@incollection{pham_upper_2013,
	address = {Dordrecht},
	title = {An upper bound algorithm for limit and shakedown analysis of bounded linearly kinematic hardening structures},
	volume = {2},
	copyright = {All rights reserved},
	isbn = {978-94-007-5424-9},
	url = {http://link.springer.com/10.1007/978-94-007-5425-6 http://link.springer.com/10.1007/978-94-007-5425-6_4},
	abstract = {The paper develops a new FEM based algorithm for shakedown analysis of structures made of elastic plastic bounded linearly kinematic hardening material. The hardening effect is simulated by using a two-surface plastic model to bound the Melan-Prager model. The initial yield surface can translate inside the bounding surface, without changing its shape and size. The translated yield surface may touch the bounding surface and ratcheting may occur with clear benefit of hardening. Or it may not touch the bounding surface, alternating plasticity may occur and there is no effect of hardening. The direct calculation of plastic limit and shakedown bounds is considered as a nonlinear programming problem. The upper bound of the shakedown load is obtained as the minimum of the plastic dissipation function, which is based on the von Mises yield criterion.},
	booktitle = {Limit {State} of {Materials} and {Structures}},
	publisher = {Springer Netherlands},
	author = {Phạm, Phu Tinh and Staat, Manfred},
	editor = {de Saxcé, Géry and Oueslati, Abdelbacet and Charkaluk, Eric and Tritsch, Jean-Bernard},
	year = {2013},
	doi = {10.1007/978-94-007-5425-6_4},
	note = {ZSCC: NoCitationData[s0] },
	pages = {71--87},
}

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The initial yield surface can translate inside the bounding surface, without changing its shape and size. The translated yield surface may touch the bounding surface and ratcheting may occur with clear benefit of hardening. Or it may not touch the bounding surface, alternating plasticity may occur and there is no effect of hardening. The direct calculation of plastic limit and shakedown bounds is considered as a nonlinear programming problem. The upper bound of the shakedown load is obtained as the minimum of the plastic dissipation function, which is based on the von Mises yield criterion.","booktitle":"Limit State of Materials and Structures","publisher":"Springer Netherlands","author":[{"propositions":[],"lastnames":["Phạm"],"firstnames":["Phu","Tinh"],"suffixes":[]},{"propositions":[],"lastnames":["Staat"],"firstnames":["Manfred"],"suffixes":[]}],"editor":[{"propositions":["de"],"lastnames":["Saxcé"],"firstnames":["Géry"],"suffixes":[]},{"propositions":[],"lastnames":["Oueslati"],"firstnames":["Abdelbacet"],"suffixes":[]},{"propositions":[],"lastnames":["Charkaluk"],"firstnames":["Eric"],"suffixes":[]},{"propositions":[],"lastnames":["Tritsch"],"firstnames":["Jean-Bernard"],"suffixes":[]}],"year":"2013","doi":"10.1007/978-94-007-5425-6_4","note":"ZSCC: NoCitationData[s0] ","pages":"71–87","bibtex":"@incollection{pham_upper_2013,\n\taddress = {Dordrecht},\n\ttitle = {An upper bound algorithm for limit and shakedown analysis of bounded linearly kinematic hardening structures},\n\tvolume = {2},\n\tcopyright = {All rights reserved},\n\tisbn = {978-94-007-5424-9},\n\turl = {http://link.springer.com/10.1007/978-94-007-5425-6 http://link.springer.com/10.1007/978-94-007-5425-6_4},\n\tabstract = {The paper develops a new FEM based algorithm for shakedown analysis of structures made of elastic plastic bounded linearly kinematic hardening material. The hardening effect is simulated by using a two-surface plastic model to bound the Melan-Prager model. The initial yield surface can translate inside the bounding surface, without changing its shape and size. The translated yield surface may touch the bounding surface and ratcheting may occur with clear benefit of hardening. Or it may not touch the bounding surface, alternating plasticity may occur and there is no effect of hardening. The direct calculation of plastic limit and shakedown bounds is considered as a nonlinear programming problem. The upper bound of the shakedown load is obtained as the minimum of the plastic dissipation function, which is based on the von Mises yield criterion.},\n\tbooktitle = {Limit {State} of {Materials} and {Structures}},\n\tpublisher = {Springer Netherlands},\n\tauthor = {Phạm, Phu Tinh and Staat, Manfred},\n\teditor = {de Saxcé, Géry and Oueslati, Abdelbacet and Charkaluk, Eric and Tritsch, Jean-Bernard},\n\tyear = {2013},\n\tdoi = {10.1007/978-94-007-5425-6_4},\n\tnote = {ZSCC: NoCitationData[s0] },\n\tpages = {71--87},\n}\n\n","author_short":["Phạm, P. 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