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Journal ArticleDOI

Buckling of unilaterally constrained plates: Applications to the study of delaminations in layered structures

TL;DR: In this article, a combined experimental and analytical investigation of the problem of buckling of unilaterally constrained, finite, rectangular, elastic plates is reported, where the plates are modeled along the lines of classical plate theory employing the Kirchhoff-love hypothesis.
Abstract: The results from a combined experimental and analytical investigation of the problem of buckling of unilaterally constrained, finite, rectangular, elastic plates is reported. The plates are modeled along the lines of classical plate theory employing the Kirchhoff-Love hypothesis. The presence of a unilateral constraint is accounted for through the use of a nonlinear elastic foundation model that exhibits a deformation sign dependent force-displacement relation. Using Galerkin's method, the resulting system of governing nonlinear equations are solved iteratively. Different boundary conditions are considered and the results for some boundary conditions are compared and shown to be in good agreement with ‘exact’ results reported earlier for infinite plates. The results from an experimental investigation has further revealed that the buckling mode of the plate may involve regions or points of contact with the substrate beneath the buckling plate. The shadow Moire technique is used to show clearly that the mode shape is periodic and contains points and/or regions of contact. The results obtained from the theoretical investigation are found to bound the experimental values. It is clear that the stiffness of a post-buckled plate with unilateral constraints is highly influenced by whether the buckled portion involves points (or regions) of contact or not. Thus, in analytical model development, associated with addressing the problem of delamination buckling in layered plates, the possibility of the delaminated portion contacting the substrate beneath cannot be excluded. The present study has demonstrated the validity of using nonlinear foundation models in the buckling analysis of unilaterally constrained rectangular plates.
Citations
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Journal ArticleDOI
Herzl Chai1
TL;DR: In this article, a combined experimental/analytical effort is carried out to elucidate the post-buckling response of bilaterally constrained columns and plates under monotonically increasing edge displacement.

46 citations

Journal ArticleDOI
TL;DR: In this paper, numerical geometrically nonlinear analyses have been performed to investigate the influence of contact phenomena on multiple embedded delaminations growth in composite panels under compressive load.
Abstract: In this paper, numerical geometrically non-linear analyses have been performed to investigate the influence of contact phenomena on multiple embedded delaminations growth in composite panels under compressive load. An in-house FEM code based on the Modified Virtual Crack Closure Technique to analyse delaminations growth and with the Penalty Method Approach to take into account contact phenomena has been used for computations. Compressed composite panels with two embedded delaminations has been investigated for various geometrical configurations with different delaminations’ sizes and positions. Comparisons with a single embedded delamination model adopted in previous works have been presented. Finally a comparison between contact and no-contact approaches has been shown for a significant geometrical configuration.

34 citations

Journal ArticleDOI
TL;DR: In this paper, a linear structural analysis is used to investigate the behavior of an all-composite wing-box under a compressive load taking into account the presence of concurrent inter-laminar damages such as delaminations and skin-stringer debonds and their propagation.

32 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear finite-element formulation based on Marguerre's nonlinear shallow shell theory, modified by Mindlin's hypothesis, is employed to model the plate response and overcome difficulties in solving the plate-foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition.
Abstract: The buckling and large deflection postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated. A nonlinear finite-element formulation based on Marguerre’s nonlinear shallow shell theory, modified by Mindlin’s hypothesis, is employed to model the plate response. To overcome difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition, two different approaches are used: (1) the unilateral constraint is accounted for indirectly by a bilinear constitutive law and (2) the problem is formulated as a mathematical programming problem with inequality constraints from which a linear complementarity problem is derived and solved by the Lemke algorithm. To obtain the nonlinear equilibrium paths, the Newton–Raphson algorithm is used together with path-following strategies. Plate–foundation interaction leads to interesting deformation sequences, chara...

26 citations

Journal ArticleDOI
TL;DR: In this paper, a simplified linear analysis-based approach to simulate the delamination growth initiation in stiffened composite panels, suitable as preliminary design and optimization tool implemented into a finite element code, is presented.
Abstract: In this article, a simplified linear analysis-based approach to simulate the delamination growth initiation in stiffened composite panels, suitable as preliminary design and optimization tool implemented into a finite element code, is presented. The proposed approach is based on the determination of the delamination buckling and on the evaluation of the energy released during the delamination propagation by means of eigenvalue and linear static analyses. Stiffened composite panels with circular embedded bay delaminations, under compression loads, were adopted as a benchmark to test the simulation capabilities of the method. Obtained results, in terms of delamination growth initiation load and energy release rate distributions along the delamination front, have been compared to nonlinear results obtained by the virtual crack closure technique and experimental data for preliminary validation purposes. Comments and considerations upon the applicability of this methodology are, finally, provided with particul...

20 citations


Cites methods from "Buckling of unilaterally constraine..."

  • ...The importance of a suitable model for the contact phenomena between the sub-laminates has been highlighted in [17,18], where a numerical approach based on unilaterally constrained, finite, rectangular plates has been employed....

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References
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Journal ArticleDOI
TL;DR: In this article, an analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites, where the growth conditions and growth behavior of this defect are studied by breaking the overall problem into an elastic stability problem and a fracture problem.
Abstract: An analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites. The delaminated region is elliptic in shape, separating a thick isotropic plate from a thin orthotropic layer whose material axes coincide with the ellipse axes. The growth conditions and growth behavior of this defect are studied by breaking the overall problem into an elastic stability problem and a fracture problem. Post-buckling solution for the elliptic section is obtained using the Rayleigh-Ritz method while an energy balance criterion based on a self-similar disbond growth governs the fracture. The parameters controlling the growth or arrest of the delamination damage are identified as the fracture energy, disbond depth and elastic properties of the materials from both sides of the delaminating interface. By varying the degree of material anisotropy relative to the loading axis a range in growth behavior was found including stable or unstable crack growth parallel to or normal to the loading axis.

311 citations

Journal ArticleDOI
TL;DR: In this paper, the behavior of elastic plates of rectangular shape on a tensionless Winkler foundation is analyzed by using an auxilliary function, and the displacement function of the plate is approximated by using the eigenfunctions of the completely free beam.
Abstract: In this analysis of the behavior of elastic plates of rectangular shape on a tensionless Winkler foundation, the tensionless character of the foundation is taken into account by using an auxilliary function. The displacement function of the plate is approximated by using the eigenfunctions of the completely free beam. The difference between the free-end boundary conditions of the plate and the beam is compensated for by considering a differential operator in addition to the governing equation of the plate. The problem is reduced to the solution of a system of algebraic equations by using Galerkin's method. The configurations of the contact curve and the displacement are given in figures for various values of the external uniformly distributed load, concentrated load, and moment.

58 citations

Journal ArticleDOI
TL;DR: In this article, the authors define a deflection function for a given width of a plate and a fraction of half-buckle wavelength representing the length of the region of the plate in which the foundation is compressed.
Abstract: A, B = constants appearing in deflection functions b = width of plate c = fraction of half-buckle wavelength representing length of region of plate in which the foundation is compressed D = flexural stiffness of plate [D = Et*/12(1 v)} E = Young's modulus of plate material F(x) = function representing variation in ^-direction of the plate deflection k = buckling load coefficient (k = bN/wD) k = foundation modulus N = critical compressive load per inch of plate width t = plate thickness w = plate deflection x = distance along plate longitudinal axis [see Fig. 1(b)] y = distance along width of plate 7 = foundation modulus parameter (7 = bk/irD) V^ = (d/dx) + 2(d/dxdy) + ( d 4 / ^ 4 ) X = ' half-wavelength of buckle v = Poisson's ratio

48 citations