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Second‐order cone programming formulation of discontinuous deformation analysis
Author(s) -
Meng Jingjing,
Cao Ping,
Huang Jinsong,
Lin Hang,
Chen Yu,
Cao Rihong
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6006
Subject(s) - discontinuous deformation analysis , second order cone programming , linear complementarity problem , mathematical optimization , block (permutation group theory) , mathematics , quadratic programming , complementarity (molecular biology) , stiffness , complementarity theory , cone (formal languages) , numerical analysis , optimization problem , regular polygon , convex optimization , computer science , algorithm , mathematical analysis , geometry , finite element method , structural engineering , engineering , nonlinear system , quantum mechanics , biology , genetics , physics
Summary In classic discontinuous deformation analysis (DDA), artificial springs must be employed to enforce the contact condition through the open‐close iteration. However, improper stiffness parameters might cause numerical problems. The main goal of this paper is to propose a new framework of DDA using second‐order cone programming. The complementarity relationship at contacts can be formulated directly; thus, artificial springs are avoided. Stemming from the equations of momentum conservation of each block, the governing equations of DDA can be cast as convex optimization problems. The basic variables in the formulations can be either block displacements or contact forces. The derived optimization problems can be reformulated into a standard second‐order cone programming program, which can be solved using standard efficient optimization solvers. The proposed approach is validated by a series of numerical examples.