In this paper semi-exact methods are introduced for estimating the distribution of tangential displacement and shear stress in non-uniform rotating disks. At high variable angular velocities, the effect of shear stress on Von Mises stress is important and must be considered in calculations. Therefore, He’s homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) is implemented for solving equilibrium equation of rotating disk in tangential direction under variable mechanical loading. The results obtained by these methods are then verified by the exact solution and finite difference method. The comparison among HPM and ADM results shows that although the numerical results are the same approximately but HPM is much easier, straighter and efficient than ADM. Numerical calculations for different ranges of thickness parameters, boundary conditions and angular accelerations are carried out. It is shown that with considering disk profile variable, level of displacement and stress in tangential direction are not always reduced and type of changing the thickness along the radius of disk and boundary condition are an important factor in this case. Finally, the optimum disk profile is selected based on the tangential displacement-shear stress distribution. The presented algorithm is useful for the analysis of rotating disk with any arbitrary function form of thickness and density that it is impossible to find exact solutions. Manuscript profile

In this research, the thermal buckling analysis of a truncated conical shell made of porous materials on elastic foundation is investigated. The equilibrium equations and the conical shell`s stability equations are obtained by using the Euler`s and the Trefftz equations .Properties of the materials used in the conical shell are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved shell is expressed in terms of the Donnell`s assumptions. Non-linear strain-displacement relations are obtained according to the von Kármán assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical shell. The stability equations of conical shell are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the buckling Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the buckling. Manuscript profile