Задача о склейке двух пластин Кирхгофа–Лява

An equilibrium problem of two parallel elastic plates is considered in the paper. The plates are located without a gap and have the same size and shape. They are clamped at their edges and joined to each other along a straight interval. The deflections of the plates satisfy the nonpenetration condition. The case is considered when at the contact surface of the plates not only the lateral load from another plate, but also additional elastic force acts. It is assumed that this elastic force acts both in contact plane and orthogonal to it, and its value is characterized by a so-called damage parameter. Two extreme cases are studied when the parameter equals zero or tends to infinity. The first case corresponds to contact without friction of two plates. The second one corresponds to equilibrium of two-layer plate. The strong convergence of the solutions sequence of equilibrium problem of two plates with elastic force acting at the contact surface to the solutions of extreme problem is proved when the damage parameter tends to zero or to infinity. For the case of the contact without friction singular solution is found near the tip of the interval along which the plates are glued.