Abstract
An asymptotic theory of thin composite plates with multi-stage high-temperature phase transformations is proposed. The theory is based on an asymptotic analysis of 3-dimensional equations of the mechanics of composite materials, taking into account phase transformations. Phase transformations are described by a system of kinetic equations, which is solved in conjunction with the equations of internal heat and mass transfer. The so-called local problems for plate theory are obtained and the averaged equations of plate theory with phase transformations are derived. An example of a composite based on an aluminum-chromo-phosphate matrix under uneven heating is considered. A numerical-analytical solution showed that although the heating is uneven due to the peculiarities of phase transformations, the stress-strain state changes significantly in time and is variable across the plate thickness. The developed theory allows us to calculate the stress distribution in the plate with high accuracy.
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