Buckling of antisymmetric cross- and angle-ply laminated plates

Sharma, Sudhakar; Iyengar, N.G.R.; Murthy, P.N.

doi:10.1016/0020-7403(80)90077-6

Cited by 30 publications

(6 citation statements)

References 8 publications

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“…( 43) can be found in Appendix A.2. Equation ( 43) can be transformed into the following first-order differential equation system using (40):…”

Section: Clpt Angle-ply Laminatementioning

confidence: 99%

“…For the CLPT, FSDT and TSDT this procedure is presented for antisymmetric cross-ply laminates in [39] for the boundary conditions simply supported, clamped and free edges. In [40] antisymmetric cross-ply and angle-ply laminates are treated in the context of CLPT. The three coupled differential equations are transformed into a single differential equation of eighth degree.…”

Section: Introductionmentioning

confidence: 99%

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Lévy-type solutions for the buckling analysis of unsymmetrically laminated plates with rotational restraints for various plate theories

Schreiber

Mittelstedt

2023

Arch Appl Mech

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The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups.

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“…( 43) can be found in Appendix A.2. Equation ( 43) can be transformed into the following first-order differential equation system using (40):…”

Section: Clpt Angle-ply Laminatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lévy-type solutions for the buckling analysis of unsymmetrically laminated plates with rotational restraints for various plate theories

Schreiber

Mittelstedt

2023

Arch Appl Mech

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“…in which, the displacements in the x, y, and z directions, u 0 , v 0 , and w, respectively, are presented in terms of the displacement function Φ(x, y) (Sharma et al [24])…”

Section: Governing Equations For Antisymmetric Laminated Plate Stripsmentioning

confidence: 99%

Analytical solution to bending of stiffened and continuous antisymmetric laminates

Sun

Harik

2015

Curved and Layered Structures

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Analytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

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“…For unsymmetric laminates, in addition to the plate differential equations, the coupled in-plane displacement differential equations must now be considered. In the framework of CLPT, a method is presented in [13] that reduces the problem to one higher order differential equation. In [14] a solution for antisymmetric angle-ply laminates is presented in the framework of FSDT.…”

Section: Introductionmentioning

confidence: 99%

Lévy‐type solutions for buckling of shear deformable unsymmetrically laminated plates with rotational restraints

Schreiber,

Mittelstedt

2023

Proc Appl Math and Mech

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The local stability of unsymmetric laminated structures is significantly affected by bending‐extension coupling and the comparatively low transverse shear stiffnesses, which have to be included in the structural analysis. If such structures have flat surfaces in segments, they can be investigated with the discrete plate analysis. In this analysis, the individual segments are considered as plates with rotational restraints that represent the supporting effect of the surrounding structure. The aim of this work is to improve the analytical stability of laminated plates. Therefore, Lévy‐type solutions for the buckling load of the mentioned laminated plates are considered and refined. This offers exact solutions for unsymmetrical cross‐ply laminates as well as antisymmetric angle‐ply laminates. In order to show the influence of shear deformations, the solutions for classical laminated plate theory (CLPT), first‐order shear deformation theory (FSDT), and third‐order shear deformation theory (TSDT) are worked out and compared to each other. In the context of TSDT, a new formulation for the rotational elastic restraint is presented, which affects the rotation and the warping of the plate cross‐section. This investigation presents the influence of shear deformations on different laminates and classifies the benefits of the different laminated plate theories with respect to the stability behaviour under different boundary conditions. In addition, the influence of bending‐extension coupling on different fibre angles and layer sequences is analysed.

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Buckling of antisymmetric cross- and angle-ply laminated plates

Cited by 30 publications

References 8 publications

Lévy-type solutions for the buckling analysis of unsymmetrically laminated plates with rotational restraints for various plate theories

Lévy-type solutions for the buckling analysis of unsymmetrically laminated plates with rotational restraints for various plate theories

Analytical solution to bending of stiffened and continuous antisymmetric laminates

Lévy‐type solutions for buckling of shear deformable unsymmetrically laminated plates with rotational restraints

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