Enhanced layerwise model for laminates with imperfect interfaces – Part 1: Equations and theoretical validation

Alvarez-Lima, René; Diaz, Alberto Díaz; Caron, Jean; Chataigner, Sylvain

doi:10.1016/j.compstruct.2011.12.007

Cited by 11 publications

(9 citation statements)

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“…The Hellinger-Reissner functional and the stress approximation helps to identify 2D generalized displacements. More recent developments of Pagano's approach can be found in [11][12][13], where some simplifications are adopted to obtain more operational layerwise models. In [13], Alvarez-Lima et al enhanced a layerwise model called M4-5N (originally developed by Chabot in [11]) in order to include the Poisson's effect of outof-plane normal stresses on in-plane strains which may have an important impact on plasticity and failure mechanisms.…”

Section: Introductionmentioning

confidence: 99%

A Stress Approach Model of Moderately Thick, Homogeneous Shells

Alvarado

Díaz

2018

Mathematical Problems in Engineering

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This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner’s variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson’s effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.

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Section: Introductionmentioning

confidence: 99%

A Stress Approach Model of Moderately Thick, Homogeneous Shells

Alvarado

Díaz

2018

Mathematical Problems in Engineering

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“…Thin flat plates can be modeled by the classical or Kirchhoff plate theory, 91,92 while for relatively thick plates the first-order shear deformation theory (FSDT or Mindlin), [93][94][95][96][97][98][99][100] second-order shear deformation theory (SSDT), [101][102][103][104][105] general third-order theory (TSDT), [106][107][108] Reddy third-order theory, [109][110][111][112] other higher-order shear deformation theories (HSDT), [113][114][115] layerwise theories, [116][117][118][119][120][121] and the 3D elasticity solutions 122,123 are developed. These theories have been utilized to model curved shells [124][125][126] and delaminated and cracked laminates 9,10,[127][128][129] subsequently in the near past.…”

Section: Department Of Applied Mechanics Budapest University Of Techmentioning

confidence: 99%

“…The parametric excitation in delaminated plates is possible to appear, as well. 9,10,[127][128][129] subsequently in the near past.In this paper, it is shown that the phenomenon of parametric excitation can take place in free vibrating delaminated plates. Since-to the best of the author's knowledge-there is not available publication for the solution of this problem, the classical (or Kirchhoff) laminated plate theory (CLPT) is applied in this paper.…”

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Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Szekrényes

2015

Journal of Composite Materials

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This paper revisits the problem of free vibration of delaminated composite plates with Lévy type boundary conditions. The governing equations are derived for laminated Kirchhoff plates including through-width delamination. The plate is divided into two subplates in the plane of the delamination. The kinematic continuity of the undelaminated part is established by using the system of exact kinematic conditions. The free vibration analysis of orthotropic simply supported Lévy plates reveals that the delaminated parts are subjected to periodic normal and in-plane shear forces. This effect induces parametric excitation leading to the susceptibility of the plates to dynamic delamination buckling during the vibration. An important aspect is that depending on the vibration mode the internal forces have a two-dimensional distribution in the plane of the delamination. To solve the dynamic stability problem the finite element matrices of the delaminated parts are developed. The distribution of the internal forces in the direction of the delamination front was considered. The mode shapes including a half-wave along the width of the plate accompanied by delamination buckling are shown based on the subsequent superimposition of the buckling eigenshapes. The analysis reveals that the vibration phenomenon is amplitude dependent. Also, the phase plane portraits are created for some chosen cases showing some special trajectories. KeywordsDelamination, free vibration, laminated plate theory, dynamic stability, parametric excitation, harmonic balance, finite element method IntroductionDelaminations are typical defects in composite and sandwich structures induced by indentations (e.g. local loading by spherical indentors), 1,2 low-velocity impact and free edge effects (normal and shear stress concentration between layers at free edges), 3-6 finally by fabrication defects. 7,8 The cracks and delaminations reduce significantly the strength and stiffness of composite laminates.9-11 The material defects also influence the dynamic behavior of the structures.12-20 One of the widely known dynamic phenomena is parametric excitation, which takes place in machine tools, 21 [73][74][75][76][77][78] and sandwich beams. 79In Burlayenko and Sadowski, 80 the foam/core debonding in sandwich plates was investigated during free vibration. However, the existence of the parametric excitation was not revealed in any of the former papers.To the best of the author's knowledge, the existence of the parametric excitation in the course of free vibration of delaminated composite beams was first revealed in Szekre´nyes 81 and was solved effectively by the FE and harmonic balance methods in Szekre´nyes.82 It was also shown that the delamination buckling takes place only if the free vibration amplitude exceeds the so-called critical amplitude at a specified point of the beam. The existence of the critical amplitude was also proved experimentally. The parametric excitation in delaminated plates is possible to appear, as well. 9,10,[127][128][129] subseq...

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“…Other advanced theories including 3D elasticity and exact solutions are also available [98][99][100][101][102][103][104][105][106]. Finally, the layerwise and Zig-Zag theories should be mentioned [85,[107][108][109][110][111][112][113][114][115][116][117]. For plates without assumed material defects the improvement in the plate solution by higher-order theories compared with CLPT and FSDT is only slight, at the same time the computational efforts increase significantly [85].…”

Section: Introductionmentioning

confidence: 99%

Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

Szekrényes

2016

Mathematics and Mechanics of Solids

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The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton's principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

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Enhanced layerwise model for laminates with imperfect interfaces – Part 1: Equations and theoretical validation

Cited by 11 publications

References 30 publications

A Stress Approach Model of Moderately Thick, Homogeneous Shells

A Stress Approach Model of Moderately Thick, Homogeneous Shells

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

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