Shakedown of creeping structures

Klebanov, J.M.; Boyle, J.T.

doi:10.1016/s0020-7683(97)00359-4

Cited by 9 publications

(6 citation statements)

References 4 publications

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“…3) Substituting Eq. 21into (18), the nodal displacement rate     n t u is obtained by solving the equilibrium equations in Eq. (22).…”

Section: T ρ Xmentioning

confidence: 99%

“…The first route of these researches is concerned with the extensions of shakedown theorem, where the material hardening [7][8][9][10][11][12], geometric nonlinearities [13,14], non-stationary loads [15,16], creeping effect [17,18] and frictional contact [19] are considered respectively. The second route of these researches is concerned with the development of efficient and robust numerical methods [20][21][22][23][24][25][26][27][28][29][30] towards the solution of the shakedown problem, which is also the major objective of this article.…”

Section: Introductionmentioning

confidence: 99%

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A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

2018

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In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

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“…3) Substituting Eq. 21into (18), the nodal displacement rate     n t u is obtained by solving the equilibrium equations in Eq. (22).…”

Section: T ρ Xmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

2018

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“…where K is the structural elastic stiffness matrix; the adjoint structural displacement vector 2 is the solution of Equation (19), that is, the structural displacement under the equivalent structural nodal force…”

Section: Kkt Conditions Of (10) and Physical Reinterpretation Of Dual Variablesmentioning

confidence: 99%

“…On the basis of classical shakedown theory, many researchers make some extensions of shakedown theory, such as geometric nonlinearities, [10][11][12] material hardening model, [13][14][15][16][17][18] creeping effect 19,20,21 , frictional contact, 22 nonstationary loads, 23,24 cracked bodies 25 and so on.…”

Section: Introductionmentioning

confidence: 99%

A novel primal‐dual eigenstress‐driven method for shakedown analysis of structures

Cheng

Wang

et al. 2021

Numerical Meth Engineering

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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.

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“…The most widely discuss methods of this type are based upon the shakedown theorems [6] where the objective is to evaluate a load parameter for which a particular mode of structural behaviour occurs, the absence of cyclic plastic growth or reverse plasticity. An optimal upper or lower bound to the shakedown load is then found by the application of a linear or non-linear programming method with the objective function derived from the upper and lower bound shakedown theorems [7][8][9][10]. There has, however, developed an alternative approach where the shakedown limit state solution has been mimicked as a linear solution with spatially varying linear moduli.…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis and evaluation of design limits for structural materials in a cyclic state of creep

Boulbibane

Ponter

2003

Numerical Meth Engineering

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SUMMARYIn this paper a direct non-time stepping method derived from the minimum theorems given by the authors (European Journal of Mechanics -A/Solids 2002; 21:915-925) is outlined. This method can be used in the prediction of the deformation and life assessment of structures subjected to cyclic mechanical and thermal loadings. It produces accurate predictions of failure modes based on material behaviour incorporated into constitutive equations. It also can be used to deÿne limit loads related to certain design criteria.Generally, for complex geometries and load histories, the identiÿcation of load histories that correspond to predeÿned design conditions, in the form of time or number of cycles to failure, can only be achieved by extensive and repeated calculations. For the Linear Matching Method, however, the representation of materially non-linear stress and strain ÿelds by linear behaviour with spatially varying moduli, indicates the possibility that direct evaluation of loads and temperature ranges that correspond to a design restriction may be evaluated directly through the construction of the exact cyclic state and via sequence of approximations. The technique employs the ÿnite element method combined with the cyclic state solution. The description of the material behaviour is given by a non-linear viscous model (Norton's law). It can also apply to any class of material behaviour that includes internal state variables. This technique has been applied successfully to a set of characteristics problems (Bree problem and plate containing a circular hole and subjected to radial temperature gradient).

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Shakedown of creeping structures

Cited by 9 publications

References 4 publications

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

A novel primal‐dual eigenstress‐driven method for shakedown analysis of structures

Finite element analysis and evaluation of design limits for structural materials in a cyclic state of creep

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