Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates

Yang, Lianzhi; Li, Yang; Gao, Yang; Pan, Ernian

doi:10.1016/j.apm.2018.06.050

Cited by 28 publications

(13 citation statements)

References 45 publications

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“…The inherent thermoelastic problems are of critical importance since the interaction between the elastic strain and thermal mismatches and also the corresponding thermal stress concentrations may influence the local driving forces for crack propagation in composite materials (Khaund et al, 1977), which is a major cause of fracture and interfacial delamination of thermal barrier coating systems (Evans and Hutchinson, 2007). Under static deformation, additional coupling effects including piezoelectric fields in layered plates have been formulated (Wang and Pan, 2007), whilst Yang et al (2018) has recently investigated the thermoelastic quasicrystal response in layered plates by surface loading. To the best of the authors' knowledge, however, the corresponding time-dependent thermoelastic vibration response of a multilayered composite with imperfect interface conditions and nonlocal effects has not yet been treated.…”

Section: Introductionmentioning

confidence: 99%

Thermoelasticity of multilayered plates with imperfect interfaces

Vattré

Pan²

2021

International Journal of Engineering Science

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Three-dimensional exact solutions for temperature and thermoelastic stresses in multilayered anisotropic plates are derived for advanced boundary-value problems with general boundary conditions. The extended Stroh formalism is formulated to include the thermal coupling with the Eringen nonlocal elasticity theory that captures small scale effects. The simply supported structures are subjected to time-harmonic distributions of temperature, combined with tractions, which are represented by means of Fourier series expansions. In particular, the prescribed loads on both the bottom and top surfaces include the uniformly and heterogeneously distributed normal stresses, while imperfect thermal and mechanical contacts between constituents are incorporated at the internal interfaces. Recursive field relations for multilayered plates with imperfect interfaces are consistently articulated by virtue of the traditional propagation matrix method, which is further completed by the dual variable and position technique to overcome numerical instability issues. Three application examples are proposed to throw light on various effects of the externally applied loads and internal imperfections on the thermoelastic fields in multilayered structures. The residual stress fields in graphite fiber-reinforced epoxy matrix composites are shown to be drastically different from those predicted by the classical elasticity theory when nonlocal effects are significant. The stacking sequence and the number of copper and molybdenum in laminated anisotropic plates are of great importance in tailoring interfacial properties, especially if the thermally conducting boundaries are taken into account. The forced vibration analysis of thermal barrier coatings on nickel based superalloys is investigated, including interfacial bonding effects between adjoining layers. Depending on the input frequency amplitude, severe oscillating displacements and stresses take place in the single crystal superalloys that can endanger the safety-related stability and integrity of aircraft engines. Overall, the present formalism should be utilized in the optimal design of sophisticated multilayered structures with desired steady-state and time-harmonic thermoelastic responses.

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Section: Introductionmentioning

confidence: 99%

Thermoelasticity of multilayered plates with imperfect interfaces

Vattré

Pan²

2021

International Journal of Engineering Science

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“…In most practical engineering problems, however, the effect of the strain rate in the heat conduction equation has been neglected in the static, quasi-static and dynamic problems of thermoelasticity, including the forced and free vibration analysis of isotropic, orthotropic, laminated composite, sandwich and functionally graded plates with temperature-dependent material properties in thermal environments. Along this line, various analytical investigations using exact closed-form thermoelastic solutions [7][8][9][10][11][12][13], classical and higher-order plate theories [14][15][16][17][18], hierarchical Ritz-based models [19,20] and numerical finite-element approaches [21][22][23][24][25][26] have been widely proposed for thermal analysis of homogeneous and heterogeneously laminated plates. In the aforementioned approaches, the partially coupled governing equations for the displacement field solutions require a priori the temperature distribution along the thickness direction, thus separately determined through thermal analysis alone and then prescribed for subsequent stress analysis.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Vattré

Pan

Chiaruttini

2021

Composite Structures

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A fully coupled thermoelastic framework is formulated to cope with the free vibration response of anisotropic multilayered plates in three dimensions. The laminated structure consists of homogeneous laminae of arbitrary thickness and width under simply supported edge conditions in thermal environment. The general and exact field expressions of the temperature, heat flux, displacement and stress components are expressed in terms of double Fourier series expansions in any rectangular plate, which lead to the extended Stroh formalism with thermomechanical coupling effects in a concise and compact matrix form. Different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the bounding interfaces, and further to determine the finite complex valued coefficients in the suitable series relations. The complete time-harmonic solutions in the laminated composites in the presence of perfect/imperfect interfaces are recursively obtained by means of the modified dual variable and position technique with explicit layer-to-layer transfer matrices. Results are obtained for different layups, length-to-thickness ratios and interfacial boundary conditions for two application examples, namely the graphite/epoxy cross-ply composites and the thermal barrier coatings on superalloys, without suffering from numerical exponential instability. These investigations reveal that the natural frequencies and first and higher vibration mode shapes of the multilayered structures can be considerably affected by increasing the environmental temperature and the severity of the interfacial imperfections. Since the through-thickness stress distribution in 2, 5, and 10 layered composites appears to be strongly correlated to the layups, such modal stress analysis could be exploited to locate the fatigue hotspots operated in dynamic structures and to guide the structural design of aircraft and spacecraft composite laminates subjected to residual vibrations.

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“…Using the nonlocal elasticity theory, the static bending deformation was investigated by Zhang et al [9] for 1D hexagonal piezoelectric QC nanoplates. For 2D QC simply supported nanoplates, Yang et al [10] obtained a 3D thermo-elastic analytical solution subjected to a temperature change on the top surface. By alternating QC layers and V layers, the brittleness of Al-Cu-Fe-based QCs are overcome [3].…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions and analysis of an interfacial crack in a one-dimensional hexagonal quasicrystal bi-material

Fan

Chen

Zhang

et al. 2020

Mathematics and Mechanics of Solids

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Using the Stroh formalism, Green’s functions are obtained for phonon and phason dislocations and opening displacements on the interface of a one-dimensional hexagonal quasicrystal bi-material. The integro-differential equations governing the interfacial crack are then established, and the singularities of the phonon and phason displacements at the crack tip on the interface are analyzed. To eliminate the oscillating singularities, we represent the delta function in terms of the Gaussian distribution function in the Green’s functions and the integro-differential equations, which helps reduce these equations to the standard integral equations. Finally, a boundary element numerical approach is also proposed to solve the integral equation for the crack opening displacements, the asymptotic expressions of the extended intensity factors, and the energy release rate in terms of the crack opening displacements near the crack tip. In numerical examples, the effect of the Gaussian parameter on the numerical results is discussed, COMSOL software is used to validate the analytical solution, and the influence of the different phonon and phason loadings on the interfacial crack behaviors is further investigated.

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Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates

Cited by 28 publications

References 45 publications

Thermoelasticity of multilayered plates with imperfect interfaces

Thermoelasticity of multilayered plates with imperfect interfaces

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

Fundamental solutions and analysis of an interfacial crack in a one-dimensional hexagonal quasicrystal bi-material

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