Sensitivity analysis to geometrical imperfections in shell buckling via a mixed generalized path-following method

This paper is mainly focused on the numerical methods which are used to calculate realistically the load-carrying behaviour of reticulated shell structures. It is generally assumed that for an economical analysis, aimed at the saving of material, the material non-linearity has to be taken into consideration if dead loads prevail. For this in the context of finite element analysis the stiffness matrices of elastic and elastic-plastic rod elements are presented. In order to ensure the stability of structures it is indispensable to detect limit loads such as snap-through loads and bifurcation loads. Assuming that snap-through phenomena are quasi static, path-following algorithms can be implemented to trace the load-deflection curves in the postbuckling domain. The testing of the reliability and stability of the algorithms requires a sufficient number of numerical examples. Few will be presented.

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On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen–Loève expansions

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.2141 ◽

2008 ◽

Vol 73 (12) ◽

pp. 1715-1726 ◽

Cited By ~ 16

Author(s):

K. J. Craig ◽

W. J. Roux

Keyword(s):

Shell Buckling ◽

Geometrical Imperfections

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Sensitivity Analysis of the Added Mass Computation for a Rod Vibrating in a Fluid-Filled Cavity

Journal of Applied Mechanics ◽

10.1115/1.3423516 ◽

1975 ◽

Vol 42 (1) ◽

pp. 199-204 ◽

Cited By ~ 2

Author(s):

D. Krajcinovic

Keyword(s):

Sensitivity Analysis ◽

Boundary Conditions ◽

Added Mass ◽

Virtual Mass ◽

Qualitative And Quantitative ◽

Geometrical Imperfections ◽

Quantitative Analyses ◽

Acoustic Fluid

This paper considers influence of small geometrical imperfections, such as out-of-roundedness and eccentricity, on the magnitude of the added (apparent, virtual) mass for a rod vibrating in acoustic fluid contained within a rigid cavity. Using the perturbation of boundary conditions method derived are simple formulas allowing qualitative and quantitative analyses for several types of imperfections.

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Optimization of shell buckling incorporating Karhunen-Loève-based geometrical imperfections

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-008-0331-7 ◽

2008 ◽

Vol 37 (2) ◽

pp. 195-195

Author(s):

K. J. Craig ◽

Nielsen Stander

Keyword(s):

Shell Buckling ◽

Geometrical Imperfections

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Optimization of shell buckling incorporating Karhunen-Loève-based geometrical imperfections

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-007-0178-3 ◽

2007 ◽

Vol 37 (2) ◽

pp. 185-194

Author(s):

K. J. Craig ◽

Nielen Stander

Keyword(s):

Shell Buckling ◽

Geometrical Imperfections

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Effects of structural openings on the buckling strength of cylindrical shells

Advances in Structural Engineering ◽

10.1177/1369433218764625 ◽

2018 ◽

Vol 21 (16) ◽

pp. 2466-2482 ◽

Cited By ~ 9

Author(s):

Emanuele Brunesi ◽

Roberto Nascimbene

Keyword(s):

Computational Models ◽

Geometrical Nonlinearity ◽

Large Set ◽

Response Curves ◽

Shell Buckling ◽

Numerical Assessment ◽

Geometrical Imperfections ◽

Post Buckling ◽

Cylindrical Steel ◽

Assessment Strategies

Computational models, which follow numerical assessment strategies codified by current European rules for shell buckling, were developed so as to study the buckling and post-buckling response of a large set of cylindrical steel thin-shell prototypes with structural openings. Behavioural changes as a consequence of variations in the cutout configuration, that is, shape, size, location and number, were predicted and the obtained numerical estimates were related to the test data of previous experiments in order to explore critical design aspects. Damage modes and axial force–axial displacement response curves were presented and discussed, decoupling the roles played by material nonlinearity and geometrical nonlinearity, as well as the contribution of initial geometrical imperfections to the buckling mechanism of axially compressed cylindrical thin shells.

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Sensitivity analysis based multi-scale methods of coupled path-dependent problems

Computational Mechanics ◽

10.1007/s00466-019-01762-8 ◽

2019 ◽

Vol 65 (1) ◽

pp. 229-248

Author(s):

Nina Zupan ◽

Jože Korelc

Keyword(s):

Boundary Condition ◽

Sensitivity Analysis ◽

Automatic Differentiation ◽

Path Following ◽

Material Model ◽

Solution Algorithm ◽

Analytical Sensitivity ◽

Essential Boundary Condition ◽

Multi Scale ◽

Path Dependent

Abstract In the paper, a generalized essential boundary condition sensitivity analysis based implementation of $$\text {FE}^2$$FE2 and mesh-in-element (MIEL) multi-scale methods is derived as an alternative to standard implementations of multi-scale analysis, where the calculation of Schur complement of the microscopic tangent matrix is needed for bridging the scales. The paper presents a unified approach to the development of an arbitrary MIEL or $$\text {FE}^2$$FE2 computational scheme for an arbitrary path-dependent material model. Implementation is based on efficient first and second order analytical sensitivity analysis, for which automatic-differentiation-based formulation of essential boundary condition sensitivity analysis is derived. A fully consistently linearized two-level path-following algorithm is introduced as a solution algorithm for the multi-scale modeling. Sensitivity analysis allows each macro step to be followed by an arbitrary number of micro substeps while retaining quadratic convergence of the overall solution algorithm.

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