Paper and board. Determination of bending stiffness. General principles for two-point, three-point and four-point methods

2012 ◽  
Keyword(s):  
Bending Stiffness

Anomalously low electrostatic bending stiffness of graphene oxide 2D membranes regulates its environmental fate in aquatic ecosystems

2021 ◽  
Author(s):  
Mohamad Ali Sanjari Shahrezaei ◽  
Seyed Mohammad-Reza Taheri ◽  
Hesam Nikfazan ◽  
Alexandra Satalov ◽  
Mohsen Moazzami Gudarzi ◽  
...  
Keyword(s):  
Graphene Oxide ◽  
Environmental Impact ◽  
Surface Waters ◽  
Aquatic Ecosystems ◽  
Environmental Fate ◽  
2D Materials ◽  
Bending Stiffness ◽  
High Importance

Though deemed to be of high importance for the determination of environmental impact of 2D materials upon their release into surface waters, control over the conformational engineering of atomically thin...

Tables for Frequencies and Modes of Free Vibration of Infinitely Long Thin Cylindrical Shells

1954 ◽  
Vol 21 (2) ◽  
pp. 178-184
Author(s):  
M. L. Baron ◽  
H. H. Bleich
Keyword(s):  
Free Vibration ◽  
Poisson’S Ratio ◽  
Cylindrical Shells ◽  
Bending Stiffness ◽  
Poisson's Ratio ◽  
Underlying Theory ◽  
Half Wave ◽  
Quick Determination ◽  
Circumferential Waves

Abstract Tables are presented for the quick determination of the frequencies and shapes of modes of infinitely long thin cylindrical shells. To make the problem tractable, the shells are first treated as membranes without bending stiffness, and the bending effects are introduced subsequently as corrections. The underlying theory is based on the energy expressions for cylindrical shells. The tables cover the following range: lengths of longitudinal half wave L from 1 to 10 radii a; number n of circumferential waves from 0 to 6. The results apply for Poisson’s ratio ν = 0.30.

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.

Stiffness and strength properties of five paperboards and their moisture dependency

TAPPI Journal ◽  
2020 ◽  
Vol 19 (2) ◽  
pp. 71-85
Author(s):  
GUSTAV MARIN ◽  
MIKAEL NYGARDS ◽  
SOREN OSTLUND
Keyword(s):  
Mechanical Properties ◽  
Mechanical Property ◽  
Shear Strength ◽  
Three Dimensional ◽  
Strength Properties ◽  
Bending Stiffness ◽  
Moisture Ratio ◽  
Machine Direction ◽  
Product Series

Five commercial multiply folding boxboards made on the same paperboard machine have been analyzed. The paperboards were from the same product series but had different grammage (235, 255, 270, 315, 340 g/m2) and different bending stiffness. The paperboards are normally used to make packages, and because the bending stiffness and grammage varies, the performance of the packages will differ. Finite element simulations can be used to predict these differences, but for this to occur, the stiffness and strength properties need to be deter-mined. For efficient determination of the three-dimensional properties in the machine direction (MD), cross direction (CD), and Z direction (ZD), it is proposed that the paperboard should be characterized using in-plane tension, ZD-tension, shear strength profiles, and two-point bending. The proposed setups have been used to determine stiff-ness and strength properties at different relative humidity (20,% 50%, 70%, and 90% RH), and the mechanical proper-ties have been evaluated as a function of moisture ratio. There was a linear relation between mechanical properties and moisture ratio for each paperboard. When the data was normalized with respect to the standard climate (50% RH) and plotted as a function of moisture ratio, it was shown that the normalized mechanical properties for all paperboards coincided along one single line and could therefore be expressed as a linear function of moisture ratio and two constants. Consequently, it is possible to obtain the mechanical properties of a paperboard by knowing the structural prop-erties for the preferred level of RH and the mechanical property for the standard climate (50% RH and 23°C).

Analysis and Optimization of Automotive Structure’s Bending Stiffness Using Beam Elements

2012 ◽  
Author(s):  
Steven Tebby ◽  
Ahmad Barari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Bending Stiffness ◽  
Major Drawback ◽  
Cross Sectional ◽  
Beam Elements ◽  
Complex Interactions ◽  
Design Changes ◽  
Vehicle Structure ◽  
Reaction Forces ◽  
Numerical Finite Element

Optimum design of vehicle’s structure is an important task in its development. The structure of a vehicle plays complex interactions with the other vehicle components and has significant impact on the performance of the vehicle. Structural design is usually completed by a complex iterative process. The design changes at late design stages effect many other parameters in the design of vehicle. Therefore, it is highly valuable for designers to employ simple but effective analyses at the early design stages. One method of analysis is using Simple Structural Surfaces. This method utilizes planar sheets to model the vehicle structure and allows the determination of the forces in each sheet. The major drawback of this method is its inability to easily determine deflections in a structure. To overcome this drawback a method that uses beam elements to represent the vehicle structure has been developed. This method uses a numerical finite element method and is able to determine unknown deflections and reaction forces as well as the internal loading on each member. This method can also be readily adapted to allow for parametric optimization for bending stiffness. The parameters associated with each beam element are the length, orientation and the beam characteristics of beams’ cross-sectional area and moment of inertia. An automated process is developed that manipulates some of these parameters to develop a structure that will have the greatest bending stiffness.

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