Abstract
A vector of residual forces of the ideally elastic-plastic structure at shakedown is obtained by solving the static analysis problem. A unique distribution of the residual forces is determined if the analysis is based on the minimum complementary deformation energy principle. However, the residual displacements developing in the shakedown process of ideally elastic-plastic structures under variable repeated loads can vary non-monotonically. Nevertheless mathematical models for the optimization problems of steel structures at shakedown must include the conditions for strength (safety) and stiffness (serviceability). Residual displacements determined by the plastic deformations are included in the stiffness conditions; therefore to improve the optimal solution it is necessary to determine upper and lower bounds of the residual displacement variations. This paper describes an improved methodology for estimating the variation bounds of the residual displacements at shakedown.
Highlights
The classic term “structural shakedown” implies understanding that paper refers to the ideal elastic-plastic structures subjected to variable repeated load F (t) (Casciaro, Garcea 2002; Chaaba et al 2010; Giambanco et al 2004; Koiter 1960; König 1987; Maier 1969; Polizzotto et al 1991; Raad, Weichert 1995; Staat, Heitzer 2003; Stein et al 1992; Weichert, Maier 2002)
Optimization problems of elastic-plastic steel structures subjected to Variable repeated load (VRL) are nonconvex mathematical programming problems (Atkočiūnas 2012; Rozvany 2011)
Residual displacements of structures at shakedown depend on loading history
Summary
The classic term “structural shakedown” implies understanding that paper refers to the ideal elastic-plastic structures subjected to variable repeated load F (t) (vectors are denoted as bold letters) (Casciaro, Garcea 2002; Chaaba et al 2010; Giambanco et al 2004; Koiter 1960; König 1987; Maier 1969; Polizzotto et al 1991; Raad, Weichert 1995; Staat, Heitzer 2003; Stein et al 1992; Weichert, Maier 2002). The residual displacements developing during shakedown process of ideally elastic-plastic structures under variable repeated load can vary non-monotonically. At shakedown state the total response due to a par- formulation is written on the basis of the minimum comticular load combination contains elastic and residual plementary deformation energy principle Sr,ζ T are self-balanced: 2012): of all statically admissible vectors Sr of residual forces, the actual one corresponds to the minimum of complementary deformation energy of the structure. Strength (yield) condition is verified of residual forces as follows: In this case, the following extreme problem corresponds to the in every design section i∈I , for every load combination principle:.
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