Asymptotic theory of constructive-orthotropic plates with two-periodic structures

The theory of thin constructive-orthotropic plates with a two-periodic structure was suggested. Examples of such structures are honeycomb sandwich panels and backed plates. The theory is based on equations of a three-dimensional elasticity theory with the help of asymptotic expansions in terms of a small parameter being the ratio of a plate thickness and a characteristic length without introducing any hypotheses on a distribution character for displacements and stresses through the thickness. Local problems were formulated for finding stresses in all structural elements of a plate. It was shown that the global (averaged by the certain rules) equations of the plate theory are similar to equations of the Kirchhoff-Love plate theory, but they differs by a presence of three-order derivatives of longitudinal displacements. The method developed allows to calculate all 6 components of the stress tensor including transverse normal stresses and stresses of interlayer shear. For this, local problems should be solved numerically up to the third approximation. The example was demonstrated for finite-element solving the local problems of the zero approximation for a cellular structure, which showed that the developed method for plate calculation and its numerical realization are sufficiently effective - they allow us to conduct computations for complex constructive-orthotropic plates with very different values of elastic characteristics.