Thermoelasticity of multilayered plates with imperfect interfaces

Abstract

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.