The work is mainly focuses on the analysis of thermal gradients and its effect on thermal stresses in FGM (functional gradient material) grading-strip made up of TiC-Ni due to thermal heat with different rate: thermal shock, transient exponential and linear heat. In this paper, asymptotic analytical solution for exponential and linear heat will be investigated. Few models of material grading are considered: (a) models which depend on different volume content of TiC and (b) models with homogeneous layers. Thermal and mechanical properties of the material are assumed different along axis. It is assumed that Poisson's ratio and Young's modulus varies exponentially with the coordinate of the strip. The dependence on different material property idealizations is also investigated. As well for research maximum and minimal thermal stresses in paper compared laminated non-FGM and FGM strip. The maximum tensile stress obtained for FGM case. At the same time compressive stresses near heated surface for two-layered strip lager then for three-layered and less or absent for FGM strip. Heating/cooling opposite edge to thermal shocked ones leads to increase/decrease compressive stress in metal phase part in FGM and layered strip. At the beginning of heat the differences in compressive stress for thermal shock and exponential heat could differ in ten times. Compressive stress in linear heat case increase from beginning and stay stable as maximum from three heat cases as long as edge heat up to maximum temperature. The results obtained in this research paper allow us to analyze the validity of this method and to understand principles of thermal behavior on FGM-strip in a case of different conditions and different heat transfer rate.

In this article, we present an analytical solution for an imperfect functionally graded plate based on higher order shear deformation theory with cubic variation of in-plane displacements according to thickness and linear/quadratic transverse displacement. The developed solution is used to analyze the static responses of a plate with a porous layer to mechanical loading. Two porosity types and their influences on material properties, displacement, and stress behaviors are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using power-law distribution idealization in terms of the volume fractions of constituents. The computed results are presented to illustrate the accuracy of the proposed solutions based on comparisons to previously reported analytical and numerical solutions in the literature. We also analyzed the effects of different volume fractions and thicknesses of porous layers on the mechanical loading and mechanical behavior of the imperfect functionally graded plate.

The theory of deep rock mass is proposed as the complex hierarchy of block structures on the basis of the discontinuous and self-stressed rock mass structure in depth. We study the block structure of the rock mass steady-state response to the external periodic excitation. We get the resonance equation and the resonance condition for the block rock mass structure under external periodic excitations. The effects of the local mass and stress state between the adjacent rock blocks in block rock mass structure on the steady-state displacement of rock blocks are analyzed.

This study presents the dynamic response analyze of a simply supported and isotropic functionally graded (FG) double curved panel under mechanical loading. The aim of the research was to investigate mechanical behavior in a FGM curved panel due to different excitation mode of dynamic loading. The novelty of this research is an investigation of von Mises equivalent stress distribution in double curved panel due to different excitation mode. Computed results are found to agree well with the results reported in the literature. Moreover, influence of volume fraction of the material is studied.