A Fourier-related double scale analysis on the instability phenomena of sandwich plates

Huang, Qun; Liu, Yin; Hu, Heng; Shao, Qian; Yu, Kun; Giunta, Gaetano; Belouettar, Salim; Potier‐Ferry, Michel

doi:10.1016/j.cma.2017.01.021

Cited by 42 publications

(10 citation statements)

References 48 publications

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“…This benchmark is motivated by wrinkling instabilities of film‐substrate systems , where one observes many spatial oscillations. Here one accounts only for the substrate and the film is represented by a prescribed sinusoidal displacement.…”

Section: A Very Large‐scale Testmentioning

confidence: 99%

“…Hence one considers a three-dimensional case divided into many subdomains to check the robustness and efficiency of TMM when solving large scale problems. This benchmark is motivated by wrinkling instabilities of film-substrate systems [45][46][47], where one observes many spatial oscillations. Here one accounts only for the substrate and the film is represented by a prescribed sinusoidal displacement.…”

Section: A Very Large-scale Testmentioning

confidence: 99%

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Least‐square collocation and Lagrange multipliers forTaylor meshless method

Yang

Potier‐Ferry

2018

Numerical Methods Partial

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A recently proposed meshless method is discussed in this article. It relies on Taylor series, the shape functions being high degree polynomials deduced from the Partial Differential Equation (PDE). In this framework, an efficient technique to couple several polynomial approximations has been presented in (Tampango, Potier‐Ferry, Koutsawa, Tiem, Int. J. Numer. Meth. Eng. vol. 95 (2013) pp. 1094–1112): the boundary conditions were applied using the least‐square collocation and the interface was coupled by a bridging technique based on Lagrange multipliers. In this article, least‐square collocation and Lagrange multipliers are applied for boundary conditions, respectively, and least‐square collocation is revisited to account for the interface conditions in piecewise resolutions. Various combinations of these two techniques have been investigated and the numerical results prove their effectiveness to obtain very accurate solutions, even for large scale problems.

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Section: A Very Large‐scale Testmentioning

confidence: 99%

Section: A Very Large-scale Testmentioning

confidence: 99%

Least‐square collocation and Lagrange multipliers forTaylor meshless method

Yang

Potier‐Ferry

2018

Numerical Methods Partial

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“…Two correction factors to the classical deflection formula were proposed by them based on the higher-order theory approach. By expanding the displacement field into Fourier series, Huang et al [13] studied the instability phenomena of sandwich plates. Saoud and Grognec [14] introduced an advantageous 1D finite element model to analyze the post-buckling behavior of sandwich beams.…”

Section: Introductionmentioning

confidence: 99%

A 1D nonlinear finite element model for analysis of composite foam-insulated concrete sandwich panels

Lezgy-Nazargah

Vidal

Polit

2019

Composite Structures

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“…The nonlinear governing equations were derived by the Principle of Virtual Displacements and solved via the Asymptotic Numerical Method (ANM). Based on this work, Huang et al [15] proposed a more effective twodimensional model by using the technique of slowly variable Fourier coefficients. Garcia-Vallejo et al [16] introduced a new absolute nodal coordinate finite element together with a reduced integration procedure in order to mitigate the locking phenomena in dynamic structural problems.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

Hui

Pietro

Giunta

et al. 2018

Mathematical Problems in Engineering

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The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

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A Fourier-related double scale analysis on the instability phenomena of sandwich plates

Cited by 42 publications

References 48 publications

Least‐square collocation and Lagrange multipliers forTaylor meshless method

Least‐square collocation and Lagrange multipliers forTaylor meshless method

A 1D nonlinear finite element model for analysis of composite foam-insulated concrete sandwich panels

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

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