An analytical form for presenting a filler for three-layer systems, consisting of staggered cone-shaped elements

DOI: 10.34759/trd-2022-123-04

Аuthors

Zotov A. A.

e-mail: aa-zotov@inbox.ru

Abstract

This paper considers the problem of analytical determination for the stiffness characteristics due to the use of a filler in the form of a regular cone-shaped (or pyramidal) cell’s system arranged in a checkerboard pattern for three-layer plates

At the moment, the most widespread are honeycomb, corrugated or folded fillers. The main filler’s advantages are low weight and high rigidity. However, there are circumstances that prevent their wider use. The closed volume formed by the core’s cells e promotes the accumulation of condensate, at the same time preventing its removal. On the other hand, there are technological difficulties associated with the provision and control of a reliable connection between a filler and bearing layers (especially on curved surfaces), thereby increasing the product cost. The structure of the cellular filler considered in the article largely allows to solve the above problems.

Due to the complexity and laboriousness of solving strength and stability problems for systems of variable stiffness, analytical solutions for a wide class of such structures are practically absent or hardly applicable in solving problems related to the design of products.

The article proposes a method for analytical filler’s representation in the form of a regular discrete cone-shaped cell’s system, with the aim of further determining the geometric properties.

Based on the analysis of the filler’s shape under study, contemplation its shape as a surface described by the trigonometric Fourier series was proposed. However, upon further analysis of the problem, it was possible to reduce the function describing the filler’s geometry to a simpler form. The final version of the shape function was a set of coefficient, cosine and sine. Filler’s representation in the form of a similar function allows one to determine the variable bending stiffness of a three-layer package when solving the problems of bending of plates with variable stiffness.

Representation of the shape of the considered filler in this form with high accuracy conveys the true geometry of the product and allows to analytically describe the geometric stiffness characteristics of the structure (areas, moments of inertia and static section moments) included in the differential equations of bending and buckling of a variable stiffness plate.

Keywords:

rectangular three-layer plate, analytical methods, stress-strain state, strength, buckling

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