure Mechanisms of Soft-Core Sandwich Panels for Storage Halls Applications.

In this paper, an experimental investigation is presented for sandwich panels with various core layer materials (polyisocyanurate foam, mineral wool, and expanded polystyrene) when subjected to a justified blast load. The field tests simulated the case for when 5 kg of trinitrotoluene (TNT) is localized outside a building's facade with a 5150 mm stand-off distance. The size and distance of the blast load from the obstacle can be understood as the case of both accidental action and a real terroristic threat. The sandwich panels have a nominal thickness, with the core layer equal 100 mm and total exterior dimensions of 1180 mm × 3430 mm. Each sandwich panel was connected with two steel columns made of I140 PE section using three self-drilling fasteners per panel width, which is a standard number of fasteners suggested by the producers. The steel columns were attached to massive reinforced concrete blocks via wedge anchors. The conducted tests revealed that the weakest links of a single sandwich panel, subjected to a blast load, were both the fasteners and the strength of the core. Due to the shear failure of the fasteners, the integrity between the sandwich panel and the main structure is not provided. A comparison between the failure mechanisms for continuous (polyisocyanurate foam and expanded polystyrene) and non-continuous (mineral wool) core layer materials were conducted.

Temperature Measurement of a Bullet in Flight.

This study answers a primary question concerning how the temperature changes during the flight of a bullet. To answer the question, the authors performed unique research to measure the initial temperatures of bullet surfaces and applied it to four kinds of projectiles in a series of field experiments. The technique determines the temperature changes on metallic objects in flight that reach a velocity of 300 to 900 m/s. Until now, the tests of temperature change available in the literature include virtual points that are adopted to ideal laboratory conditions using classic thermomechanical equations. The authors conducted the first study of its kind, in which is considered four projectiles in field conditions in which a metallic bullet leaves a rifle barrel after a powder deflagration. During this process, heat is partly transferred to the bullet from the initial explosion of the powder and barrel-bullet friction. In this case, the temperature determination of a bullet is complex because it concerns different points on the external surface. Thus, for the first time the authors measured the temperatures at different position on the bullet surface. Moreover, the authors showed that basic thermodynamic equations allow for the credible prediction of such behavior if the initial conditions are identified correctly. This novel identification of the initial conditions of temperature and velocity of flying bullets was not presented anywhere else up to now.

Torsional and Transversal Stiffness of Orthotropic Sandwich Panels.

In the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse shear becomes an important component if the analyzed plate or shell is thick with respect to the in-plane dimensions and/or its core has significantly lower stiffness than the outer faces. The popular example of such a sandwich plate is a corrugated cardboard, widely used in the packaging industry. The flat layers of a corrugated board are usually made of thicker (stronger) material than that used for the corrugated layer, the role of which is rather to keep the outer layers at a certain distance, to ensure high bending stiffness of the plate. However, the soft core of such a plate usually has a low transverse shear stiffness, which is often not considered in the plate analysis. Such simplification may lead to significant calculation errors. The paper presents the generalization of the Reissner's analytical formula, which describes the torsional stiffness of the plate sample including two transverse shear stiffnesses. The paper also presents the implementation of the numerical model of the plate torsion test including the transverse shear stiffnesses. Both approaches are compared with each other on a wide range of material parameters and different aspect ratios of the specimen. It has been proved that both analytical and numerical formulations lead to an identical result. Finally, the performance of presented formulations is compared with other numerical models using commercial implementation of various Reissner-Mindlin shell elements and other analytical formulas from the literature. The comparison shows good agreement of presented theory and numerical implementation with other existing approaches.

The Role of Buckling in the Estimation of Compressive Strength of Corrugated Cardboard Boxes.

This paper presents analytical methods for estimating the static top-to-bottom compressive strength of simple corrugated packaging, in which the torsional and shear stiffness of corrugated cardboard as well as the panel depth-to-width ratio are included. The methods are compared herein with a basic and more detailed buckling description with the successful McKee formula, which is over fifty years old but still widely used among packaging designers and quality control departments. Additionally, the assumptions and applied simplifications used in the literature are analyzed, and the limits of applicability of different versions of the selected methods are checked. Finally, all approaches are verified with the experiment results of various packaging designs made of corrugated cardboard. The results show that, for certain proportions of dimensions of simple flap boxes, simplified methods give an even two times larger estimation error than the analytical approach proposed in the paper. Furthermore, it is evidenced that including all flexural, torsional and shear stiffnesses in the buckling force estimation gives a very precise prediction of the box compressive strength for the full range of package dimensions.

Role of Transverse Shear Modulus in the Performance of Corrugated Materials.

In a description of materials for orthotropic panels with a soft and/or corrugated core, it is important to correctly determine all constitutive parameters. In laboratory practice, the determination of transverse shear modulus is often overlooked. This paper presents a method for determining this property based on a plate torsion test and a correctly formulated analytical description. It has been proved that the transverse shear effect in some cases cannot be omitted because it significantly influences the mechanical behavior of corrugated board. The method of transverse shear modeling used so far can be modified to eliminate dimensionless, physically unjustified coefficient and replace them with coefficients that have a physical basis. It is shown here that such modification leads to results with lower error. The effective modeling of transverse shear effects enables a more conscious design of corrugated board structures, where the final goal is to obtain packaging with high strength and durability but low material consumption.

Numerical assessment of the human body response to a ground-level explosion.

This paper presents the results of a numerical analysis of the behaviour of a human body after a ground-level explosion. The explosions were generated by condensed charges for different stand-off distances and various masses of explosive. The detonations points were located at distances of 1.0 and 2.0 meters from the dummy (human model) obstacle. The different masses of spherically-shaped TNT charges (0.4-1.0 kg) were initiated centrally. The blast wave propagation was generated using a coupled numerical design, which included Eulerian and Lagrangian descriptions for different domains, i.e. the dummy, air, and explosive domains. The main objective of this work was to present the actual pressures and accelerations around the dummy and the body motion caused by the rapid shock of the pressure action. Reaction forces and moments of anatomical joints were provided. Furthermore, the safety criteria presented in the official standards were compared to the simulation results. In this research, different positions against the loading masses were analysed. In each analysis the same standing human model was used. The dummy geometry was based on a medium size male (1.79 m, 84.8 kg). The human body was modelled as consisting of separate, rigid parts (with adequate masses and inertia moments) connected by joints exhibiting nonlinear behaviour. Anatomical ranges of motion were taken into consideration, and a dedicated numerical technique was proposed to model the resistance moment vs. the range of motion relations for the most important human body joints.

The influence of the nylon balloon stiffness on the efficiency of the intra-aortic balloon occlusion.

In interventional procedures, the balloon inflation is used to occlude the artery and thus reduce bleeding. There is no practically accepted measure of the procedure efficiency. A finite element method model with state-of-the-art modelling techniques was built in order to predict the occlusion levels under the influence of different balloon inflation and its material stiffness. The geometries of a healthy human thoracic aorta and an occlusion balloon were idealized. The non-linear constitutive material of Gasser-Ogden-Holzapfel model was employed for the thoracic aorta; the balloon was model as the hyperelastic model. The realistic physiological blood pressure and the balloon inflation pressures were applied to simulate the different occlusion levels. The final outcome shows an important influence of the material stiffness on the balloon deformation and thus the occlusion efficiency.