Analysis of interlaminar stresses in general cross-ply laminates with distributed piezoelectric actuators

Jnl of Sandwich Structures & Materials

2017

The first-, second-and third-order shear deformation plate theories are applied in this work to model thick rectangular sandwich plates with through-width delamination. The models are based on the concept of the four equivalent single layers and the system of exact kinematic conditions. Three different scenarios are considered: the failure of the core, the delamination between the top facesheet and the core, and finally, the case when the delamination takes place in the local midplane of the top facesheet. A general model is derived and applied to sandwich plates with Lévy type boundary conditions. The governing equations are summarized and the state-space model of the system is created. The mechanical fields are calculated and compared to finite element results. The comparison shows that the first-order sandwich plate model is inaccurate, on the other hand, the second-and third-order theories capture very well the mechanical fields compared to finite element results. The J-integral distribution is also calculated along the delamination front and it is concluded that the third-and second-order models give very good approximations of the results by finite element analysis and the virtual crack closure technique.

Section: The Sekcmentioning

confidence: 99%

Analytical solution of some delamination scenarios in thick structural sandwich plates

Jnl of Sandwich Structures & Materials

2017

“…Similarly to the theory of laminated and composite beams [83][84][85][86][87][88][89][90] the literature is very rich in the different theories to model laminated composite plates and shells. 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 …”

Section: Department Of Applied Mechanics Budapest University Of Techmentioning

confidence: 99%

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Journal of Composite Materials

2015

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...

“…The literature offers numerous plate theories, such as the classical laminated plate theory (CLPT) [85][86][87], first-order (FSDT) [85,88,89], second-order (SSDT) [90][91][92] and third-order (TSDT) [85,88,[93][94][95][96][97] shear deformable plate theories, the latter offer several subtheories, as well [85]. Other advanced theories including 3D elasticity and exact solutions are also available [98][99][100][101][102][103][104][105][106].…”

Section: Introductionmentioning

confidence: 99%

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

Mathematics and Mechanics of Solids

2016

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.