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A novel primal‐dual eigenstress‐driven method for shakedown analysis of structures
Author(s) -
Li Kai,
Cheng Gengdong,
Wang Yu,
Liang Yuan
Publication year - 2021
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.6641
Subject(s) - shakedown , karush–kuhn–tucker conditions , finite element method , mathematical optimization , mathematics , lagrange multiplier , multiplier (economics) , computer science , structural engineering , engineering , economics , macroeconomics
The shakedown load of elastoplastic structures under multiple variable loading is an important factor in structural design and integrity analysis. In classical plasticity shakedown analysis is an essential and challenging problem. Most existing methods are based on the solution of super large‐scale mathematical programming, basis reduction or mechanics insight method which have their own limitations in practical engineering problem. In the present study, the proposed method explores the Karush–Kuhn–Tucker (KKT) conditions and the physical reinterpretation of its primal‐dual variables of the Melan's lower bound theorem, and establishes the relation of the primal‐dual variables in finite element formulation. Based on the primal‐dual theory, the primal‐dual eigenstress‐driven method is proposed which is a two‐level nested algorithm: the inner level is the eigenstress‐driven incremental algorithm for constructing the beneficial residual stress field and calculating the safe multiplier and the outer level is the load multiplier descent algorithm for searching the shakedown multiplier. For the purpose of algorithm's universality, the proposed algorithm is fully integrated with the commercial finite element software ANSYS APDL without special optimization solvers, which is well suited for large‐scale practical engineering structures. Several numerical examples are provided to demonstrate the accuracy and efficiency of the proposed algorithm.