Layerwise Theories of Laminated Composite Structures and Their Applications: A Review

Li, Dinghe

doi:10.1007/s11831-019-09392-2

Cited by 97 publications

(27 citation statements)

References 225 publications

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“…Figure 2 demonstrates a good agreement between two exact dispersion curves calculated from transcendental relation (5) and polynomial approximation (12) for the chosen set of parameters. In this figure, Ω sh ≈ 0.18 and |K bl | ≈ 0.13, according to asymptotic formulae ( 8) and ( 10), respectively.…”

Section: Asymptotic Analysis Of Dispersion Relationmentioning

confidence: 66%

“…Thin multi-layered structures have always been among main focuses in structural and solid mechanics. There is a substantial literature on the subject, including in particular advanced research monographs [1,2] as well as most recent review articles [3][4][5], and insightful papers [6][7][8], to name a few. Modern industrial applications provide additional motivation to studying laminates, especially with high contrast geometric and physical properties of the layers, see for example [9][10][11][12] for photovoltaic panels and laminated glass, [13] for components of lightweight vehicles, [14] for sandwich panels in building construction.…”

Section: Introductionmentioning

confidence: 99%

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Antiplane shear of an asymmetric sandwich plate

Kaplunov

Prikazchikova

Alkinidri

2021

Continuum Mech. Thermodyn.

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An asymmetric three-layered laminate with prescribed stresses along the faces is considered. The outer layers are assumed to be much stiffer than the inner one. The focus is on long-wave low-frequency anti-plane shear. Asymptotic analysis of the original dispersion relation reveals a low-frequency harmonic supporting a slow quasi-static (or static at the limit) decay along with near cut-off wave propagation. In spite of asymmetry of the problem, the leading order shortened polynomial dispersion relation factorises into two simpler ones corresponding to the fundamental mode and the aforementioned harmonic. The associated 1D equations of motion derived in the paper are also split into two second-order operators in line with the factorisation of the shortened dispersion relation. Asymptotically justified boundary conditions are established using the Saint-Venant’s principle modified by taking into account the high-contrast properties of the laminate.

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Section: Asymptotic Analysis Of Dispersion Relationmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Antiplane shear of an asymmetric sandwich plate

Kaplunov

Prikazchikova

Alkinidri

2021

Continuum Mech. Thermodyn.

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“…A brief review of previous studies in this field is given in this section; however, interested readers seeking a more detailed literature review are referred to Refs. [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories

Khaniki

Ghayesh

Chin

et al. 2022

Continuum Mech. Thermodyn.

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In this study, the time-dependent mechanics of multilayered thick hyperelastic beams are investigated for the first time using five different types of shear deformation models for modelling the beam (i.e. the Euler–Bernoulli, Timoshenko, third-order, trigonometric and exponential shear deformable models), together with the von Kármán geometrical nonlinearity and Mooney–Rivlin hyperelastic strain energy density. The laminated hyperelastic beam is assumed to be resting on a nonlinear foundation and undergoing a time-dependent external force. The coupled highly nonlinear hyperelastic equations of motion are obtained by considering the longitudinal, transverse and rotation motions and are solved using a dynamic equilibrium technique. Both the linear and nonlinear time-dependent mechanics of the structure are analysed for clamped–clamped and pinned–pinned boundaries, and the impact of considering the shear effect using different shear deformation theories is discussed in detail. The influence of layering, each layer’s thickness, hyperelastic material positioning and many other parameters on the nonlinear frequency response is analysed, and it is shown that the resonance position, maximum amplitude, coupled motion and natural frequencies vary significantly for various hyperelastic and layer properties. The results of this study should be useful when studying layered soft structures, such as multilayer plastic packaging and laminated tubes, as well as modelling layered soft tissues.

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“…In LW theories, the displacement field is defined layer by layer and continuity conditions for stresses and displacements are ensured at layer interfaces. 19 LW theories are highly capable of capturing accurate stresses and strains, however the number of unknowns in these theories depends on the number of layers. Thus, the computational effort can be excessive especially for the analyses of structures with several layers.…”

Section: Introductionmentioning

confidence: 99%

Mixed finite element formulation for bending of laminated beams using the refined zigzag theory

Kutlu

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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This study presents a mixed finite element formulation for the stress analysis of laminated composite beams based on the refined zigzag theory. The Hellinger–Reissner variational principle is employed to obtain the first variation of the functional that is expressed in terms of displacements and stress resultants. Due to C0 continuity requirements of the formulation, linear shape functions are adopted to discretize the straight beam domain with two-noded finite elements. The proposed formulation is shear locking free from nature since it introduces displacement and stress resultant terms as independent field variables. A monolithic solution of the global finite element equations is preferred, hence the stress resultants are directly obtained from the solution of these equations. The in-plane strain measures of the beam are obtained directly at the nodes over the compliance matrix and stress resultants by avoiding error-prone spatial derivatives. Following, transverse shear stresses are calculated from the equilibrium equations at the post-processing level. This simple but effective finite element formulation is first verified and tested for convergence behavior. The robustness of the approach is shown through some examples and its accuracy in predicting the displacement and stress components is revealed.

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Layerwise Theories of Laminated Composite Structures and Their Applications: A Review

Cited by 97 publications

References 225 publications

Antiplane shear of an asymmetric sandwich plate

Antiplane shear of an asymmetric sandwich plate

Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories

Mixed finite element formulation for bending of laminated beams using the refined zigzag theory

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