Bending plates at shakedown: analysing the residual displacements by the scanning method

Abstract

Structural elements (frames, plates, shells) during exploitation are acted by variable repeated load (VRL). Theory of the shakedown is investigating steel structures in the elastic-plastic state. Structure adapted to shakedown satisfies the strength requirements, however, there also can exist deformations and displacements, which do not match exploitation conditions (residual displacements can vary non-monotonically). Developing the scanning method allows to determine residual displacement limits of variation avoiding investigation of load history. The basis of the method: although plastic deformations can be accumulated from increments at different points of the yield surface, however, the final residual stresses depend only on the accumulated deformations and are not related to how they have emerged. The technique of the method: load area is divided into the scanning zones. The vertexes of the zone show intermediate load combinations in which the problem of plate static and kinematic formulation analysis have solved and obtained searchable values (residual stresses, plastic deformations and residual displacements). The idea of the scanning method is based on progressive analysis, i.e. by expanding the bound of load variation, the aim is to expand the zones of potential plastic deformations, each time determining the residual displacements (or their increments). If comparing the precise analysis of ideally elastic- plastic structure the scanning method is approximate, but it will allow to link the design of structures with strength and serviceability limit states. The scanning method is illustrated by a benchmark of bending circular steel plate; Mises yield condition is taken into account. Markings are according to the paper. Research has been done with the assumption of small displacements.