Nonlinear elastic buckling and postbuckling analysis of cylindrical panels

Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, Michael

doi:10.1016/j.finel.2014.12.001

Cited by 68 publications

(26 citation statements)

References 39 publications

(72 reference statements)

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“…The Koiter-Newton method is based on a step by step procedure to trace the equilibrium path of the deforming structure, that is similar to classical path-following techniques [21]. The unique properties and algorithmic differences compared to standard technologies are given in the following with the help of Figs.…”

Section: Construction Of the Reduced Order Modelmentioning

confidence: 99%

Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method

Liang

Ruess

2016

Aerospace Science and Technology

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Liang, K., and Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method. Aerospace Science and Technology, 55, There may be differences between this version and the published version. AbstractThin-walled conical and cylindrical shells subjected to axial compression often show a snap-back response in the presence of buckling. Newton iterations based path-following methods cannot trace reliably the snap-back response due to the extremely sharp turning angle near the limit point, and the original Koiter-Newton method also meets difficulties to achieve a complete post-buckling response beyond the limit point. In this paper, the improved KoiterNewton method is proposed to trace the post-buckling path of cylinders and cones, in the framework of the reducedorder modeling technique. The polynomial homotopy continuation (PHC) method is used to solve the lower-order nonlinear reduced order model reliably and efficiently. The simplified Green-Lagrange (SGL) kinematics which consider the stress redistribution after buckling are implemented into the construction of the reduced order model to produce accurate results for curved shells. The numerical results presented reveal that the improved method is a robust and efficient technology to achieve the entire nonlinear response for the snap-back case.

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Section: Construction Of the Reduced Order Modelmentioning

confidence: 99%

Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method

Liang

Ruess

2016

Aerospace Science and Technology

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“…Wagner et al [11] and Wriggers et al [12] proposed a branch-switching method by using the buckling mode as a prediction of the secondary path. Zhou et al [13] improved the method and applied to the postbuckling analysis of cylindrical panels. Huang and Atluri [14] presented a simple method to identify the limit points or bifurcation points and to conduct branch-switching based on Koiter's initial postbuckling analysis.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Study on shear postbuckling failure of composite sandwich plates by a quasi-conforming finite element method

Bao-zong

2015

Composites Science and Technology

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“…In many cases, it is crucial to assess the load‐carrying capability of a structure at which buckling occurs as well as the behavior of the structure beyond that buckling point. () To this end, geometrically nonlinear analysis has been widely used to study the buckling and postbuckling characteristics of structures …”

Section: Introductionmentioning

confidence: 99%

“…[2][3][4] To this end, geometrically nonlinear analysis has been widely used to study the buckling and postbuckling characteristics of structures. 5 The development of techniques for solving large-scale nonlinear structural problems has been, and continues to be, an active research area. Conventional path-following techniques, eg, the arc-length method and its variants, [6][7][8][9] combined with the finite element (FE) method, work well for tracing the nonlinear equilibrium path of the structure, and the buckling load can be easily indicated from the nonlinear response curve.…”

mentioning

confidence: 99%

“…Conventional path-following techniques, eg, the arc-length method and its variants, [6][7][8][9] combined with the finite element (FE) method, work well for tracing the nonlinear equilibrium path of the structure, and the buckling load can be easily indicated from the nonlinear response curve. 5 In view of the high cost of computing usually required for nonlinear FE analysis of large complex structures, the attractiveness in reducing the problem size by the reduced basis method is obvious. 10 The primary objective of using reduced-order modeling techniques is to reduce the size of the governing large system of equations resulting in a corresponding reduced-order models (ROMs) and, hence, to reduce the computational effort involved in the solution of the problem.…”

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confidence: 99%

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A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures

Liang

Abdalla

Qin

2017

Numerical Meth Engineering

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Summary The Koiter‐Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced‐order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton‐Raphson method using the full model. In this paper, we proposed a modified Newton‐type KN method to trace the geometrically nonlinear response of structures. The developed predictor‐corrector strategy is applied to each predicted solution of the reduced‐order model. The reduced‐order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced‐order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced‐order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems.

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Nonlinear elastic buckling and postbuckling analysis of cylindrical panels

Cited by 68 publications

References 39 publications

Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method

Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method

Study on shear postbuckling failure of composite sandwich plates by a quasi-conforming finite element method

A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures

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