Bending of a wavy plate of a periodic profile on an elastic foundation

As a roofing material profiled sheets are most often used in large areas in industrial and civil construction. The weight of snow on the roof, especially in snow-covered regions of Russia, can exceed the weight of the roof itself, so it is necessary to take into account the snow load in the winter period in calculations for strength and rigidity. Nowadays the steel with polymer coatings, which give the sheets more decorative, is increasingly used in individual and low-rise buildings. To increase the rigidity of metal sheets, they undergo profiling, wavy shaping. In this paper, we consider the bending of a wavy plate on an elastic foundation rigidly clamped along the edges. Plate in the plan has a rectangular form. The plate material is isotropic. For the calculation scheme of the receiving orthotropic plate, take different cylindrical stiffness in two mutually perpendicular directions. The elastic foundation is adopted by Winkler, so it is believed that the reaction of the base is directly proportional to the deflection of the plate at each point. To determine the deflection, the Bubnov-Galerkin method is used. To solve the problem, we use special orthonormal Legendre polynomials satisfying the boundary conditions. Investigations of the stress-strain state of a wavy plate loaded with a distributed load depending on the amplitude, the length of the half-wave and the modulus of subgrade reactions, as well as the stress-strain state of the flat plate, were carried out.