Thermo-mechanics of multi-directional functionally graded elastic sandwich plates

The static, stability, and free vibration behaviour of multi-layer multi-directional functionally graded (MDFG) sandwich thin rectangular plates subjected to thermo-mechanical loadings are investigated in this paper using the principle of virtual displacement and Kirchhoff's hypothesis. Effects of varying the physical properties through the thickness, length and width directions and different boundary conditions are considered. The temperature-position-dependent physical properties are obtained via the rule of mixture using the power law, exponential and sigmoidal law functions. A modified differential quadrature method is presented for modelling different types of plates, i.e. isotropic, functionally graded in axial (AFG), depth (DFG), and MDFG ordinary and sandwich plates. The comparison indicates that the applied methodology to solve plate problems for static, stability and free vibration is effective, simple and very accurate. Results for MDFG plates and layered composite combination of such structures with an isotropic/FG core layer and isotropic/FG surface layers are investigated for the first time in thermo-mechanical conditions and the accuracy of the current methodology is discussed in details by modelling simplified plate models using different alternative techniques. The static, stability and vibration response of MDFG plates is presented for different case studies considering their physical and geometric properties as well as temperature rise. The results obtained in this paper are useful as a benchmark and to validate future experimental results. The significant advantage of using MDFG sandwich plates is to prevent delamination and stress singularities between layers and the behaviour of such plates is are also discussed.

Automated summary

This paper investigates the static, stability, and free vibration behavior of multi-layer multi-directional functionally graded sandwich thin rectangular plates under thermo-mechanical loadings. Various physical properties and boundary conditions are considered, and the temperature-position-dependent physical properties are obtained using the rule of mixture. The modified differential quadrature method is used to model different types of plates. The results suggest that this methodology is effective, simple, and accurate. The study also presents the first investigation of MDFG plates and layered composite structures under thermo-mechanical conditions, and discusses the advantages of using MDFG sandwich plates.