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The development of modern commodity economy has promoted the circulation of goods. In order to avoid damage in the process of commodity transportation, cushioning packaging technology came into being. Cushioning packaging plays an important role in product packaging. With the enhancement of people's awareness of environmental protection, many countries have proposed to use paper cushioning materials with good environmental compatibility

due to its rich raw materials, corrugated board is easy to be mass produced, processed and cut into various shapes and sizes, and has good cushioning performance. In particular, it can be recycled without waste and pollution. It is a typical green cushioning packaging material. In transportation and packaging, corrugated cardboard accounts for a large proportion, and is widely used to make various cushioning packaging structural parts. Its application methods mainly include corrugated boxes, cushioning pads, pallets, etc. At present, corrugated cardboard liner has been widely used in cushioning packaging

corrugated board has the following three structural characteristics:

(1) it has multiphase, and the market capacity of plastic extruder will be further expanded, including solid phase, liquid phase and gas phase

(2) anisotropic

(3) corrugated cardboard sandwich board structure

this spatial structure feature of corrugated board directly affects the mechanical properties of corrugated board liner, especially the properties closely related to cushioning packaging, such as static compression characteristics, dynamic impact characteristics and vibration transmission characteristics

according to the spatial structure characteristics of corrugated board liner, the corrugated board liner is approximately regarded as a thin plate with orthotropic from the macro perspective, and it is theoretically analyzed by using the orthotropic plate theory, which makes a breakthrough in the previous analysis of corrugated board liner, and provides a new analysis method for analyzing the cushioning performance of corrugated board liner

second, analysis of orthotropic plate

corrugated cardboard liner can be approximated as a thin plate with orthotropic in macro view, so it can be studied by thin plate theory. Throughout the development of thin plate theory, there are two research methods. One is the mathematical elasticity theory of classical plane problems represented by Cauchy and Poisson; The other is the engineering thin plate theory represented by Kirchhoff. The latter is an important branch of applied elasticity, which is also the theoretical basis of this paper

The small deflection bending theory of elastic thin plates is based on Kirchhoff hypothesis. The basic assumptions of thin plate theory are as follows:(1) assume that the plate material is a uniform and continuous ideal elastomer

(3) it is assumed that there is no in-plane deformation (expansion or shear deformation) on the middle surface of the plate when the thin plate is bent, which is the property of rigid plate bending

(4) straight normal assumption: the straight line segment perpendicular to the middle surface of the plate before deformation is still a straight line segment after deformation, and it is still perpendicular to the middle surface after deformation, and the length of the straight line segment remains unchanged

(5) it is assumed that there is no extrusion in the parallel interlaminar deformation of the middle plane of the plate, that is, the normal stress perpendicular to the middle plane of the plate is ignored σ 2。

in order to investigate the equilibrium condition of the orthotropic plate, the differential faceelement is intercepted on the middle surface of the plate, which can be expressed by the micro area DXDY of the middle surface, and the internal force and internal moment acting on each side of the differential faceelement are shown in the figure below

equation (8) is the equilibrium differential equation of the bending theory of a large amount of chemical raw materials in China's chemical market rising in turn under the vertical load of the orthotropic plate, that is, the differential equation of the transverse vibration control of the orthotropic plate

using Navier solution, the expression of deflection can be obtained from formula (8), and the deflection can be solved, so that the corresponding parameters such as stress and strain can be obtained. According to the relationship between stress, strain and buffer coefficient, the buffer coefficient is obtained, and the adjustment or increase or decrease of the sizing block under the base is analyzed. Therefore, the cushioning characteristics of corrugated cardboard liner can be analyzed, which provides a theoretical basis for the cushioning packaging design of corrugated cardboard liner

source: China Association of food and packaging machinery

Author: Ma Yanping unit: School of printing and packaging, Xi'an University of Technology

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