Extending interior‐point methods to nonlinear second‐order cone programming: Application to finite‐strain elastoplasticity

Abstract

Interior-point methods are well suited for solving convex non-smooth optimization problems which arise for instance in problems involving plasticity or contact conditions. This work attempts at extending their field of application to optimization problems involving either smooth but non-convex or non-smooth but convex objectives or constraints. A typical application for such kind of problems is finite-strain elastoplasticity which we address using a total Lagrangian formulation based on logarithmic strain measures. The proposed interior-point algorithm is implemented and tested on 3D examples involving plastic collapse and geometrical changes. Comparison with classical Newton-Raphson/return mapping methods shows that the interior-point method exhibits good computational performance, especially in terms of convergence robustness. Similarly to what is observed for convex small-strain plasticity, the interior-point method is able to converge for much larger load steps than classical methods.

Gudermannian neural network procedure for the nonlinear prey-predator dynamical system

“…Therefore, the hybridization of GA with the IPA is performed to solve this model. Recently, IPA is applied in the brittle/ductile breakage [ 49 ], multistage nonlinear nonconvex programs [ 50 ], simulation of aircraft parts riveting [ 51 ], nonlinear second‐order cone programming [ 52 ], large-scale convex optimization [ 53 ], and efficient single objective optimization problem [ 54 ]. The mutual strength of GNNs-GA-IPA is used to present the solutions of six different cases of NDPPS described in Table 1 .…”

Formulation for wave propagation in dissipative media and its application to absorbing layers in elastoplastic analysis using mathematical programming

“…Equation ( 27) corresponds to Equations ( 16) and (17). Equations (28)(29)(30) are related to Equation (7).…”

“…10 Moreover, the convergence of modern IPM is super linear and the number of iterations for desirable convergence is almost unaffected by the number of unknowns. 11,12 In light of its advantages, this solution strategy has been extended for solving many challenging problems in geotechnical and geological engineering such as limit analysis, 13,14 elastoplastic analysis, 10,[15][16][17] viscoplastic analysis, 18,19 contact analysis 20,21 , analyses of fracture propagation 22,23 , etc. Many recent publications indicate that this MP strategy is very efficient when analyzing engineering problems with plasticity.…”

Applications of conic programming in non-smooth mechanics

“…Although alternative approaches have been proposed, the conic programming approach has emerged as the method of choice for solving large-scale limit analysis problems with applications ranging from soil mechanics [Krabbenhøft et al, 2008] to steel construction [El Boustani et al, 2020], reinforced concrete [Vincent et al, 2018] or masonry structures [Portioli et al, 2014]. Following the success of such methods in a limit analysis setting, some contributions explored their application to elastoplastic problems [Krabbenhoft et al, 2007, Krabbenhøft et al, 2007, including a recent extension towards non-convex finite strain plasticity [El Boustani et al, 2021]. Topology optimization and plastic design of structures [Strang and Kohn, 1983] have also been formulated either as LP programs for trusses [Gilbert and Tyas, 2003] or generic conic programs for solids [Mourad et al, 2021].…”