Averaging of an orthotropic elastic plate weakened by periodic hinges of finite stiffness

A formal asymptote of a solution of the title problem is constructed using the averaging method of N. S. Bakhvalov. The averaged equation is of an elliptic type; for small stiffness of the hinge, it is singularly perturbed, and for zero stiffness of the hinge, it is of a composite type. For the first boundary-value problem, a solution of the original problem is proved to converge to that of the limiting problem. A situation where natural boundary conditions are specified for the composite equation is treated. It is shown that the solution space of the homogeneous problem is infinite-dimensional.