A three-dimensional analysis of laminated orthotropic plates

A mathematical apparatus is developed for the analysis of the three-dimensional stress–strain state with small deflections of laminated orthotropic plates of any thickness and non-symmetrical layer structure through the thickness. This theory is based on the representation of the displacement vector in terms of products of the given functions in the direction of the axes x1, x2 and the unknown functions over the axis x3. Both the real and complex roots of the characteristic equation describing the representation of the sought functions through the thickness of the plate are taken into account. Such an approach allows us to expand the scope of physical and mechanical relationships among the material characteristics.