Koiter–Newton analysis of thick and thin laminated composite plates using a robust shell element

Liang, Ke

doi:10.1016/j.compstruct.2016.10.071

Cited by 9 publications

(3 citation statements)

References 31 publications

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“…Finally, to obtain an accurate asymptotic approximation of the equilibrium response in the deep post-buckling regime two strategies can be adopted. The first one involves a combination of Newton and Koiter approaches, effectively using Koiter's approach as a predictor and the Newton arc-length technique as a corrector step to trace the entire equilibrium path of a structure in a step-by-step manner [74][75][76]. The second strategy enlarges the space T (see equation (3.2)), involves including more terms in equation (3.3) (i.e.…”

Section: Results and Commentsmentioning

confidence: 99%

The role of symmetry in the post-buckling behaviour of structures

Zucco

2020

Proc. R. Soc. A.

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Symmetry plays an integral role in the post-buckling analysis of elastic structures. We show that the post-buckling response of engineering systems with given symmetry properties can be described using a preselected set of buckling modes. Therefore, the main original contribution of this paper is to prove the existence of these influential buckling modes and reveal some insights about them. From an engineering point of view, this study leads to the possibility of reducing computational effort in the analysis of large-scale systems. Firstly, symmetry groups for nonlinear elastic structural problems are discussed. Then, we invoke Curie’s principle and describe the relationship between these groups and related pre-buckling and linear buckling deformation patterns. Then, for structural systems belonging to a given symmetry group, we re-invoke Curie’s principle for describing the relationship between linear buckling modes and post-buckled deformation of the structure. Subsequently, we furnish a simplified asymptotic description which is obtained by projecting the equilibrium equations onto the subset of the most representative modes. As examples, classic bifurcation problems including isotropic and composite laminate panels under compression loading are investigated. Finally, the accuracy and computational advantages given by this new approach are discussed.

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Section: Results and Commentsmentioning

confidence: 99%

The role of symmetry in the post-buckling behaviour of structures

Zucco

2020

Proc. R. Soc. A.

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“…Equation 9 is a reduced-order model (ROM) relating the load and displacement around the equilibrium point [ , ]. Note that this ROM could have been built around any equilibrium point, a property that is explored in the Koiter-Newton approach [41,42,43,44]. Koiter's expansion given by Eq.…”

Section: Single-mode Asymptotic Analysismentioning

confidence: 99%

Displacement-based formulation of Koiter’s method: application to multi-modal post-buckling finite element analysis of plates

Castro¹,

Jansen²

2020

Preprint

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Koiter’s asymptotic method enables the calculation and deep understanding of the initial post-buckling behaviour of thin-walled structures. For the single-mode asymptotic analysis, Budiansky (1974) presented a clear and general formulation for Koiter’s method, based on the expansion of the total potential energy function. The formulation from Budiansky is herein revisited and expanded for the multimodal asymptotic analysis, of primordial importance in structures with clustered bifurcation modes. Given the admittedly difficult implementation of Koiter’s method, especially for multi-modal analysis and during the evaluation of the third– and fourth–order tensors involved in Koiter’s analysis; the presented study proposes a formulation and notation with close correspondence with the implemented algorithms. The implementation is based on state-of-the-art collaborative tools: Python, NumPy and Cython. The kinematic relations are specialized using von Kármán shell kinematics, and the displacement field variables are approximated using an enhanced Bogner-Fox-Schmit (BFS) finite element, modified to reach third-order interpolation also for the in-plane displacements, using only 4 nodes per element and 10 degrees-of-freedom per node, aiming an accurate representation of the second-order fields. The formulation and implementation are verified by comparing results for isotropic and composite plates against established literature. Finally, results for multi-modal displacement fields with up to 5 modes and corresponding post-buckling factors are reported for future reference.

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“…Over the last decades, the research activity has focused on the development of shell and plate models incorporating the effects mentioned above [9,10]. Most recent efforts describe well the open research topics and refinement techniques related to shells, such as, improvements of classical models [11] and higher-order models [12][13][14]; asymptotic approaches [15]; improvement of FE performances regarding membrane and shear locking [16][17][18][19][20][21], mesh accuracy [22], and distortion [23]; improved modeling of the interlaminar shear stresses [24]; Layer-Wise (LW) models [25,26]; Zig-Zag models [27,28]; mixed formulations [29][30][31]; variable kinematics finite elements with multifield effects [32]; extensions to non-linear problems [33,34] and peridynamics [35]; innovative solution schemes such as the numerical manifold method [36].…”

Section: Introductionmentioning

confidence: 99%

Best theory diagrams for multilayered structures via shell finite elements

Petrolo

Carrera

2019

Adv. Model. and Simul. in Eng. Sci.

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Composite structures are convenient structural solutions for many engineering fields, but their design is challenging and may lead to oversizing due to the significant amount of uncertainties concerning the current modeling capabilities. From a structural analysis standpoint, the finite element method is the most used approach and shell elements are of primary importance in the case of thin structures. Current research efforts aim at improving the accuracy of such elements with limited computational overheads to improve the predictive capabilities and widen the applicability to complex structures and nonlinear cases. The present paper presents shell elements with the minimum number of nodal degrees of freedom and maximum accuracy. Such elements compose the best theory diagram stemming from the combined use of the Carrera Unified Formulation and the Axiomatic/Asymptotic Method. Moreover, this paper provides guidelines on the choice of the proper higher-order terms via the introduction of relevance factor diagrams. The numerical cases consider various sets of design parameters such as the thickness, curvature, stacking sequence, and boundary conditions. The results show that the most relevant set of higher-order terms are third-order and that the thickness plays the primary role in their choice. Moreover, certain terms have very high influence, and their neglect may affect the accuracy of the model significantly.

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Koiter–Newton analysis of thick and thin laminated composite plates using a robust shell element

Cited by 9 publications

References 31 publications

The role of symmetry in the post-buckling behaviour of structures

The role of symmetry in the post-buckling behaviour of structures

Displacement-based formulation of Koiter’s method: application to multi-modal post-buckling finite element analysis of plates

Best theory diagrams for multilayered structures via shell finite elements

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