A min-max procedure for the shakedown analysis of skeletal structures

Janas, Marek; Pycko, S.; Zwoliński, Janisław

doi:10.1016/0020-7403(94)00087-z

Cited by 14 publications

(7 citation statements)

References 11 publications

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“…Comparing equations (17) and (15) it is clearly seen that Using equation (18) the following interpretation can be given to the shakedown problem. Namely, for the given vector of plastic strains U p the body V with the ÿnite number of load vertices P k , k = 1; : : : ; n k (forming the load cycle) can be replaced by the same body composed of separate parts V l each of them subjected to the only one loading vertex P l .…”

Section: Interpretation Of the Shakedown Problemmentioning

confidence: 97%

“…Relations (21) constitute the shakedown criterion formulated by equation (15) and will be directly used for development of the concept of cycle-oriented incremental analysis. It is worthy to recall here that each component of the yield vector G P p ( ; U p ) can be identiÿed with the yield function computed for the speciÿed load vertex P l only (see (18)), i.e.…”

Section: Cycle-oriented Incremental Analysismentioning

confidence: 99%

“…The numerical procedure outlined in the previous section for arbitrary type of structure will be now applied to 3-D frames. The procedure was positively tested with the same accuracy of results as for examples presented in the paper by Janas et al 15 The procedure will be now applied to the analysis of a one-storey space frame shown in Figure 5. The frame with tubular cross-section is subjected to cyclic loading consisting of three load systems: one horizontal and two vertical sets of forces.…”

Section: Examplesmentioning

confidence: 99%

“…The problem was then rigorously proved by Pycko and MrÃ oz. 13 More advanced optimization algorithms were proposed by ZwoliÃ nski 14 and Janas et al 15 The proposed method of a cycle-oriented incremental analysis allows to determine the steadystate response for structures subjected to cyclic (or variable repeated) loading below or at the shakedown limit. It adapts the concept of shakedown analysis centred on the min-max formulation 16; 17 to incremental formulation based on Melan's theorem.…”

Section: Introductionmentioning

confidence: 99%

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A cycle-oriented incremental analysis of shakedown problems

Pycko

1997

Int. J. Numer. Meth. Engng.

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An e ective method for determination of a quasi-static shakedown loading and of a steady-state response is proposed. The classical optimization problem based on Melan's theorem is suitably reformulated to meet the requirements of incremental analysis. The main attention is focused on the reduction of a computational time required for a completion of a transient elastic-plastic phase of deformation. The method di ers signiÿcantly from classical incremental analyses. Here, a load cycle is approximated by the ÿnite number of loading systems covering the cycle. Each system is then combined with a separate domain of the structure in which the load system can be treated as a dominant one. In this manner, the structure consists of parts, each of them undergoing suitably chosen one-parameter loading only. Such a modiÿcation allows us to build a set of non-linear equations for all loading systems covering the whole load cycle. As a consequence the structure can be treated as the one in which the transient plastic phase of deformation is analysed load cycle by load cycle without making load increments inside the considered cycle. Due to this innovation a signiÿcant reduction of the computational time required for the solution of the steady-state response of the structure is obtained what is illustrated on 3-D frames. ?

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Section: Interpretation Of the Shakedown Problemmentioning

confidence: 97%

Section: Cycle-oriented Incremental Analysismentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A cycle-oriented incremental analysis of shakedown problems

Pycko

1997

Int. J. Numer. Meth. Engng.

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“…Transient and asymptotic responses can be distinguished for a structure subjected to quasi-static repeated loading cycles above the elastic limit. The former is characterized by the subsequent plastic deformations during the load cycles [7,15] . The transient phase leads to stress redistribution inside the structure and then the asymptotic cyclic response is achieved with the same time period as the external load [2,8,18] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling for Shakedown Analysis of Offshore Structures

Fadaee¹,

Saffari²,

Tabatabaei³

2007

American J. of Applied Sciences

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Abstract:The shakedown analysis process of an offshore structure having elastic-plastic material presented. The finite element model of the structure has been developed first, and then a simple method has been applied for shakedown analysis using matrix tool. Simplifying the relationships together with applying the theory concepts of shakedown analysis is one of the characteristics of the presented method for practical problems. Here, shakedown analysis formulation discussed in four steps. First, the Morison equation adopted for converting the velocity and acceleration terms into resultant forces and it extended to consider arbitrary orientations of the structural members. Then the loads due to the waves have been calculated and they have been converted to specific repeating cyclic loads on the structure nodes. In the second step, the finite element model of the structure has been developed and considered under nodal loads resulted from the specific combined wave loads. Thirdly, the shakedown multiplier has been calculated using shakedown static theorem based upon the stress domain governing the problem. Finally, in the fourth step, a graph has been developed indicating the critical sea waves domain that cause the structure shakedown. The formulation has been applied for two types of offshore structures to verify the concept employed and its analytical capabilities.

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Direct Methods: History, Present and Future

Weichert

2023

Lecture Notes in Applied and Computational Mechanics

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A min-max procedure for the shakedown analysis of skeletal structures

Cited by 14 publications

References 11 publications

A cycle-oriented incremental analysis of shakedown problems

A cycle-oriented incremental analysis of shakedown problems

Mathematical Modeling for Shakedown Analysis of Offshore Structures

Direct Methods: History, Present and Future

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