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Remarks on some properties of conic yield restrictions in limit analysis

Remarks on some properties of conic yield restrictions in limit analysis
Remarks on some properties of conic yield restrictions in limit analysis
A major difficulty when applying the kinematic theorem in limit analysis is the derivation of expressions of
the dissipation functions and the set of plastically admissible strains. At present, no standard methodology
exists. Here, it is shown that they can be readily obtained, provided that the yield restriction can be
rewritten as an intersection of cones, and that the expression defining the dual cones is available. This is
always possible for the case of self-dual cones and some other classes, and covers many of the well-known
criteria. Therefore, a difficult obstacle with respect to the use of the kinematic theorem in conjunction
with any numerical method can be overcome. The methodology is illustrated by giving the expressions of
the dissipation functions for various conic yield restrictions. A special emphasis is given on upper bound
finite element limit analysis. Taking advantage of duality in conic programming, we can obtain the dual
problem, where knowledge of the dual cone is not necessary. Therefore, this formulation is feasible for
any cone. Finally, it is interesting that the form of the dual problem, for varying yield strength within the
finite element, differs from that presented in other papers.
upper bound, dissipation function, conic optimization
1069-8299
1449-1461
Makrodimopoulos, Athanasios
ba87ad2d-2351-4bd4-bd22-de921b3a8070
Makrodimopoulos, Athanasios
ba87ad2d-2351-4bd4-bd22-de921b3a8070

Makrodimopoulos, Athanasios (2010) Remarks on some properties of conic yield restrictions in limit analysis. Communications in Numerical Methods in Engineering, 26 (11), 1449-1461. (doi:10.1002/cnm.1224).

Record type: Article

Abstract

A major difficulty when applying the kinematic theorem in limit analysis is the derivation of expressions of
the dissipation functions and the set of plastically admissible strains. At present, no standard methodology
exists. Here, it is shown that they can be readily obtained, provided that the yield restriction can be
rewritten as an intersection of cones, and that the expression defining the dual cones is available. This is
always possible for the case of self-dual cones and some other classes, and covers many of the well-known
criteria. Therefore, a difficult obstacle with respect to the use of the kinematic theorem in conjunction
with any numerical method can be overcome. The methodology is illustrated by giving the expressions of
the dissipation functions for various conic yield restrictions. A special emphasis is given on upper bound
finite element limit analysis. Taking advantage of duality in conic programming, we can obtain the dual
problem, where knowledge of the dual cone is not necessary. Therefore, this formulation is feasible for
any cone. Finally, it is interesting that the form of the dual problem, for varying yield strength within the
finite element, differs from that presented in other papers.

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More information

Submitted date: 18 July 2007
Published date: 2010
Keywords: upper bound, dissipation function, conic optimization

Identifiers

Local EPrints ID: 65036
URI: http://eprints.soton.ac.uk/id/eprint/65036
ISSN: 1069-8299
PURE UUID: b2339980-7b58-42a8-b4a7-e79bfd1b6579

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Date deposited: 28 Jan 2009
Last modified: 15 Mar 2024 12:05

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Author: Athanasios Makrodimopoulos

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