Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques

Abstract

The shakedown theory for dynamic external actions is expounded considering elastic-plastic internal-variable material models endowed with hardening saturation surface and assuming small displacements and strains as long with negligible effects of temperature variations on material data. Two sorts of dynamic shakedown theories are presented, i.e.: i) Unrestricted dynamic shakedown, in which the structure is subjected to (unknown) sequences of short-duration excitations belonging to a known excitation domain, with no-load no-motion time periods in between and for which a unified framework with quasi-static shakedown is presented; and ii) Restricted dynamic shakedown, in which the structure is subjected to a specified infinite-duration load history. Two general bounding principles are also presented, one is non evolutive in nature and holds for repeated loads below the shakedown limit, the other is evolutive and holds for a specified load history either below and above the shakedown limit. Both principles are applicable in either statics and dynamics to construct bounds to the actual plastic deformation parameters. A continuum solid mechanics approach is used throughout, but a class of discrete models (finite elements with piecewise linear yield and saturation surfaces and plastic deformability lumped at Gauss points) are also considered. Extensions of shakedown theorems to materials with temperature dependent yield and saturation functions are also presented.