Limit and Shakedown Analysis of Thin Plates under Random Strength by Probabilistic Constrained Programming
Received: 11 November 2024 | Revised: 9 January 2025 | Accepted: 12 January 2025 | Online: 22 March 2025
Corresponding author: Hoang An Le
Abstract
This work presents a new model for the shakedown analysis of Kirchhoff plates under uncertain conditions of the plastic moment by the direct method. The stochastic models of the plastic moment are normal or lognormal distribution. New formulations are derived to compute the lower bound and upper shakedown loads and a dual algorithm is established to calculate the upper and lower bound shakedown load factors simultaneously for a chosen structural reliability level. An example is examined to illustrate the algorithm and shows robust results of the stochastic analysis.
Keywords:
plates, limit load, shakedown, reliability, stochastic programming, chance constraintsDownloads
References
E. N. Fox and J. R. Baker, "Limit analysis for plates: the exact solution for a clamped square plate of isotropic homogeneous material obeying the square yield criteron and loaded by uniform pressure," Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 277, no. 1265, pp. 121–155, Jan. 1997.
P. G. Hodge Jr. and T. Belytschko, "Numerical Methods for the Limit Analysis of Plates," Journal of Applied Mechanics, vol. 35, no. 4, pp. 796–802, Dec. 1968.
J. Bleyer, "A novel upper bound finite-element for the limit analysis of plates and shells," European Journal of Mechanics - A/Solids, vol. 90, Nov. 2021, Art. no. 104378.
A. Makrodimopoulos, "An upper bound limit analysis formulation for thin plates," Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, vol. 168, no. 4, pp. 133–143, Dec. 2015.
K. Krabbenhoft and L. Damkilde, "A general non-linear optimization algorithm for lower bound limit analysis," International Journal for Numerical Methods in Engineering, vol. 56, no. 2, pp. 165–184, 2003.
C. V. Le, M. Gilbert, and H. Askes, "Limit analysis of plates using the EFG method and second-order cone programming," International Journal for Numerical Methods in Engineering, vol. 78, no. 13, pp. 1532–1552, 2009.
C. V. Le, H. Nguyen-Xuan, and H. Nguyen-Dang, "Upper and lower bound limit analysis of plates using FEM and second-order cone programming," Computers & Structures, vol. 88, no. 1, pp. 65–73, Jan. 2010.
A. A. Abdulhussein and M. H. Al-Sherrawi, "Experimental and Numerical Analysis of the Punching Shear Resistance Strengthening of Concrete Flat Plates by Steel Collars," Engineering, Technology & Applied Science Research, vol. 11, no. 6, pp. 7853–7860, Dec. 2021.
A. N. Dalaf and S. D. Mohammed, "The Impact of Hybrid Fibers on Punching Shear Strength of Concrete Flat Plates Exposed to Fire," Engineering, Technology & Applied Science Research, vol. 11, no. 4, pp. 7452–7457, Aug. 2021.
N. T. Tran and M. Staat, "Direct plastic structural design under random strength and random load by chance constrained programming," European Journal of Mechanics - A/Solids, vol. 85, Jan. 2021, Art. no. 104106.
17 E. Melan, Theorie statisch unbestimmter Systeme aus idealplastischem Baustoff. Hölder-Pichler-Tempsky in Komm., 1936.
M. A. Save, C. E. Massonnet, and G. de Saxce, Plastic Limit Analysis of Plates, Shells and Disks. Amsterdam, Netherlands: Elsevier, 1997.
W. T. Koiter, "General theorems for elastic plastic solids," in Progress in Solid Mechanics. IAmsterdam, Netherlands: North-Holland Press, 1960, pp. 165–221.
K. D. Andersen, E. Christiansen, and M. L. Overton, "Computing Limit Loads by Minimizing a Sum of Norms," SIAM Journal on Scientific Computing, vol. 19, no. 3, pp. 1046–1062, Jan. 1998.
S. Kataoka, "A Stochastic Programming Model," Econometrica, vol. 31, no. 1/2, pp. 181–196, 1963.
M. Jirasek and Z. P. Bazant, Inelastic Analysis of Structures. New York, NY, USA: John Wiley & Sons, 2001.
K. W. Johansen, Pladeformler (yield-line formulae for slabs). London, UK: Cement and Concrete Association, 1968.
Å. Ingerslev, "Om en elementær beregningsmetode af krydsarmerede plader," Ingeniøren, vol. 30, no. 69, pp. 507–515, 1921.
J. Lubliner, Plasticity Theory. New York, NY, USA: Dover, 2008.
Downloads
How to Cite
License
Copyright (c) 2025 Ngoc Trinh Tran, Manfred Staat, Hoang An Le
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
