Formulation and solution of some plasticity problems as conic programs

By Kristian Krabbenhøft, Andrei Lyamin, Scott W. Sloan. 2007

360 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/18ec55a8da1a8494da7aa194616118a9c7e07efa

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In Biomedical Engineering

In Civil and Structural Engineering

In Computational Theory and Mathematics

Citations in the corpus

Second-order cone programming formulation for consolidation analysis of saturated porous media (2016, methodology): “theorem [51] following the work in [34,52].”
Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming (2018, methodology): “Thus, FELA with SOCP can be applied to 2D problems with yield criteria, including Tresca, Mohr‐Coulomb, and von Mises, and is established as more advantageous over FELA with LP in terms of computational efficiency and accuracy.(28) The LB FELA with SOCP approach was also developed for 2D problems wi”
Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming (2007, background): “the Mohr–Coulomb criterion may be cast in terms of two semidefinite constraints [7] R+ I 0 −R+ (k − a )I 0 (2)”
Limit analysis of masonry vaults by means of curved shell finite elements and homogenization (2008, background): “On the other hand, it is worth noting that recent trends in limit analysis have demonstrated that the linearization of the strength domain can be circumvented using conic/semidefinite programming (e.g. Makrodimopoulos and Martin, 2006; Krabbenhoft et al., 2007; Krabbenhoft et al., in press).”
Upper and lower bound limit analysis of plates using FEM and second-order cone programming (2010, methodology): “The algorithm is also suitable for solving lower-bound limit analysis since most of yield conditions can be cast as a conic constraint [20].”
Limit analysis of plates using the EFG method and second‐order cone programming (2009, background): “This algorithm is of particular interest in the field of limit analysis since most plasticity problems can be formulated as conic programming problems [22].”
Numerical lower bound shakedown analysis of engineering structures (2011, neutral): “in [22–25].”
Limit analysis of plates and slabs using a meshless equilibrium formulation (2010, background): “SECOND-ORDER CONE PROGRAMMING (SOCP) It was recognized in [28] that most commonly used yield criteria can be cast in the form of conic constraints, and optimization problems involving such constraints can be solved using highly efficient solvers [15].”