The Boundary Condition Influence on a Stress-Strain State of a Corrugated Plate on an Elastic Foundation

Abstract

In this paper, we consider the influence of the conditions for fixing a wavy plate lying on an elastic foundation on its stressed-deformed state. The profiled plates are widely used in construction practice as fencing structures, for siding works, for roofing and others. The stress-strain state of the wavy plates varies depending on geometry, materials mechanical properties, foundation characteristics and boundary condition. Steel with polymer coatings, which make the sheets a decorative material, is increasingly used in individual and low-rise buildings. The elastic foundation is considered as Winkler base, so we suppose that the reaction of the base is directly proportional to the deflection of the plate at each point. The Bubnov-Galerkin method is used to determine the stress-strain state of the plate. To solve the problem, we use special orthogonal Legendre polynomials satisfying the boundary conditions: simply supported and clamped edges. The results of the calculations were compared for different types of fixation.