TY - CHAP

T1 - R-adaptivity in limit analysis

AU - Muñoz, José J.

AU - Hambleton, James

AU - Sloan, Scott W.

N1 - Publisher Copyright:
© Springer International Publishing AG 2018. All Rights Reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2017/8/22

Y1 - 2017/8/22

N2 - Direct methods aim to find the maximum load factor that a domain made of a plastic material can sustain before undergoing full collapse. Its analytical solution may be posed as a constrained maximisation problem, which is computationally solved by resorting to appropriate discretisation of the relevant fields such as the stress or velocity fields. The actual discrete solution is though strongly dependent on such discretisation, which is defined by a set of nodes, elements, and the type of interpolation. We here resort to an adaptive strategy that aims to perturb the positions of the nodes in order to improve the solution of the discrete maximisation problem. When the positions of the nodes are taken into account, the optimisation problem becomes highly non-linear. We approximate this problem as two staggered linear problems, one written in terms of the stress variable (lower bound problem) or velocity variables (upper bound problem), and another with respect to the nodal positions. In this manner, we show that for some simple problems, the computed load factor may be further improved while keeping a constant number of elements.

AB - Direct methods aim to find the maximum load factor that a domain made of a plastic material can sustain before undergoing full collapse. Its analytical solution may be posed as a constrained maximisation problem, which is computationally solved by resorting to appropriate discretisation of the relevant fields such as the stress or velocity fields. The actual discrete solution is though strongly dependent on such discretisation, which is defined by a set of nodes, elements, and the type of interpolation. We here resort to an adaptive strategy that aims to perturb the positions of the nodes in order to improve the solution of the discrete maximisation problem. When the positions of the nodes are taken into account, the optimisation problem becomes highly non-linear. We approximate this problem as two staggered linear problems, one written in terms of the stress variable (lower bound problem) or velocity variables (upper bound problem), and another with respect to the nodal positions. In this manner, we show that for some simple problems, the computed load factor may be further improved while keeping a constant number of elements.

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U2 - 10.1007/978-3-319-59810-9_5

DO - 10.1007/978-3-319-59810-9_5

M3 - Chapter

AN - SCOPUS:85035357862

SN - 9783319598086

SP - 73

EP - 84

BT - Advances in Direct Methods for Materials and Structures

PB - Springer International Publishing

ER -