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Fast and robust RSDM shakedown solutions of structures under cyclic variation of loads and imposed displacements. (English) Zbl 07537293

Summary: The Residual Stress Decomposition Method (RSDM) is an iterative numerical procedure developed to directly estimate the kind of asymptotic stress states under cyclic loading of inelastic structures. The method has been modified (RSDM-S) to establish safety margins for elastic shakedown under mechanical and/or thermal loads. In the present work, the formulation of the shakedown problem to account for the coexistence of loads and imposed displacements is presented. An updated RSDM-S procedure in terms of robustness and computational efficiency is also proposed. It is proved that a monotonically decreasing sequence of the iterative steps is created that converges to the shakedown loading factor, thus making the procedure absolutely robust. Based on the monotonicity, a numerical scheme with proven super-linear convergence is suggested that renders the approach very fast. The procedure is then applied to structures under cyclic loadings of loads combined with applied displacements. Shakedown domains, not frequently met in the literature under these two actions, are constructed. Additionally, shakedown values of displacements, simulating quasi-static earthquake loading on structural components, are estimated.

MSC:

74S99 Numerical and other methods in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
74K30 Junctions

Software:

FEAP
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