# Mathematical modeling of shape stability of parquet board glued with thermoplastic adhesives.

• Б.М. М’якуш
• Б.Я. Кшивецький

### Abstract

The article is concerned with block flooring. Special consideration is given to three-layered parquet board as a modern covering material for the floor. The advantages and disadvantages of using three-layered parquet boards are shown. Considering the design of this type of floorboard, due attention is paid to its shape stability. Therefore, the aim of this work is construction of a mathematical model of the operation-dependent shape stability of three-layered parquet board glued with thermoplastic polyvinyl acetate adhesives. The shape stability of parquet board depends on changes in its stress-strain state. That is why, in order to construct the mathematical model, we should consider the changes in stress-strain state of the structure of three-layered parquet board depending on the materials it is made of, the adhesive it is glued with, and the conditions it is operated in. To study stress-strain state, the parquet board is viewed as a three-layered plate for which mathematical modeling is applied to study its thermal state. Given are boundary conditions for the mathematical model, namely, the surface of the ends is heat insulated, boundary conditions on the top surface describe the interaction with the environment, the perfect slight contact is allowed be-tween the layers. To construct a model for determining the stress-strain state, Hooker’s law is used, while for modeling of shape stability a finite element method is applied, which provides for variational calculation of mathematical models based on the principle of a minimum of total potential energy. For the inner layer of the parquet board, the hypothesis of linearity is true for which the Caushy ratio is used. The computation of the local matrices of proximity was followed by building a global matrix. Based on the calculations results, a mathematical model was constructed to study the shape stability of three-layered parquet board glued with thermoplastic adhesives. Algorithmic aspects have been given for numerical realization of the mathematical model.

### References

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Published
2016-06-02
How to Cite
М’якуш, Б., & Кшивецький, Б. (2016). Mathematical modeling of shape stability of parquet board glued with thermoplastic adhesives. Problems of Tribology, 79(1), 42-47. Retrieved from http://tribology.khnu.km.ua/index.php/ProbTrib/article/view/512
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