A general non‐linear optimization algorithm for lower bound limit analysis

By Kristian Krabbenhøft, Lars Damkilde. 2003

194 citations recorded by the source corpus.

Subfields: Building and Construction, Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e6d0511dbb7c32179448bdc0ec93d3d4c62f41c5

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Citations in the corpus

Lower bound limit analysis with adaptive remeshing (2005, methodology): “Because the objective function and equality constraints are linear, and the functions fj are convex, problem (3) is equivalent to the system of Karush–Kuhn–Tucker (KKT) optimality conditions [11, 12] BT = p + p0 f( ) 0 ⎫⎬ ⎭ primal-lower bound Bu − ∇f( ) = 0 pTu = 1 0 ⎫⎪⎪⎬ ⎪⎪⎭ dual-‘upper bound’ f( )”
Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming (2006, methodology): “Krabbenhoft and Damkilde [26] also included a cohesive-frictional example problem, but they did not discuss how the apex of the yield surface was treated (it appears that they employed a ‘squared’ form of the Mohr–Coulomb criterion, and this is discussed in more detail in Section 3.”
Mesh adaptive computation of upper and lower bounds in limit analysis (2008, methodology): “Since the formulation in [17] coincides with the lower bound approach presented in this article, the numerical results are the same when uniform meshing is used.”
An edge‐based smoothed finite element method for primal–dual shakedown analysis of structures (2010, unknown): “[4, 5].”
Second-Order Cone and Semidefinite Representations of Material Failure Criteria (2007, methodology): “Some recent methods, based on interior-point methods (IPMs), treat wide classes of criteria [33, 34].”
An interior‐point algorithm for elastoplasticity (2007, methodology): “More elaborate rules are given in the interior-point literature, see, e.g. References [42–44, 66] and references therein.”
A new discontinuous upper bound limit analysis formulation (2005, methodology): “The velocity jumps between the elements in Reference [9] were constrained to comply with the appropriate flow rule, and the total internal rate of dissipation, i.e. comprising contributions from both the triangular elements and the discontinuities, was minimized in an → min type problem similar to (”
Shakedown analysis of engineering structures with limited kinematical hardening (2012, methodology): “Since not all problems can be formulated as SOCP and for efficiency reasons, alternative algorithms have been presented (Zouain et al., 2002; Lyamin and Sloan, 2002; Krabbenhøft and Damkilde, 2003; Vu et al., 2004; Akoa et al., 2007; Krabbenhøft et al., 2007c; Vu and Staat, 2007; Pastor et al., 2008”
Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading (2009, methodology): “Early numerical methods for limit analysis were developed more than thirty years ago [2, 23], but more recently these problems have gained increasing attention (see for instance references [3, 5, 15 , 20, 24]).”
A cell‐based smoothed finite element method for kinematic limit analysis (2010, background): “[54] and became a popular benchmark test for plastic analysis procedures, particularly for rigid-plastic limit analysis [2, 3, 5, 55, 56].”
Numerical lower bound shakedown analysis of engineering structures (2011, unknown): “[26–34].”
Limit analysis of plates and slabs using a meshless equilibrium formulation (2010, methodology): “Reinforced concrete slab examples The first example comprises a clamped square slab, as shown in Figure 6, which has been investigated numerically by Chan [4], Krabbenhoft and Damkilde [12, 13] and Krenk et al.”
Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming (2007, background): “In this context, it should be emphasized that the problems solved by no means are easy—for example, the footing problems involving a cohesionless soil are known to cause severe problems, both for general nonlinear programming algorithms such as those presented in [4, 5, 17] as well as for convention”
Homogenization approach for the limit analysis of out-of-plane loaded masonry walls (2006, methodology): “It is stressed here that the simplex method can rarely compete favourably with the recent and more efficient interior-point methods (IPMs) (see Krabbenhoft and Damkilde 2003).”