Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler

Abstract

Objective. In most cases, when determining the stress-deformed state of three-layer structures, it is assumed that bearing layers obey the Kirchhoff-Love hypothesis, while a filler obey the Neit (vanderNeit), or “broken line”, hypothesis. But in many cases, the results of our research show that this is not always accurate. Methods. It is proposed to solve the three-dimensional problem of determining the stress-deformed state of a three-layer structure using cubic functions of the law of aggregate deformation distribution along the normal line, obtained on the basis of the law of deformation compatibility at “filler – bearing layer” boundaries and the construction of boundary conditions in joint zones. Results. Equilibrium equations of a three-layer beam obtained on the basis of this hypothesis are shown in Table 1. The given partial differential equations are of the 12th order and we transformed them into homogeneous equations of the 1st order to simplify the solution. This solution is implemented using the mathematical modelling software package Mаple 5.4. Conclusion. The work of the filler in the direction of OX axis has a certain value, which affects the overall stress state of the three-layer structure (in existing hypotheses, it is zero).

Keywords

• three-layer structure
• bearing layer
• filler
• hypothesis
• stress-deformed state
• equilibrium equations