This is an efficient tool for practical computation, especially for complicated structures subject to mechanical loads. The proposed algorithm gives results that are close to the results in literatures. In the preceding expression, the left equality occurs if the subsequent yield surface translates inside the bounding surface, the middle equality occurs if the subsequent yield surface fixed on the bounding surface and the last equality occurs when yield surface translates unboundedly.

If the structure shakes down in alternating plasticity mode, then there is no difference between perfectly plastic and kinematic hardening models. Ing-Arch , 8: — Prager W: A new method of analyzing stress and strain in work hardening plastic solids. Maier GA: Shakedown matrix theory allowing for work hardening and second-order geometric effects. In Foundations of plasticity.

Edited by: Sawczuk A. North-Holland, Amsterdam: Springer; — Ponter ARS: A general shakedown theorem for elastic plastic bodies with work hardening. In Inelastic behaviour of structures under variables loads.

Springer, Netherlands: Kluwer Academic Publishers; — Int J Mech Sci , — Pham DC: Shakedown static and kinematic theorems for elastic-plastic limited linear kinematic-hardening solids. Pham DC: Shakedown theory for elastic plastic kinematic hardening bodies. Int J Plast , — Nguyen QS: On shakedown analysis in hardening.

J Mech Phys Solids , — Staat M, Heitzer M: The restricted influence of kinematic hardening on shakedown loads. Volume Stein E, Zhang G: Theoretical and numerical shakedown analysis for kinematic hardening materials. In Proc. Barcelona, Spain: Pineridge Press; — Yan AM, Nguyen Dang H: Direct finite element kinematical approaches in limit and shakedown analysis of shells and elbows. Int J Num Mech Engng , — NIC Series.

## Inelastic Analysis of Structures

Comp Appl Mech Eng , 1 Nr. Int J Solids Struct , 41 1 — In Complimentarily, duality and symmetry in nonlinear mechanics. Volume 6. Edited by: David Y. PhD Thesis. In Direct Methods. Netherlands: Springer; Int J Numer Mech Engng , — Int J Numer Engng , — Download references. Reprints and Permissions. Search all SpringerOpen articles Search.

Abstract This paper develops a new finite element method FEM -based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. Background Shakedown analysis for hardening structures has been investigated by many researchers. Methods Bounded kinematic hardening model For kinematic hardening model, the initial yield surface can translate in the multi-axial stress space, without changing its shape and size.

Figure 1. Unbounded kinematic hardening model. Full size image. Figure 2. A simple two-surface plasticity with fixed bounding surface. Results and discussions Two examples are reported. Figure 3. Continuous beam. Figure 4.

## Publikationen - Institut für Allgemeine Mechanik

Load domain for example 4. Figure 5. FEM mesh. Table 1 Comparison of plastic limit collapse and shakedown results Full size table.

## Engineering Transactions

Figure 6. Figure 7. FEM mesh of cylindrical pipe. Figure 8. Figure 9.

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Table 2 Limit and shakedown load multipliers of cylindrical pipe subjected to internal pressure and bending Full size table. Conclusions The paper developed a new upper bound algorithm for shakedown analysis of elastic plastic-bounded linearly kinematic hardening structures.

References 1. Article Google Scholar 2. MathSciNet Google Scholar 3.

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