Development of mathematical models for predicting dimensional stability of furniture boards using the finite element method

T.I. Podibka

doi:10.36930/42214809

Authors

T.I. Podibka

DOI:

https://doi.org/10.36930/42214809

Keywords:

furniture panel, lamella, beech (Fagus sylvatica L.), technology, gluing, form of stability, modeling, forecasting, splicing, anisotropy, wood properties, mathematical model, heat-and-moisture transfer, finite element method, iterative method, stress, deformation, orthotropic materials, polyvinyl acetate adhesives, adhesive wooden joint, strength, humidity, temperature.

Abstract

An approach for predicting the properties of furniture boards made of common beech wood (Fagus sylvatica L.) based on the finite element method is proposed. It has been found that in the constructions of furniture panels made of beech wood, an orthogonal, cylindrical or transversal calculation scheme of anisotropy can be attributed depending on the dimensions of the furniture panels and the orientation of the fibers in the rails. A model of the physical and mechanical properties of monolithic or jointed slats made of beech wood during the finite element analysis of furniture boards based on the cylindrical coordinate system of the anisotropy of constant elasticity is proposed. It has been established that the practical use of the cylindrical anisotropy scheme when solving the problems of the mechanics of a rigid deformed body for the calculation of furniture boards made of beech wood is expedient when it is not possible to ignore the curvature of the annual layers, that is, when analyzing the dimensional stability of furniture boards and monolithic or jointed reibukaak made of beech wood with swelling and shrinkage. An applied methodology for calculating furniture boards made of beech wood has been developed, which makes it possible to take into account the peculiarities of the anisotropy of the physical and mechanical characteristics of the rails, taking into account their shrinkage and swelling when the temperature and humidity conditions of the environment change. The substantiation of new designs of furniture boards made of beech wood, which is based on the use of finite element analysis systems, allows identifying the shortcomings of these products at the conceptual stage of the project and correcting them before the start of production, taking into account the specified technical conditions. An optimal arrangement scheme of annual layers in adjacent slats of furniture panels made of beech wood is proposed, which ensures improvement of dimensional stability (reduction of gouging) of the structure while simultaneously reducing the stresses that arise when the humidity of the product increases during operation. Mathematical models are proposed that predict (describe) the strength and dimensional stability of furniture boards made of common beech wood. The developed model can be used for research and optimization of furniture boards of new designs according to the conditions of strength and deformability.

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