Analysis of pressure equipment by application of the primal-dual theory of shakedown. (English) Zbl 1107.74007

Summary: The paper describes the application of the primal-dual theory of limit and shakedown analysis in safety assessment and design of pressure components according to the new European approach to design by analysis. Two methods, the static and kinematic one, and their combination, the primal-dual method, are discussed. A numerical example is presented to show the robustness of the primal-dual method compared with two other methods recently used in two European projects on safety assessment and design.


74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74S05 Finite element methods applied to problems in solid mechanics
74R20 Anelastic fracture and damage


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[1] Maier, Shakedown theory in perfect elastoplasticity with associated flow-laws, Meccanica 4 pp 250– (1969) · Zbl 0219.73039
[2] Yan, NIC Series, in: Numerical Methods for Limit and Shakedown Analysis pp 85– (2003)
[3] Andersen, An efficient primal-dual interior-point method for minimizing a sum of Euclidean norms, SIAM Journal on Scientific Computing 22 pp 243– (2000) · Zbl 0966.65053
[4] Zouain, An iterative algorithm for limit analysis with nonlinear yield functions, International Journal of Solids and Structures 30 pp 1397– (1993) · Zbl 0773.73032
[5] 2000
[6] Taylor, The Design-by-Analysis Manual; Report EUR 19020 EN (1999)
[7] Staat M Schwarz M Lang H Wirtz K Heitzer M Design by analysis of pressure components by nonlinear optimization 2003 59 65
[8] Heitzer, NIC Series, in: Numerical Methods for Limit and Shakedown Analysis pp 1– (2003)
[9] Vu DK Dual limit and shakedown analysis of structures 2002
[10] Vu, A dual form for discretized kinematic formulation in shakedown analysis, International Journal of Solids and Structures 41 pp 267– (2004) · Zbl 1069.74005
[11] Vu, A primal-dual algorithm for shakedown analysis of structures, Computer Methods in Applied Mechanics and Engineering 193 pp 4663– (2004) · Zbl 1112.74546
[12] König, Shakedown of Elastic-Plastic Structures (1987)
[13] 2000
[14] Muscat M Computational methods of design by analysis for pressure vessel components 2002
[15] Boulbibane, Finite element analysis and evaluation of design limits for structural materials in a cyclic state of creep, International Journal for Numerical Methods in Engineering 58 pp 2065– (2002) · Zbl 1027.74062
[16] Stein, Shakedown with nonlinear strain-hardening including structural computation using finite element method, International Journal of Plasticity 8 pp 1– (1992) · Zbl 0766.73026
[17] Heitzer, Basis reduction for the shakedown problem for bounded kinematic hardening material, Journal of Global Optimization 17 pp 185– (2000) · Zbl 1011.74009
[18] Staat, Local and global collapse pressure of longitudinally flawed pipes and vessels, International Journal of Pressure Vessels Piping 82 (3) pp 217– (2005)
[19] Staat, Limit analysis of flaws in pressurized pipes and cylindrical vessels. Part I: Axial defects, Engineering Fracture Mechanics (2006)
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